Aerodynamics

Pretraining a neural PDE surrogate can reduce the amount of new CFD data needed when geometry or modeled physics changes. However, it remains unclear how different components of distribution shift affect this benefit. We pretrain a surrogate on 254,909 RANS solutions from one airfoil family and fine-tune it on a new family under two target settings with matched freestream ranges: the same Spalart-Allmaras (SA) modeling and SA with added $e^N$ transition modeling. At $N=1000$, the pretrained model matches the accuracy of a model trained from scratch on $3.25\times$ as many samples for the same-SA target, but $2.58\times$ as many for the transition-modeled target. By $N=5000$, this ordering reverses ($1.56\times$ versus $1.86\times$). At $N=1000$, sampling more distinct airfoils lowers error on both targets, but only for the same-SA target is the gain increase larger than the observed draw-to-draw variation ($3.3\times$ to $4.0\times$). These results show that pretraining value depends jointly on target-data budget, target-data coverage, and whether source and target differ in modeled physics.

For non-stationary tethered multirotor UAVs in real-world conditions, simulating the forces imposed on the drone by the aerodynamic drag of the tether becomes crucial, with online use cases placing a hard bound on the maximum solve time. In previous work, a quasi-analytical catenary tether model reached a mean solve time of 0.51 ms using a general-purpose root finder, but without any worst-case guarantees or proven convergence. In this work, we reformulate the inner solver by reducing the catenary boundary-value problem to a single transcendental equation in one well-conditioned unknown. We derive a closed-form bracket and prove monotonicity and convexity as well as existence and uniqueness of the root, which together guarantee convergence of the solver. We further propose a two-regime initial guess which approximates the true root within 3.4% and reduces the mean iteration count by 68.0% to 2.36 compared to the textbook initialization. Building on the hybrid root-finding method rtsafe (Newton-Raphson with bisection fallback giving bounded iteration counts), we implement a specialized variant that exploits the problem structure to omit unnecessary checks while retaining correctness, which gives up to 1.3 times speedup. With the proposed solver the full tether model achieves a nearly constant solve time of 6.9 us on average and 7.7 us at worst, a 40 times speedup over an optimized re-implementation of the previous method, while agreeing with it to a relative deviation of 8.7e-9. Because the reformulation leaves the underlying physical model untouched, the experimental validation of the previous work carries over unchanged. We further demonstrate its suitability for embedded, resource-constrained platforms with a Lua implementation running directly in ArduPilot on a drone's flight controller, where it stays well inside the scheduling budget with a mean solve time of 0.74 ms.

Latent neural operators improve the efficiency of operator learning for partial differential equations (PDEs) by performing the main computation on compact latent representations. However, directly compressing the input representation to obtain such compact representations may discard solution-relevant spatial information, especially for PDE solutions with multiscale structures. To address this problem, we propose HiLNO, a hierarchical latent neural operator that constructs a fine-to-coarse-to-fine latent space and further introduces multi-scale supervision (MSS) and anisotropic Gaussian attention. The hierarchy mitigates potential information loss during compression, while MSS aligns intermediate predictions with downsampled target fields, encouraging solution-relevant structures to be captured across multiple spatial scales. Anisotropic Gaussian attention enables feature transfer across the hierarchy, making HiLNO applicable to general geometries. Experiments on representative PDE benchmarks and a large-scale automotive aerodynamics task show that HiLNO achieves competitive predictive accuracy, while reducing the parameter count by an average of 84.4% and FLOPs by an average of 69.2% compared with LinearNO. Additional experiments demonstrate effective generalization to unseen spatial resolutions. Code is available at https://github.com/JcLimath/HiLNO.

Machine-learning surrogate models offer a promising alternative to high-fidelity Computational Fluid Dynamics (CFD) simulations for aerodynamic analysis and design. However, constructing accurate surrogates for realistic aircraft configurations remain challenging due to complex geometries, multiple flow regimes, and limited training data. This work presents the methodology that achieved first place in the ONERA CRM Wall Distribution Regression Challenge, which focuses on predicting pressure and skin-friction coefficient distributions over the NASA Common Research Model wing-body-pylon-nacelle configuration under different operating conditions. The proposed approach formulates the problem as a conditional neural field mapping spatial coordinates, surface normals, and operating conditions to aerodynamic wall quantities. Fourier feature encoding, a relative squared error objective aligned with the challenge metric, ensemble learning, and $k$-fold cross-validation are progressively introduced to improve prediction accuracy and exploit the limited training data. Beyond presenting the final methodology, the paper documents the successive model design choices that led to the winning solution through a comprehensive ablation study and discusses several alternative approaches that were investigated but ultimately discarded. On the hidden competition test set, the proposed methodology achieves an overall score of 8.81, outperforming the strongest organizer-provided baseline, which achieved a score of 8.64, while requiring approximately three orders of magnitude fewer trainable parameters. These results illustrate that carefully designed coordinate-based neural fields constitute an efficient and robust framework for aerodynamic surrogate modeling on complex geometries under limited-data conditions.

This paper presents a coordinated trajectory generation and tracking control framework for a tail-sitter unmanned aerial vehicle (UAV), which does not require aerodynamic priors identified for a specific airframe while addressing the challenge of flight control under highly nonlinear aerodynamics across the full flight envelope. The core innovation lies in employing phase-specific aerodynamic modeling strategies for planning and tracking, tailored to their distinct functional characteristics, without requiring airframe-specific aerodynamic priors. Specifically, the phi-theory model under coordinated flight is employed to derive an analytic differential flatness mapping, and a simplified but locally accurate model is established for predictive control to enable real-time aerodynamic parameter estimation. The proposed framework is evaluated extensively through both simulation and challenging real-world flight tests under mild wind conditions, showing high-precision tracking and adaptability across the tested aerodynamic conditions. To the best of our knowledge, this is the first real-world demonstration of accurate trajectory tracking over tested flight regimes spanning the full envelope of a tail-sitter UAV without relying on aerodynamic identification campaigns. The source code of our framework is available at: https://github.com/SYSU-HILAB/AP-PnC.

Neural operators are fast, differentiable surrogates for physical simulation, but their accuracy often degrades when domain geometry, size, or operating conditions differ from training. Supervised adaptation can recover accuracy, but even a small target set requires costly high-fidelity simulations. We therefore ask how pretraining and transfer can be designed together to reduce this deployment cost. LatentDDM first pretrains a neural operator to predict fields on small subdomains. For a new setting, it freezes this operator and trains only a lightweight module that composes the local predictions. We evaluate our method on two complementary problems: steady Darcy flow, where long-range pressure coupling must extend across increasingly large porous domains, and unsteady incompressible flow around a pitching airfoil, where rollout errors compound as target pitching frequencies exceed the training range. Compared with the capacity-matched models that process the full domain at once, LatentDDM's error is 36-56% lower on larger Darcy domains after adaptation with 16 target simulations. It also improves 20-step field rollouts in fast-pitching airfoil flow, both zero-shot and after few-shot calibration. These results identify the co-designed local pretraining and composition-level transfer as a promising design principle for physical foundation models.

Accurate prediction of unsteady separated flows is challenging because the aerodynamic loads depend on nonlinear separation and vortex-shedding dynamics. Although high-fidelity CFD resolves these mechanisms, its cost limits repeated use in design and control. Standard field-level surrogate training, however, does not distinguish the flow regions that contribute most strongly to the aerodynamic loads. We introduce VATO (Vortex-Force-Aware Transformer Operator), which couples the Vortex Force Map (VFM) method to a geometry-aware neural operator through two complementary mechanisms. VATO-S adds training-only supervision of the local VFM force-contribution field, with no increase in model size or inference cost. VATO-A uses VFM contribution and sensitivity fields to prioritise force-relevant source locations for residual cross attention. The methods are evaluated on unsteady CFD data for double-edged-plate aerofoils over 54 trajectories from nine geometries. Over lead times of 1-20~ms, VATO-S reduces velocity, pressure, and vorticity errors by 10.4%, 1.0%, and 15.6%, respectively, while VATO-A achieves reductions of 15.8%, 7.5%, and 31.2%. VATO-S gives the lowest VFM-derived drag error, whereas VATO-A gives the lowest pressure-derived lift and drag errors. Over lead times extending 50% beyond the training range, VATO-A retains a 26.9% reduction in vorticity error and larger improvements in all four force readouts, despite reduced gains in velocity and pressure. These results show that force-aware operator learning can improve both flow-field prediction and aerodynamic functional accuracy in unsteady separated flows.

