Neural Surrogate Modeling

Data-driven neural networks are increasingly used as surrogate forward models in geophysics, but it remains unclear whether they recover only the data mapping or also the underlying physical sensitivity structure. Here we test this question using surface-wave dispersion. By comparing automatically differentiated gradients from a neural-network surrogate with theoretical sensitivity kernels, we show that the learned gradients can recover the main depth-dependent structure of physical kernels across a broad range of periods. This indicates that neural surrogate models can learn physically meaningful differential information, rather than acting as purely black-box predictors. At the same time, strong structural priors in the training distribution can introduce systematic artifacts into the inferred sensitivities. Our results show that neural forward surrogates can recover useful physical information for inversion and uncertainty analysis, while clarifying the conditions under which this differential structure remains physically consistent.

Cardiovascular modeling has rapidly advanced over the past few decades due to the rising needs for health tracking and early detection of cardiovascular diseases. While 1-D arterial models offer an attractive compromise between computational efficiency and solution fidelity, their application on large populations or for generating large in silico cohorts remains challenging. Certain hemodynamic parameters like the terminal resistance/compliance, are difficult to clinically estimate and often yield non-physiological hemodynamics when sampled naively, resulting in large portions of simulated datasets to be discarded. In this work, we present a systematic framework for training machine learning (ML) models, capable of instantaneous hemodynamic prediction and parameter estimation. We initially start with generating a parametric virtual cohort of patients which is based on the multivariate correlations observed in the large Asklepios clinical dataset, ensuring that physiological parameter distributions are respected. We then train a deep neural surrogate model, able to predict patient-specific arterial pressure and cardiac output (CO), enabling rapid a~priori screening of input parameters. This allows for immediate rejection of non-physiological combinations and drastically reduces the cost of targeted synthetic dataset generation (e.g. hypertensive groups). The model also provides a principled means of sampling the terminal resistance to minimize the uncertainties of unmeasurable parameters. Moreover, by assessing the model's predictive performance we determine the theoretical information which suffices for solving the inverse problem of estimating the CO. Finally, we apply the surrogate on a clinical dataset for the estimation of central aortic hemodynamics i.e. the CO and aortic systolic blood pressure (cSBP).

Operational flood forecasting still relies on high-fidelity two-dimensional hydraulic solvers, but their runtime can be prohibitive for rapid decision support on large urban floodplains. In parallel, AI-based surrogate models have shown strong potential in several areas of computational physics for accelerating otherwise expensive high-fidelity simulations. We address this issue on the lower Têt River (France), starting from a production-grade Telemac2D model defined on a high-resolution unstructured finite-element mesh with more than $4\times 10^5$ nodes. From this setup, we build a learning-ready database of synthetic but operationally grounded flood events covering several representative hydrograph families and peak discharges. On top of this database, we develop a graph-neural surrogate based on projected meshes and multimesh connectivity. The projected-mesh strategy keeps training tractable while preserving high-fidelity supervision from the original Telemac simulations, and the multimesh construction enlarges the effective spatial receptive field without increasing network depth. We further study the effect of an explicit discharge feature $Q(t)$ and of pushforward training for long autoregressive rollouts. The experiments show that conditioning on $Q(t)$ is essential in this boundary-driven setting, that multimesh connectivity brings additional gains once the model is properly conditioned, and that pushforward further improves rollout stability. Among the tested configurations, the combination of $Q(t)$, multimesh connectivity, and pushforward provides the best overall results. These gains are observed both on hydraulic variables over the surrogate mesh and on inundation maps interpolated onto a common $25\,\mathrm{m}$ regular grid and compared against the original high-resolution Telemac solution. On the studied case, the learned surrogate produces 6-hour predictions in about $0.4\,\mathrm{s}$ on a single NVIDIA A100 GPU, compared with about $180\,\mathrm{min}$ on 56 CPU cores for the reference simulation. These results support graph-based surrogates as practical complements to industrial hydraulic solvers for operational flood mapping.