Is it possible to find an objective classification criterion that organizes the complexity of gust-induced loads across many flight conditions? And one that remains as interpretable as a labelling based on coarse parameters, such as the flight attitude? Our approach encodes a large number of experimental observations through a machine-learned representation and applies a summarization procedure to select a minimal subset of highly significant exemplars. The exemplars provide a similarity-based objective classification criterion of all the observations, they can be more conveniently inspected by experts and can become subject of more refined experiments. We demonstrate the approach on a database of 3480 pressure-load measurements induced by random gusts on a flying-wing model across six flight attitudes. We find nine fundamental response types that recur across multiple attitudes; analysis of a type's transient response enables physical intuition into the underlying fluid mechanics.

Optimizing 3D shapes within the latent spaces of deep generative models is fundamental to computer assisted engineering, yet remains prone to a critical failure mode we term manifold drift: the tendency of gradient-based optimization to move latent vectors away from the manifold of valid shapes. This problem is exacerbated in state-of-the-art 3D shape generative models that operate in increasingly high-dimensional latent spaces where valid shapes occupy a vanishingly small fraction of the full space. Existing mitigation strategies, including latent regularization and flow-matching approaches, either sacrifice expressiveness, demand a difficult trade-off between objective guidance and generative fidelity that remains prone to manifold drift, or are computationally infeasible to scale to modern, large-capacity 3D shape models. We introduce a novel optimizer-corrector framework that alternates between gradient steps for objective minimization and guided flow matching to drive the latent state back to the valid shape manifold. By decoupling objective minimization from flow-based correction, optimizing freely and correcting strictly, this alternating design avoids inherent trade-offs, preserving geometric validity without sacrificing expressiveness while remaining computationally feasible on modern 3D shape models. We demonstrate its effectiveness across generative priors of varying complexity, from simple vector latent spaces to large-scale architectures across a variety of downstream optimization tasks, including aerodynamic drag reduction and object compliance optimization.

The development and testing of advanced aerial robots require experiments in controlled environments with tailored airflow profiles. This paper presents an online learning algorithm for controlling the complex airflow field in a multi-fan vertical wind tunnel. Our method combines a simplified physical model with iterative, measurement-based learning, enabling sample-efficient convergence to desired airflow distributions. We demonstrate the method's versatility by generating complex airflow, such as uniform, Gaussian, and parabolic profiles. Crucially, we show that our algorithm can produce an airflow profile specifically designed for passive soaring, greatly enhancing flight performance of a soaring robot. Variability, practical utility, and robustness of our approach are further highlighted by successful operation with a varying number of fans.

This work demonstrates experimentally the existence of a hexarotor prototype, termed Opti-Hexa, that simultaneously achieves practical resilience to single-propeller failures and energy efficiency comparable to a standard Star-shaped prototype with the same size, weight, hardware and software. Leveraging a novel open-source morphing platform, we investigate the trade-offs across a continuous range of geometries by varying the angles between adjacent propellers. We study practical efficiency through a data-fitted empirical power model and evaluate practical resilience by comparing the position accuracy and rotational kinetic energy during failure to those observed under nominal hovering conditions. Our experiments confirm the existence of a geometric viability region for this specific morphing platform, where resilience is ensured without the aerodynamic efficiency losses typically associated with practically resilient designs found in the state of the art. The complete hardware and software of the morphing platform are released to support further research.

Unsteady aerodynamic phenomena, such as gusts, turbulence, and fluid-structure interactions affect an aircraft during flight. For design, optimisation and certification, it is indispensable to quantify such unsteady aerodynamic effects. Industry-standard computational fluid dynamics methods, such as solving the unsteady Reynolds-averaged Navier-Stokes equations or the linearized frequency domain method, are either computationally expensive or restricted by assumptions like linearity. Once trained, machine learning methods are capable of computing non-linear relationships very fast, making them suitable as surrogate models. By autoregressively applying graph neural networks (GNNs), operating on a discretised spatial domain, spatio-temporal predictions can be made. However, autoregressive GNNs suffer from error accumulation leading to unstable rollouts over time. Here we show that combining GNNs with augmented Neural Ordinary Differential Equations yields temporally stable predictions of the surface forces on a pitching airfoil. We found that our approach, called GNODE, based on Graph Neural Ordinary Differential Equations, provides temporally more stable, spatially smoother, and overall more accurate results than an autoregressive GNN baseline. Tests are conducted on a dataset consisting of a simulations of a pitching airfoil, including transonic shocks, transient behaviour and dynamic non-linearities. Augmenting GNODEs with additional latent dimensions improves the expressivity and accuracy by capturing underlying history effects. The developed method demonstrates an approach that is suitable to model non-linear spatio-temporal systems with exogenous inputs.

Quadrotors flying in tight formations are severely affected by turbulent aerodynamic interactions, such as downwash, that can cause catastrophic collisions if left unmodeled. To compensate for these effects, we propose a physics-informed residual dynamics learning framework that captures complex aerodynamic interactions while ensuring the joint multi-quadrotor system remains differentially flat. We leverage this preserved flatness to design a computationally efficient feedback linearization controller that is easily tunable with linear control techniques and cancels aerodynamic disturbances via feedforward compensation. Hardware experiments demonstrate our framework reduces average tracking errors by 31% compared to nominal baselines. Crucially, our lightweight approach matches the tracking performance of state-of-the-art nonlinear model predictive control (NMPC) while requiring an order of magnitude less computation. We are the first to show that stable, tight formation flight can be achieved with under 30 seconds of training data and a 5ms loop rate, unlocking high-fidelity aerodynamic compensation for compute-constrained flight stacks.

Accurately modeling the dynamics of planetary parachute and entry vehicle systems is critical for Entry, Descent, and Landing events such as vehicle separation and sensor activation. These dynamics are difficult to capture with traditional system-identification methods as parachute motion is highly nonlinear, the governing equations are not fully known, and relevant test data are scarce and expensive to acquire. In this work, we sidestep these challenges by leveraging a physics-aware generative modeling approach that learns parachute dynamics directly from data. The proposed method, Symplectic Parachute Generative Adversarial Network (SPar-GAN), adapts a Hamiltonian generative architecture to the parachute setting by conditioning on canopy design and freestream velocity, while enforcing conservation of energy through symplectic integration. We apply SPar-GAN to subscale parachute tests conducted at the National Full-Scale Aerodynamics Complex and show that it reproduces qualitatively accurate pitch-yaw dynamics of different parachute configurations while recovering a compact two-degree-of-freedom phase-space consistent with canopy axisymmetry. These results suggest that physics-constrained generative models can characterize parachute dynamics across operating conditions and may help reduce the volume of physical testing required to assess performance.

This paper derives an analytical differential flatness transform for a tailsitter Unmanned Aerial Vehicle (UAV) under coordinated flight conditions using a simplified aerodynamic model. The proposed framework is formulated exclusively using rotation matrices, avoiding the ambiguities inherent to Euler angle representations. The method extends the applicability of an existing state-of-the-art differential flatness-based controller to flight regimes involving a significant vertical velocity component, where the previous approach becomes inapplicable. The proposed framework is validated experimentally with trajectories that highlight its advantages in these regimes.

Existing generative models learn data distributions in flat Euclidean space. However, most data in our real world are manifolds embedded in high dimensional Euclidean space. Therefore, we propose an intrinsic-geometry-based generative adversarial network (IG-GAN) for data generation in the field of aerodynamics. The generator of the IG-GAN represents aerodynamic data as a piecewise smooth manifold constructed by Bézier surfaces, and the generator tries to learn the coefficients of each Bézier surface to further combine multiple Bézier surfaces into a smooth manifold automatically. The discriminator in the IG-GAN is a radial-basis-function based discriminator (RBF-D). Experimental results show that IG-GAN achieves lower predicted Mean Squared Errors (MSEs) than those of three baselines. Specifically, on the Burgers' equation dataset, IG-GAN reduces the predicted MSE of velocity u by 97.41% compared with state of the art SSL-Transformer. Additionally, on the ONERA M6 aircraft dataset, IG-GAN reduces the overall MSE of nine aerodynamic coefficients by 82.95% compared with SSL-Transformer.

Gust disturbances, dynamic vertical inflow and ground effect are key adverse aerodynamic phenomena that induce variations in the forces acting on a multirotor and complicate its flight control. Miniature rotorcraft typically rely on simplified modelling of such effects to compute adjustments in thrust to counteract these forces. In the most basic case, disturbance force estimations are derived from the aircraft's motion and the generated thrust is assumed to exactly match that requested by the controller. However, such systems rely on the aircraft's trajectory to be affected before disturbances can be sensed and compensated. Numerous approaches presented over the last 15-20 years aim to reject external disturbances more quickly, but challenges remain. This paper presents a new approach in this category by measuring the instantaneous force of the rotors directly at the point of generation using load-cells and implementing high-speed control to accurately track the desired thrust. Measurements from load-cells were previously considered too noisy to provide meaningful input, but the experiments presented in the paper using purpose-built hardware from low-cost commodity components in single- and dual rotor see-saw models and a flying aircraft demonstrate both the feasibility and the effectiveness of the approach in the presence of complex aerodynamic phenomena.

Fine grain control and positioning of autonomous underwater vehicles (AUVs) is critical for sampling, maintenance, and survey applications. Traditional control methods for AUVs are labor intensive and are not robust to changes in the vehicle configuration or environmental conditions. Reinforcement learning (RL) promises rapid controller development while handling a range of deployment parameters via domain randomization (DR). However, DR is still limited by the capacity of the underlying simulation to model real physics. In particular, drag physics are difficult to model and are a large contributor to sim-to-real gaps. Meanwhile, computational fluid dynamics (CFD) provides high fidelity drag models but is challenging to leverage within reinforcement learning frameworks due to its computational overhead. Thus, in this paper we exploit the idea of training surrogate approximations of CFD models of a given vehicle, enabling fast inference within RL pipelines. We are the first to successfully deploy a zero-shot RL policy on a 6-DOF AUV in which policy training is performed on surrogate drag models (SDMs) trained on CFD data. We find 31% lower energy usage compared to a controller using simplified physics while traversing between waypoints 11% faster with 19% less error. Our SDM based RL controller better predicts zero-shot transfer and is more robust across reward shaping design choices. When using DR to complete a task with perturbed parameters, we find that the CFD policy is the only controller that successfully transfers. The policies are evaluated in a controlled tank environment and in the field providing extensive testing of the policies' capabilities.

Engineering shape optimization faces challenges in both expert-dependent problem setup and surrogate-model reliability. In practical aerodynamic design, optimization settings such as editable regions, deformation ranges, and design-preservation constraints are typically specified manually by experienced engineers, while surrogate-based optimization may become unreliable for heterogeneous geometry databases and out-of-distribution designs. To address these challenges, we propose a knowledge-constrained shape-optimization framework that translates knowledge-based constraints and user intent into quantifiable parameters of DFFD-based deformation operators, enabling engineering-aware and controllable constrained optimization. We further develop a Mixture-of-Experts Neural Operator (MoE-NO) to improve drag prediction and trend consistency over heterogeneous aerodynamic datasets. Based on the MoE-NO encoder and Mahalanobis distance, an uncertainty-estimation strategy is introduced to detect out-of-distribution geometries and selectively trigger physics-solver feedback for local sample enrichment. Experiments on in-house MPV, SUV, and Sedan datasets show that MoE-NO achieves a test-set MAPE of $1.16\%$ and a trend-prediction accuracy of $94.34\%$, outperforming the best baseline results of $1.52\%$ and $90.34\%$, respectively. Vehicle shape-optimization experiments further yield CFD-validated drag coefficient reductions of approximately $4\%$ to $10\%$.

We present CoFINN (Conservation Flux Informed Neural Networks), a physics-informed deep learning framework for predicting compressible flow fields governed by conservation laws. Unlike conventional data-driven convolutional neural networks (CNNs), which optimize only pixel-wise similarity metrics, CoFINN embeds finite-volume conservation physics directly into the training process. Unlike classical physics-informed methods which enforce differential-equation residuals at collocation points through automatic differentiation, CoFINN adopts a finite-volume perspective consistent with modern CFD methodology. CoFINN interprets CNN output fields as structured computational grids, where each pixel represents a finite-volume cell, and enforces conservation consistency through sophisticated numerical flux calculations. The framework is evaluated on transonic flow prediction around airfoils at (M=0.7, Re=6 * 10^6), including challenging conditions involving shock waves and high angles of attack. Results show that CoFINN improves aerodynamic force prediction accuracy, reducing drag prediction error by up to 34% at extreme angles of attack and by approximately 15% on average across the test set. Improvements are particularly significant in limited-data regimes, demonstrating that the conservation-based loss acts as an effective physical regularizer. The proposed approach maintains the computational efficiency advantages of CNN surrogates while significantly improving physical consistency and conservation behavior. The framework is architecture-agnostic and extensible to broader classes of conservation-law-governed physical systems.

Aerial physical interaction represents a promising direction for next-generation unmanned aerial vehicles (UAVs), but it requires an aerial platform that can exert contact forces while maintaining stable flight. For close-proximity tasks, this translates into three coupled design requirements: multidimensional wrench generation for stable contact, compactness for maneuverability and safety in confined spaces, and reduced lateral airflow toward the target when generating horizontal force. This article presents FLOAT Drone, a fully actuated coaxial UAV with servo-driven control surfaces for close-proximity physical interaction. The coaxial dual-rotor layout provides a compact propulsion layout, while the control surfaces, immersed in the rotor downwash, generate lateral forces and moments for 6-DoF wrench generation. A force-matched computational fluid dynamics (CFD) comparison with a tilted-rotor alternative quantifies the reduction in target-facing lateral airflow. To account for nonlinear rotor--control-surface coupling in the rotor wake, a high-fidelity polynomial aerodynamic wrench model is identified from precision force measurements and embedded in a constrained nonlinear allocator for real-time wrench tracking. Comparative flight and interaction experiments show that the proposed framework improves control accuracy over linear allocation baselines, rejects ground-effect and payload disturbances, and enables close-proximity drawer push--pull manipulation through a $2~\mathrm{cm}$ handle clearance.

Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations. Transformer-based neural operators are of particular interest, since attention can learn long-range dependencies in the computational domain. However, standard attention has two major limitations when applied to PDEs: it scales quadratically with the number of computational nodes, and it lacks an explicit bias toward local interactions. To address these issues, we introduce Local Linear Transformer (LLT) for PDE operator learning. The architecture combines linear global attention with local spatial mixing, and incorporates coordinate and geometry information. We evaluate LLT on several PDE problems, including elasticity, plasticity, airfoil flow, pipe flow, and Darcy flow. The reference data for these problems span finite-element, finite-volume, and finite-difference discretizations on structured and unstructured meshes. Compared with other neural-operator and transformer baselines from prior studies, LLT achieves competitive or lower relative $L_2$ error across these problems. On matched structured discretizations, wall-clock time per training iteration is reduced by factors of 1.8 to 2.5 relative to Transolver. We also scale the approach and apply it to a three-dimensional car aerodynamics dataset with 32,186 unstructured mesh points per sample. Together, these results indicate that LLT provides an accurate and computationally efficient operator for PDE problems across discretizations, mesh types, and problem settings.

Continuum manipulators mounted on multi-rotor UAVs enable compliant aerial manipulation, but payloads and propeller downwash amplify out-of-plane bending and twisting that degrade end-effector pose accuracy. To address this problem, we present a universal-joint-based continuum manipulator designed to improve resistance to out-of-plane deformation during aerial manipulation. The proposed design uses a tubular backbone with spring-reinforced universal joints and an integrated conduit for internal routing and fluid delivery. We evaluate the design in still air and under peak propeller downwash across varying payloads, and benchmark it against a prior Nitinol-backbone CM. Bench tests show improved resistance to out-of-plane deformation across all conditions. Under peak downwash, the proposed design reduces mean error by 2.5-4x in yaw, 2-45x in y-axis, and up to 5x in roll compared to the NiTi-backbone design. We further analyze hover stability through in-flight coupled-disturbance tests over varying payloads and actuation speeds, and demonstrate the system in water sampling, spot spraying, and object transport.

The high-angle-of-attack flip maneuver of reusable launch vehicles presents significant challenges for robust trajectory optimization due to the combined effects of highly nonlinear dynamics, aerodynamic uncertainties, and actuator saturation. This paper presents a differentiable physics framework for saturation-aware robust trajectory optimization. At its core, a Differentiable Particle Tube Control (DPTC) scheme is developed to optimize uncertainty evolution through an ensemble-based distribution shaping strategy. State uncertainty is represented by a Lagrangian particle ensemble, while hard actuator projection operators are embedded directly into the computational graph, enabling the joint optimization of the nominal feedforward trajectory and a time-varying feedback policy via end-to-end backpropagation. The proposed framework is evaluated against an automatic differentiation-based Successive Convexification (AD-SCvx) baseline combined with a conventional covariance steering feedback strategy. Six-degree-of-freedom Monte Carlo simulations demonstrate that, although the baseline achieves nominal fuel-optimal solutions, its unconstrained feedback formulation becomes susceptible to actuator saturation under aerodynamic disturbances, leading to degraded closed-loop robustness. In contrast, the proposed DPTC framework proactively performs a constraint-aware performance trade-off by relaxing spatial tracking to preserve critical control authority. These results demonstrate that integrating differentiable physics with ensemble-based optimization provides an effective and practical framework for robust guidance in highly constrained aerospace flight systems.

Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation. Although recent geometry-adaptive neural operators have made substantial progress, they are mainly designed for forward problems in which inputs and outputs share the same spatial domain. This limits their applicability for boundary value problems (BVPs) and inverse problems, where inputs and outputs may live on different domains. We introduce the Geometry-Adaptive Integral Autoencoder (GAIA), an operator learning model that encodes the domain boundary and the interior field distribution into geometry tokens, and conditions integral transform layers on these tokens via cross-attention, allowing the kernel to adapt locally to geometric features. This yields a single architecture for forward (including BVPs) and inverse problems on arbitrary domains in one pass, without retraining, iterative optimization, or graph construction. We evaluate GAIA on seven 2D and 3D benchmarks, four of which are new or substantially extended benchmarks for inverse problems and BVP: electrical impedance tomography, optical tomography, 3D Darcy flow on varying geometries, and a modified setting of Poisson BVP on mechanical components benchmark (MCB). GAIA sets new state-of-the-art results on every inverse and BVP task, reducing median relative $L^2$ error by 64% on airfoil flow reconstruction and 27% on EIT relative to the next best amortized method, and outperforming all baselines on every shape category of MCB. On other forward problems, GAIA is competitive with specialized solvers while maintaining stable accuracy across point resolutions on which transformer-based baselines degrade.

Predicting the aerodynamic performance (e.g. lift, drag, and moment coefficients) of an aircraft is challenging -- computational models are biased and direct simulations are prohibitive. A pragmatic way to overcome this limitation is by calibrating low-fidelity computational predictions with experimental measurements. This, however, requires calibrating against \emph{sparse} measurements contaminated with \emph{uncertainty} in both the control inputs and the measured aerodynamic response. We develop a methodology to address this problem based on Gaussian process surrogates and the classical Kennedy-O'Hagan calibration. A surrogate model learned on abundant-but-cheap low-fidelity data is calibrated with a sparse set of measurement data. Crucialy, we develop a Bayesian latent Gaussian process based approach that marginalizes the calibrated surrogate model over the input uncertainty, while also matching the marginal mean and variance of the measured output uncertainty. Once calibrated, our surrogate model predicts the uncertainty in aerodynamic coefficients with very high accuracy, including at extrapolative input settings. We validate our calibrated surrogate model predictions against measurement data with \emph{true} uncertainty intervals to demonstrate that the model places $94.2-95.8\%$ of its predictive samples inside the released $95\%$ truth intervals, with endpoint cumulative probabilities very close to the nominal 0.025 and 0.975 levels.

At competitive speeds and spins, a table tennis ball follows complex, counterintuitive trajectories that a robot must track and precisely counter within fractions of a second. Training a reinforcement learning policy capable of these skills is prohibitively expensive and dangerous in the real world, making high-fidelity simulation essential. Transferability of such policies, however, critically depends on how faithfully the simulation captures real-world dynamics - a requirement made even more stringent by the adversarial nature of the game, where any modeling inaccuracy becomes an exploitable weakness for the opponent. Prior state-of-the-art in robot table tennis generally focuses on a limited range of velocities and spins and fails to capture the richness of ball behaviors encountered in professional-level play. In this work, we present physics models for aerodynamic ball flight, ball-table contact, and ball-racket contact. that accurately capture the ball behavior over a vast range of speeds and spins relevant to the game. Specifically, we model drag and Magnus force coefficients as functions of Reynolds number and spin ratio in the aerodynamics equations. For the table contact model we model effects of ball buckling on the coefficient of restitution and incorporate residuals into the instantaneous point-contact models. For the racket contact model, we introduce a residual neural network component to complement coefficients related to normal and tangential coefficients of restitution as well as torsional spin damping. Evaluated on an unprecedentedly large dataset of competitive matches (277 games), the proposed models significantly reduces prediction errors (e.g., 59% median landing-position error reduction). The resulting models were used to train the RL policies for the first real-world robot table tennis AI agent capable of competing against professional players.

Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs). This architecture builds on the Kolmogorov-Arnold theorem, which endows it with universal approximation properties. While the advent of KANs has been received with excitement, there is a current debate about the possible KAN supremacy over deep multilayer perceptrons (MLPs) for classic fields such as symbolic regression, generic-purpose machine learning, natural language processing or computer vision. Here we assess the performance of KANs --and its nuanced comparison against MLPs and graph neural networks (GNNs)-- in the realm of fluid dynamics surrogate modelling. To that aim, we consider the task of predicting the surface pressure distribution over subsonic and transonic airfoils, a canonical task in aerodynamics. Our results show that KAN models show good performance in predicting the whole pressure coefficients and is able to interpolate across Mach numbers and angles of attack, however its performance is comparable --marginally inferior-- to a suitably trained MLP, where best performance is achieved by a GNN at the expense or requiring lengthier training. While the optimal KAN model have typically much lower complexity than MLP and GNN --hence resulting in faster training--, we find that KANs suffer from training instabilities, and their performance is highly dependent on a proper hyperparameter optimisation.

Numerical simulations in industrial applications often require performing numerous high-precision computations parameterized by specific experimental conditions. For instance, in vehicle body design, aerodynamic simulations are essential for evaluating the aerodynamic characteristics of various proposed body geometries. However, computational resource constraints often become a bottleneck. Therefore, achieving the desired accuracy while minimizing computational cost is crucial. To address this challenge, model reduction methods have been developed to decrease the degrees of freedom by constraining the possible states of a physical system to a lower-dimensional subspace. In particular, reduction techniques that project the system onto a nonlinear subspace using neural networks have been actively studied. Our previous research developed a reduced-order model that integrates neural-network-based model reduction with a time-evolution method, implemented as a distributed parallel training framework to process high-resolution flow field data efficiently. In this study, we extend this reduction approach by incorporating a variational autoencoder to assess its robustness in high-Reynolds-number flows around multiple vehicle bodies with varying geometries. Specifically, we evaluate the reconstruction accuracy of vortex generation across different spatial and temporal scales using a compact latent representation, with a particular focus on the flow behavior near the rear end of the vehicle body.

Quantifying the influence of hybrid aleatory and epistemic uncertainties on high-dimensional system responses remains a major challenge in global sensitivity analysis (GSA). Existing Hilbert--Schmidt Independence Criterion (HSIC)-based approaches are primarily restricted to single-output settings and lack a rigorous decomposition of heterogeneous uncertainty sources and their interactions. To address this limitation, a novel double-space tensor-product RKHS framework is proposed for sensitivity analysis under hybrid uncertainty. By constructing factorized kernels over both the latent input space and the multidimensional output space, a concurrent double Möbius inversion is derived to orthogonally decompose the global dependence measure into pure aleatory effects, pure epistemic effects, and their interaction contributions. The resulting dimension-wise sensitivity indices preserve the uncertainty attribution structure across all output dimensions. To satisfy the independence assumptions required by the decomposition, an auxiliary-variable representation based on the inverse probability integral transform is introduced, enabling the treatment of hierarchical uncertainties and Copula-induced correlations within a unified latent space. A fully vectorized single-loop implementation is further developed to avoid the computational burden of nested Monte Carlo simulation. Statistical significance and estimation uncertainty are quantified through permutation testing and Bootstrap confidence intervals. Numerical studies on a modified multi-output Ishigami function and an aerodynamic pressure-field problem demonstrate the accuracy, scalability, and practical applicability of the proposed framework.

Reliable extrapolation remains a central challenge for generative models in computational physics, because models trained over finite ranges of time, parameters, or geometries may produce physically inconsistent predictions outside the training distribution. We introduce a least-action-principle-guided diffusion, LAPG, a framework that promotes physical consistency during inference rather than relying solely on constraints imposed during training. The method combines a conditional score-based diffusion model with an action-derived physical guidance score. In the first stage, the learned score model generates an in-distribution proposal; in the second, an action-based variational prior refines this proposal toward the target out-of-distribution condition. This formulation turns the principle of least action into a differentiable inference-time correction mechanism and provides an alternative to pointwise residual penalties that often require empirical loss balancing. We evaluate LAPG on representative ordinary- and partial-differential-equation systems, including free fall, conservative and dissipative spring-mass dynamics, interacting point vortices, and potential flow over parameterized airfoils. In temporal, parameter, and geometric extrapolation tests, LAPG reduces phase drift, preserves dissipative decay, captures vortex motion, and improves the lift response of airfoil flows compared with training-time physics-informed baselines.

Aerodynamic simulation is a key component of engineering shape design, where core quantities such as the surface pressure coefficient strongly depend on flow dynamics near solid boundaries. Neural operators provide an efficient alternative to expensive Computational Fluid Dynamics (CFD) solvers. However, conventional methods treat the boundary region isotropically, failing to account for the distinct physical behaviors along the boundaries. In reality, the aerodynamic process exhibits anisotropy: along the tangential direction, flow propagates along the wall; along the normal direction, physical quantities are constrained by the wall. To explicitly model the distinct physical behaviors, we propose GeoABC, a geometry-conditioned anisotropic boundary correction framework. GeoABC leverages the boundary geometries to introduce direction-aware boundary correction into the intermediate representations of neural operators, transforming boundary geometry from static input features into a structural prior that modulates physical prediction. On 2D airfoil and 3D car tasks, GeoABC consistently adapts to multiple neural operator backbones, reducing near-boundary relative $L_2$ error by $\sim$38% on average, narrowing the structural near-wall gap shared by mainstream neural operators, and advancing neural operators toward high-fidelity aerodynamic simulation.

High-fidelity computational fluid dynamics (CFD) is crucial to vehicle aerodynamic analysis, but its cost still constrains early-stage design exploration. Machine-learning-based surface-field prediction offers a faster alternative if the model can efficiently capture both global flow context and local geometric detail. This work proposes a machine-learning-based method, named the geometry-aware triplane field network (GTF-Net), for vehicle aerodynamic pressure and wall shear stress prediction. GTF-Net constructs triplane features directly from sampled surface points through a shared multilayer perceptron (MLP) and smooth bilinear rasterization. The planes are then processed by a dual-stream backbone that combines adaptive Fourier neural operator (AFNO) spectral mixing with convolutional neural network (CNN) refinement, so long-range aerodynamic coupling and local geometry-induced variations are modeled in the same representation. At query stage, sampled triplane features are combined with vehicle-aligned directional coordinates, normal-projection features, and a voxel-based curvature proxy. GTF-Net is compared with Transolver, geometry-informed neural operator (GINO), and TripNet, a triplane-based surrogate model. GTF-Net improves the relative L2 error from the strongest baseline value of 0.157 to 0.145 for pressure prediction and from 0.237 to 0.226 for wall shear stress prediction. Ablation results show that AFNO mixing, local CNN refinement, and query-side geometric encoding each contribute to accuracy, supporting the proposed mechanism of combining structured triplane representation with explicit aerodynamic geometry cues.

Flapping-wing aerial vehicles (FWAVs) demonstrate remarkable agility but face substantial autonomy challenges due to their high sensitivity to aerodynamic disturbances and limited sensor payload capacity. Current simulation platforms typically rely on oversimplified laminar flow assumptions and idealized sensor models, failing to capture the complex turbulence patterns and perceptual limitations encountered in real-world operation. This simulation-to-reality discrepancy significantly impedes the development of robust autonomy systems for FWAVs. We introduce FWAV-Sim, a high-fidelity Unity-based simulation framework that integrates: (1) a composite aerodynamic model combining quasi-steady blade-element theory with bluff-body drag effects, (2) spatiotemporally correlated turbulence generation through fractal noise synthesis, and (3) realistic sensor simulation including noisy IMU measurements, LiDAR point clouds, and RGB camera feeds. Our platform enables scalable generation of synchronized datasets containing ground-truth vehicle states, aerodynamic forces, turbulent wind fields, and multi-modal sensor streams. Experimental validation demonstrates that autonomy pipelines (including both controllers and perception systems) developed in FWAV-Sim exhibit significantly improved simulation capability, thereby advancing the outstanding performance in simulation-based development for flapping-wing aerial systems.

Deploying Scientific Machine Learning surrogates in industrial CFD workflows requires adapting pretrained models to new vehicle families without large datasets; yet whether geometric representations learned by a geometry encoder transfer to topologically distinct shapes remains unvalidated. We address this through leave-one-family-out experiments on a 61.47M-parameter Transformer surrogate (AB-UPT) pretrained on four vehicle families (411 external aerodynamics cases) and adapted to the held-out fifth with only 20 samples. Three strategies are compared: Full Fine-Tuning (FFT), Lightweight Fine-Tuning (LFT), and Low-Rank Adaptation (LoRA). The central finding is that pretrained geometry encoders learn transferable representations, but the adaptation mechanism determines whether they can be exploited. FFT destabilizes as 61.47M unconstrained parameters overfit to 20 samples (R^2=0.40); LFT fails because the frozen encoder cannot represent unseen shapes (R^2<0). LoRA resolves both: rank-constrained adapters injected into all layers regularize the loss landscape while preserving pretrained features, achieving R^2=0.85+/-0.02 across all five families with 50% lower force RMSE than FFT and 28% lower pointwise field errors. LoRA also outperforms from-scratch training using 3x more target-family data, eliminating the need for large per-family datasets. These results recast LoRA from a memory-saving convenience into a convergence enabler for geometry transfer: a shared backbone paired with lightweight per-family adapters trainable in hours from minimal data.

Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited by the cost of repeated high-fidelity simulations required for gradient-based Markov chain Monte Carlo (MCMC) sampling. While surrogate models are commonly proposed to reduce this cost, their effect on posterior geometry and uncertainty, especially for shock-dominated flows, remains poorly understood. In this work, we demonstrate that neural operator surrogates can be embedded directly within the MCMC inference loop while preserving posterior structure. Using a fully Bayesian inverse formulation of quasi-one-dimensional nozzle flow, we demonstrate that geometry parameterization plays a decisive role in identifiability and posterior conditioning, with cubic B-splines yielding stable and physically meaningful uncertainty estimates. Building on this formulation, a Deep Operator Network trained on CFD-generated data is substituted for the CFD solver within a No-U-Turn Sampler, while keeping the likelihood model, priors, and sampling configuration unchanged. Across sparse to fully observed regimes, surrogate-based inference reproduces the posterior geometry and uncertainty trends of the CFD reference. As a result of surrogate integration, total inference time is reduced to under one second, corresponding to a speedup exceeding three orders of magnitude. In addition, a direct inverse neural operator is examined as a deterministic alternative for inverse design, enabling single-shot geometry reconstruction without posterior sampling. These results demonstrate that neural operator-accelerated Bayesian inference enables practical, uncertainty-aware inverse design workflows for aerodynamic applications.

Accurate modeling of aerodynamic loads is essential for understanding and predicting the responses of complex structural systems. However, these models often rely on simplifications of the true physical forces, introducing assumptions that can limit their accuracy. Validating such models becomes particularly challenging in the presence of noisy or incomplete data. To address this, we introduce a probabilistic physics-informed machine learning approach designed to reconstruct the underlying aerodynamic loads from noisy measurements of structural dynamic responses. The model avoids overfitting, eliminates the need for regularization schemes, and allows for the use of heterogeneous and multi-fidelity data during the training process. The efficacy of the approach is demonstrated through the reconstruction of aerodynamic loads on the Great Belt East Bridge, simulated under a linear unsteady assumption. Results show a strong agreement between true and predicted loads, particularly related to root mean squared errors, magnitude, phase angle and peak values of the signals. The method for load reconstructing holds broad applicability, such as modeling validation, future load estimation, and structural damage prognosis.

Rapid progress in aerodynamic shape optimization (ASO) has outpaced currently-available standardized evaluation frameworks. Fair comparison requires a unified benchmark spanning diverse shape classes, objective formulations, and matched-budget state-of-the-art baselines. We introduce ShapeBench, an open-source ASO benchmark with a unified API spanning 103 tasks across eight shape categories and multiple optimization regimes. Each ShapeBench task includes a validated surrogate for fast search; when feasible, a high-fidelity Computational Fluid Dynamics (CFD) pipeline for final verification is available, enabling systematic fidelity-gap analysis. ShapeBench provides a reproducible protocol with well-configured baselines to compare fairly using a consistent budget metric, allowing for comparison among both classical and LLM-driven methods, including general-purpose optimizers and a new domain-specialized evolutionary LLM baseline, ShapeEvolve. Results on ShapeBench demonstrate substantial variance in optimizer rankings across shape categories and problem formulations, with mean pairwise Spearman $ρ= 0.013$, so single-task conclusions do not reliably generalize across problem classes. The benchmark is also far from saturation; classical methods are rarely applicable across all shape categories and tasks, further highlighting the need for more general-purpose approaches.

Airfoil shape design is a fundamental task in aerospace engineering, with a direct impact on flight stability and fuel consumption. Deep learning has recently emerged as a promising tool for this task, but existing deep generative approaches remain limited in both geometric validity and physical controllability. They offer little control over the generated shapes, yielding invalid geometries, and they typically do not condition effectively on aerodynamic performance. To address these issues, this paper proposes AirfoilGen, a valid-by-construction and performance-aware latent diffusion model for airfoil. It first introduces a novel airfoil representation scheme, the circle sweeping representation, to constrain the generative process so that output shapes respect essential airfoil characteristics. It then enables explicit control over aerodynamic performance (e.g., lift and drag coefficients) by operating in a learned latent space: a transformer model encodes airfoil shapes into vector embeddings, and a conditional diffusion model denoises Gaussian noise into these latent embeddings while incorporating target aerodynamic performance. In addition, this paper presents a new dataset of over 200,000 airfoils, which is substantially larger than the widely used UIUC airfoil dataset (1,650 airfoils) and more suitable for training modern deep generative models. Experiments demonstrate that AirfoilGen enables airfoil generation with far greater geometric validity and aerodynamic performance controllability than previously achievable, with an average performance-conditioning accuracy of 98.41%.

This paper describes the first-ever open-source high-fidelity CFD dataset of a high-lift aircraft for the purpose of AI surrogate model development. The dataset is composed of 1800 samples, arising from 180 geometry variants and 10 angles of attack for the high-lift NASA Common Research Model (CRM) geometry, used within the AIAA High-Lift Prediction Workshop series. One of the novelties of this dataset is the use of a GPU-accelerated high-fidelity explicit, wall-modeled LES approach for each simulation, using solution-adapted grids between 300M and 500M cells. This ensures the greatest possible accuracy given known challenges in steady-state RANS approaches for these portions of the flight envelope. The entire dataset (geometries, time-averaged volume and surface variables and integral forces) are available, free of charge with a permissive open-source license (CC-BY-4.0). By making this data publicly available, we aim to accelerate the research and development of AI surrogate modeling within the aerospace industry.

This study investigates active flow control (AFC) of a 30P30N high-lift wing at a Reynolds number Re$_c$ = 450,000 and angle of attack $α$ = 23$^\circ$ using wallresolved large-eddy simulations (LES). Two optimization strategies are explored: open-loop Bayesian optimization (BO) and closed-loop deep reinforcement learning (DRL), both targeting the mitigation of stall and the improvement of aerodynamic efficiency via synthetic jets on the slat, main, and flap elements. The uncontrolled configuration was validated against literature data, confirming the reliability of the LES setup. The BO framework successfully identified steady jet velocities that increased efficiency by +10.9% through a -9.7% drag reduction while maintaining lift. In contrast, the DRL agent, despite leveraging instantaneous flow information from distributed sensors, achieved only minor improvements in lift and drag, with negligible efficiency gain. Training analysis indicated that the penalty-dominated reward constrained exploration. These results highlight the need for carefully designed rewards and computational acceleration strategies in DRL-based flow control at high Reynolds numbers.

We introduce Phantom Twist, a type of single-propeller UAV designed to achieve low visibility through high-speed spinning and the exploitation of motion blur. We develop a two-stage automated design pipeline that optimizes the placement of functional components including batteries, control PCB, motor-propeller assembly, and counterweights. The pipeline minimizes visibility as measured by a human-aligned perceptual metric (LPIPS) while strictly satisfying inertial and aerodynamic constraints required for stable flight. We validate this approach through fabrication and flight testing of multiple prototypes. These tests confirm that our pipeline produces stable, controllable designs and that the optimized UAV exhibits significantly reduced visual perceptibility compared to conventional quadcopters.

Recent advances in Gaussian Splatting have enabled fast, high-fidelity 3D scene generation, yet these methods remain purely visual and lack an understanding of how shapes behave in the physical world. We introduce Physics-Guided 3D Gaussian Splatting (PG-3DGS), a framework that couples differentiable physics simulation with 3D Gaussian representations to generate 3D structures satisfying physics functionalities. By allowing physical objectives to guide the shape optimization process alongside visual losses, our approach produces geometries that are not only photometrically accurate but also physically functional. The model learns to adjust shapes so that the generated objects exhibit physically meaningful behaviors, for example, teapots that can pour and airplanes that can generate lift, without sacrificing visual quality. Experiments on pouring and aerodynamic lift tasks show that PG-3DGS improves physical functionality while preserving visual quality. In addition to simulation gains, bench-top physical lift tests with 3D-printed aircraft (Cessna, B-2 Spirit, and paper plane) under identical airflow conditions show higher scale-measured lift for PG-3DGS, generated structures than an appearance-matching baseline in all three cases. Our unified framework connects appearance-based reconstruction with physics-based reasoning, enabling end-to-end generation of 3D structures that both look realistic and function correctly.

Due to the system's scale and complex fabrication, the model describing the dynamics of a flapping-wing insect-scale aerial robot is subject to parameter uncertainty; for example, in the inertia matrix and the actuator mapping of the flier. Furthermore, due to its low inertia, this type of robot is greatly affected by stochastic and systematic disturbances during flight, including power-wire tension, gusts, and undesired aerodynamic forces produced by wing misalignment. Therefore, the high-performance execution of complex maneuvers at the subdecigram scale requires the robot to adapt its behavior to counteract disturbances and model uncertainty. Toward this objective, we introduce a model-reference adaptive control (MRAC) architecture for high-performance position control of flapping-wing robotic insects that can be modeled as rigid bodies in the three-dimensional (3D) space. In addition, we demonstrate how the implementation of a hybrid multiplicative extended Kálmán filter for estimating current and desired angular velocities during flight significantly dampens attitude vibrations, especially along the roll and pitch degrees of freedom (DOFs), and also improves flight performance. To show the suitability, functionality, and high performance of the proposed approach, we conducted real-time hovering and trajectory-tracking 6-DOF flight control experiments with a 95-mg insect-scale aerial robot.

We prove that aerodynamic co-contraction in a redundant dual-rotor actuator can tune a passive, trim-defined aero-mechanical damping while keeping the commanded net force constant. In particular, we define an incremental damping coefficient as the local sensitivity of net thrust to air-relative velocity at a trim and prove that it increases monotonically along constant-force fibers under a mild aerodynamic hardening condition. We then validate the required damping and hardening properties from a first-principles Blade Element Theory derivation, which yields a minimal thrust model affine in inflow and explicitly reveals the speed--inflow coupling driving the effect. The resulting mechanism is formalized as a Variable Aerodynamic Damping Actuator (VADA) and shown to be dynamically isomorphic to stiffness modulation in antagonistic variable-stiffness actuation (VSA), similar to the co-contraction of tendons by muscle co-activation. The same fiber-density principle also enhances the active aerodynamic promptness measure of redundant multirotors. Finally, an impedance-form representation clarifies the roles of common-mode and differential-mode actuation in the control of passive impedance and the equilibrium velocity of the VADA system.

Aerodynamic surrogate models are increasingly used to replace repeated high-fidelity CFD evaluations in many-query design settings, but current approaches still face two important limitations: they often scale poorly to the very large fields arising in realistic 3D aerodynamics, and they rarely produce latent representations that are directly useful for analysis and design. We introduce AeroJEPA, a Joint-Embedding Predictive Architecture for aerodynamic field modeling that addresses both issues. Rather than predicting the full flow field directly from geometry, AeroJEPA predicts a target latent representation of the flow from a context latent representation of the geometry and operating conditions, and optionally reconstructs the field through a continuous implicit decoder. This formulation decouples latent prediction from field resolution while encouraging the latent space to organize semantically. We evaluate AeroJEPA on two complementary datasets: HiLiftAeroML, which stresses the method in a high-fidelity regime with extremely large boundary-layer fields, and SuperWing, which tests large-scale generalization and latent-space optimization over a broad family of transonic wings. Across these benchmarks, AeroJEPA is competitive as a continuous surrogate for aerodynamic fields, scales naturally to high-resolution outputs, and learns context and predicted latents that encode geometry and aerodynamic quantities not used directly as supervision. We further show that the resulting latent space supports controlled interpolation, linear probing, concept-vector arithmetic, and a constrained design latent-optimization experiment. These results suggest that predictive latent learning is a promising direction for scalable and design-meaningful aerodynamic surrogate modeling.

Factorization machine with quadratic-optimization annealing (FMQA) is a black-box optimization method that combines a factorization machine (FM) surrogate with QUBO-based search by an Ising machine. When FMQA is applied to integer or discretized continuous variables via one-hot encoding, uniform random initial sampling can leave many binary variables never active in the initial training data, and the corresponding FM parameters receive no direct gradient updates from the observed responses. We address this by designing the initial training data to achieve complete marginal bit coverage, namely, ensuring that every binary variable obtained by one-hot encoding takes the value one at least once. We use two space-filling sampling methods, Latin hypercube sampling (LHS) and the Sobol' sequence, yielding LHS-FMQA and Sobol'-FMQA. On the human-powered aircraft wing-shape optimization benchmark with 17 and 32 design variables, both proposed methods achieved numerically higher mean final cruising speeds than the baseline FMQA, with the advantage more pronounced on the 32-variable problem.

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (\textbf{\textsc{GANO}}), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. \textsc{GANO} encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-informed surrogate provides a reliable gradient pathway for geometry updates. Moreover, \textsc{GANO} supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to +55.9% lift-to-drag improvement for airfoils and ~7% drag reduction for vehicles.

The increasing flexibility of modern large wind turbine blades necessitates cost-efficient and reliable structural monitoring solutions. For this purpose, we propose to use aerodynamic pressure measurements obtained via Aerosense, a novel, non-intrusive and economical sensing system. In former work [Franz et al., 2025], we investigated the potential of aerodynamic pressure measurements for structural damage detection on elastic and aerodynamically loaded structures. An experimental campaign was conducted on a NACA 633418 airfoil mounted on a vertically vibrating cantilever beam within an open wind tunnel. Structural damage was introduced progressively through controlled saw cuts near the beam support. Aerodynamic pressure distributions were recorded under varying inflow conditions and structural states. Based on this data set, we developed a convolutional neural network to detect structural damage and classify its severity using only aerodynamic pressure signals. The results demonstrate that pressure measurements can effectively enable real-time detection and quantification of damage in elastic, beam-like structures subjected to mildly turbulent flow and varying operational conditions. Recognizing the limitations of pure black-box classification, in this study, we further incorporate physics-based insights and explainable machine learning methods to interpret how structural damage influences both the dynamic response and the aerodynamic pressure field. This leads to an enhanced damage detection pipeline, aiming to improve transparency, robustness, and physical consistency in data-driven monitoring of elastic, aerodynamically loaded structures.

Rapid aerodynamic evaluation is crucial for modern vehicle design, yet existing neural operators struggle to capture intricate spatial correlations. We propose the rotary-enhanced transformer operator (RETO), a novel neural solver featuring a dual-stage spatial awareness mechanism: sinusoidal-cosine encodings for global referencing and rotary positional encodings (RoPE) for relative displacements. RoPE encodes spatial relations via unitary rotations, enforcing translation invariance and enhancing local gradient resolution. RETO is validated on ShapeNet and the high-fidelity DrivAerML benchmark. On ShapeNet, RETO achieves a relative $L_2$ error of 0.063, outperforming RegDGCNN at 0.125 and representing a 16% improvement over the Transolver baseline, which yields an error of 0.075. These performance gains are further amplified on the DrivAerML dataset, where RETO achieves relative $L_2$ errors of 0.089 for surface pressure and 0.097 for velocity. In comparison, Transolver results in errors of 0.116 and 0.121 for the same metrics, indicating that RETO achieves precision enhancements of 23% and 19%, respectively. For comprehensive comparison, the surface pressure and velocity errors for AB-UBT are 0.102 and 0.124, while RegDGCNN yields 0.235 and 0.312, respectively. Information-theoretical analysis shows that the entropy peak of RETO at 0.35 is significantly lower than that of Transolver at 0.75 under $10^4$ resolution, indicating a focused attentional mechanism capable of preserving localized gradients against global diffusion.

Conceptual aircraft design is traditionally an expert-mediated iterative process in which a human designer proposes a configuration, runs low-order physics, inspects the result, and re-proposes. We present AlphaJet, an end-to-end automated synthesis pipeline that closes this loop. From a textual mission specification (mass, range, cruise speed, hard size envelope, engine count, areal density) AlphaJet evolves a feasible 3D aircraft in real time, scored by a transparent multi-disciplinary fitness function covering aerodynamics, structures, weights, stability, packaging, and geometric mount consistency. Three contributions distinguish our approach: (i) an Anatomically-Disentangled Variational Autoencoder (AD-VAE) whose first 25 latent dimensions are supervised to align with named anatomical parameters, providing an interpretable shape prior; (ii) a topology-elitist genetic algorithm that protects the best individual from each of five tail topologies and triggers stagnation restarts, preventing premature collapse to a single configuration; and (iii) mount-aware geometric scoring that computes signed penetration between engines and other structural parts, eliminating the redundant artifacts common in generative aircraft models. The full loop runs interactively on a CPU and streams every generation to a browser viewer, making it a practical real-world automation tool for early-phase design-space exploration.

Deep generative models and neural operators have demonstrated significant potential for 3D aerodynamic inference. However, they often face inherent challenges in maintaining physical consistency and preserving high-frequency features, primarily due to spectral bias and gradient conflicts within the governing equations. To address these issues, we propose GeoFunFlow-3D, a physics-guided generative flow matching framework. Temporally, we utilize optimal transport theory to build the generation path, ensuring stable training dynamics. Spectrally, we introduce a high-order discrete engine without automatic differentiation (No-AD) to reduce gradient stiffness. Spatially, a topology-aware super-resolution module (SATO) is employed to rigorously enforce physical laws in localized regions such as shock waves. We evaluated our framework on complex industrial datasets. On the BlendedNet dataset, the model successfully avoids mode collapse even under sparse data conditions. For the NASA Rotor37 test, it accurately captures 3D detached shock structures. Compared to conventional operators, GeoFunFlow-3D significantly improves accuracy, reducing the pressure field error (RRMSE) to 0.0215 while maintaining competitive inference efficiency. Ultimately, this work provides a reliable, geometry-driven approach for generating high-dimensional fluid fields.

To enable autonomous wind estimation for energy-efficient flight in small unmanned aerial vehicles (UAVs), this study proposes a method that estimates flight states and wind using only the low-cost essential onboard sensors required for autonomous flight, without relying on additional wind measurement devices. The core of the method includes an Extended Kalman Filter (EKF) integrated with the aerodynamic model and an Adaptive Moving Average Estimation (AMAE) technique, which improves the accuracy and smoothness of the wind estimation. Simulation results show that the approach efficiently estimates both steady and time-varying 3D wind vectors without requiring flow angle measurements. The impact of aerodynamic model accuracy on wind estimation errors is also analyzed to assess practical applicability. Flight tests validate the effectiveness of the method and its feasibility for real-time onboard computation. Additionally, uncertainties and error sources encountered during testing are systematically examined, providing a foundation for further refinement.

Computational Fluid Dynamics (CFD) is central to race-car aerodynamic development, yet its cost -- tens of thousands of core-hours per high-fidelity evaluation -- severely limits the design space exploration feasible within realistic budgets. AI-based surrogate models promise to alleviate this bottleneck, but progress has been constrained by the limited complexity of public datasets, which are dominated by smoothed passenger-car shapes that fail to exercise surrogates on the thin, complex, highly loaded components governing motorsport performance. This work presents three primary contributions. First, we introduce a high-fidelity RANS dataset built on a parametric LMP2-class CAD model and spanning six operating conditions (map points) covering straight-line and cornering regimes, generated and validated by aerodynamics experts at Dallara to preserve features relevant to industrial motorsport. Second, we present the Gauge-Invariant Spectral Transformer (GIST), a graph-based neural operator whose spectral embeddings encode mesh connectivity to enhance predictions on tightly packed, complex geometries. GIST guarantees discretization invariance and scales linearly with mesh size, achieving state-of-the-art accuracy on both public benchmarks and the proposed race-car dataset. Third, we demonstrate that GIST achieves a level of predictive accuracy suitable for early-stage aerodynamic design, providing a first validation of the concept of interactive design-space exploration -- where engineers query a surrogate in place of the CFD solver -- within industrial motorsport workflows.

Accurate machine-learning models for aerodynamic prediction are essential for accelerating shape optimization, yet remain challenging to develop for complex three-dimensional configurations due to the high cost of generating training data. This work introduces a methodology for efficiently constructing accurate surrogate models for design purposes by first pre-training a large-scale model on diverse geometries and then fine-tuning it with a few more detailed task-specific samples. A Transformer-based architecture, AeroTransformer, is developed and tailored for large-scale training to learn aerodynamics. The methodology is evaluated on transonic wings, where the model is pre-trained on SuperWing, a dataset of nearly 30000 samples with broad geometric diversity, and subsequently fine-tuned to handle specific wing shapes perturbed from the Common Research Model. Results show that, with 450 task-specific samples, the proposed methodology achieves 0.36% error on surface-flow prediction, reducing 84.2% compared to training from scratch. The influence of model configurations and training strategies is also systematically studied to provide guidance on effectively training and deploying such models under limited data and computational budgets. To facilitate reuse, we release the datasets and the pre-trained models at https://github.com/tum-pbs/AeroTransformer. An interactive design tool is also built on the pre-trained model and is available online at https://webwing.pbs.cit.tum.de.

This paper introduces a multi-agent framework guided by Large Language Models (LLMs) to assist in the early stages of engineering design, a phase often characterized by vast parameter spaces and inherent uncertainty. Operating under a human-in-the-loop paradigm and demonstrated on the canonical problem of aerodynamic airfoil design, the framework employs a team of specialized agents: a Coding Assistant, a Design Agent, a Systems Engineering Agent, and an Analyst Agent - all coordinated by a human Manager. Integrated within a set-based design philosophy, the process begins with a collaborative phase where the Manager and Coding Assistant develop a suite of validated tools, after which the agents execute a structured workflow to systematically explore and prune a large set of initial design candidates. A key contribution of this work is the explicit integration of formal risk management, employing the Conditional Value-at-Risk (CVaR) as a quantitative metric to filter designs that exhibit a high probability of failing to meet performance requirements, specifically the target coefficient of lift. The framework automates labor-intensive initial exploration through a global sensitivity analysis conducted by the Analyst agent, which generates actionable heuristics to guide the other agents. The process culminates by presenting the human Manager with a curated final set of promising design candidates, augmented with high-fidelity Computational Fluid Dynamics (CFD) simulations. This approach effectively leverages AI to handle high-volume analytical tasks, thereby enhancing the decision-making capability of the human expert in selecting the final, risk-assessed design.

Active multi-fidelity surrogate modeling is developed for multi-condition airfoil shape optimization to reduce high-fidelity CFD cost while retaining RANS-consistent aerodynamic metrics. The framework couples a low-fidelity-informed Gaussian process regression transfer model with uncertainty-triggered sampling and a synchronized elitism rule embedded in a hybrid genetic algorithm. Low-fidelity XFOIL evaluations provide inexpensive features, while sparse RANS simulations are adaptively allocated when predictive uncertainty exceeds a threshold; elite candidates are mandatorily validated at high fidelity, and the population is re-evaluated to prevent evolutionary selection based on outdated fitness values produced by earlier surrogate states. The method is demonstrated for a two-point problem at $Re=6\times10^6$ with cruise at $α=2^\circ$ (maximize $E=L/D$) and take-off at $α=10^\circ$ (maximize $C_L$) using a 12-parameter CST representation. Independent multi-fidelity surrogates per flight condition enable decoupled refinement. The optimized design improves cruise efficiency by 41.05% and take-off lift by 20.75% relative to the best first-generation individual. Over the full campaign, RANS evaluations were required for only 14.78% and 9.5% of the condition-specific candidate evaluations at cruise and take-off, respectively. These percentages quantify the reduction in high-fidelity usage relative to the fixed automated RANS workflow adopted as the high-fidelity reference in this study.

Aerodynamic promptness quantifies how rotor-speed variations generate multirotor wrench variations, but its Euclidean formulation assigns the same local cost to a given rotor acceleration at every operating speed. This work develops a capacity-aware extension for redundant multirotors with arbitrary numbers of heterogeneous rotors and wrench components. Under bounded motor torque and aerodynamic drag, each generally asymmetric instantaneous rotor-acceleration interval contains a largest zero-centered subset whose radius defines the symmetric acceleration capacity (SAC). The SAC induces a Riemannian metric on the positive-capacity rotor-speed region. Propagating its co-metric through the nonlinear rotor-speed-to-wrench differential yields a state-attached task-rate capability matrix and ellipsoid. The corresponding inverse quadratic form equals the minimum normalized rotor-acceleration effort required to realize a prescribed wrench rate, while the ellipsoid volume defines the drag-aware aerodynamic manipulability (DAAM) index. Fiberwise DAAM maximization provides a task-coordinate-invariant criterion for selecting task-equivalent actuator states; its maximizing set exists on compact regular domains and can be nonconvex and set valued. Low-dimensional two- and three-rotor studies make the resulting fiberwise geometry and parameter dependence directly visible. A complementary two-rotor use case shows how DAAM can inform a continuous allocation section subject to directional motor-torque feasibility. For two heterogeneous propulsion systems, the resulting sections reduce saturation-induced force-tracking degradation relative to the pseudoinverse in the faster command bands

Optimal sensor placement (OSP) is critical for efficient, accurate monitoring, control, and inference in complex physical systems. We propose a machine-learning-based feature attribution (FA) framework to identify OSP for target predictions. FA quantifies input contributions to a model output; however, it struggles with highly correlated input data often encountered in practical applications for OSP. To address this, we propose a Correlation-Assisted Attribution Framework (CAAF), which introduces a clustering step on the candidate sensor locations before performing FA to reduce redundancy and enhance generalizability. We first illustrate the core principles of the proposed framework through a series of validation cases, then demonstrate its effectiveness in realistic dynamical systems such as structural health monitoring, airfoil lift prediction, and wall-normal velocity estimation for turbulent channel flow. The results show that the CAAF outperforms alternative approaches that typically struggle due to the presence of nonlinear dynamics, chaotic behavior, and multi-scale interactions, and enables the effective application of FA for identifying OSP in real-world environments.

Unsteady aerodynamic effects can have a profound impact on aerial vehicle flight performance, especially during agile maneuvers and in complex aerodynamic environments. In this paper, we present a real-time planning and control approach capable of reasoning about unsteady aerodynamics. Our approach relies on a lightweight GPU-accelerated vortex particle model (VPM) and a sampling-based policy optimization strategy capable of leveraging the VPM for predictive reasoning. Through hardware experiments, we show that by replanning with our unsteady aerodynamics model, we can improve the performance of a post-stall fixed-wing perching maneuver in the presence of unsteady environmental flow disturbances.