Magnetohydrodynamic (MHD) phenomena play a pivotal role in the design and operation of nuclear fusion systems, where electrically conducting fluids (such as liquid metals or molten salts employed in reactor blankets) interact with magnetic fields of varying intensity and orientation, influencing the resulting flow dynamics. The numerical solution of MHD models entails the resolution of highly nonlinear, multiphysics systems of equations, which can become computationally demanding, particularly in multi-query, parametric, or real-time contexts. This study investigates a fully data-driven framework for MHD state reconstruction that integrates dimensionality reduction through Singular Value Decomposition (SVD) with the SHallow REcurrent Decoder (SHRED), a neural network architecture designed to reconstruct the full spatio-temporal state from sparse time-series measurements of selected observables, including previously unseen parametric configurations. The SHRED methodology is applied to a three-dimensional geometry representative of a portion of a WCLL blanket cell, in which lead-lithium flows around a water-cooled tube. Multiple magnetic field configurations are examined, including constant toroidal fields, combined toroidal-poloidal fields, and time-dependent magnetic fields. Across all considered scenarios, SHRED achieves high reconstruction accuracy, robustness, and generalization to magnetic field intensities, orientations, and temporal evolutions not seen during training. Notably, in the presence of time-varying magnetic fields, the model accurately infers the temporal evolution of the magnetic field itself using temperature measurements alone. Overall, the findings identify SHRED as a computationally efficient, data-driven, and flexible approach for MHD state reconstruction, with significant potential for real-time monitoring, diagnostics and control in fusion reactor systems.

In Europe, balance responsible parties can deliberately take out-of-balance positions to support transmission system operators (TSOs) in maintaining grid stability and earn profit, a practice called implicit balancing. Model predictive control (MPC) is widely adopted as an effective approach for implicit balancing. The balancing market model accuracy in MPC is critical to decision quality. Previous studies modeled this market using either (i) a convex market clearing approximation, ignoring proactive manual actions by TSOs and the market sub-quarter-hour dynamics, or (ii) machine learning methods, which cannot be directly integrated into MPC. To address these shortcomings, we propose a data-driven balancing market model integrated into MPC using an input convex neural network to ensure convexity while capturing uncertainties. To keep the core network computationally efficient, we incorporate attention-based input gating mechanisms to remove irrelevant data. Evaluating on Belgian data shows that the proposed model both improves MPC decisions and reduces computational time.

We investigate the data-driven discovery of constitutive closures in nonlinear reaction-diffusion systems with known governing PDE structures. Our objective is to robustly recover diffusion and reaction laws from spatiotemporal observations while avoiding the common pitfall where low residuals or short-horizon predictions are conflated with physical recovery. We propose a three-stage neural-symbolic framework: (1) learning numerical surrogates under physical constraints using a noise-robust weak-form-driven objective; (2) compressing these surrogates into restricted interpretable symbolic families (e.g., polynomial, rational, and saturation forms); and (3) validating the symbolic closures through explicit forward re-simulation on unseen initial conditions. Extensive numerical experiments reveal two distinct regimes. Under matched-library settings, weak polynomial baselines behave as correctly specified reference estimators, showing that neural surrogates do not uniformly outperform classical bases. Conversely, under function-class mismatch, neural surrogates provide necessary flexibility and can be compressed into compact symbolic laws with minimal rollout degradation. However, we identify a critical "bias inheritance" mechanism where symbolic compression does not automatically repair constitutive bias. Across various observation regimes, the true error of the symbolic closure closely tracks that of the neural surrogate, yielding a bias inheritance ratio near one. These findings demonstrate that the primary bottleneck in neural-symbolic modeling lies in the initial numerical inverse problem rather than the subsequent symbolic compression. We underscore that constitutive claims must be rigorously supported by forward validation rather than residual minimization alone.

Production optimization in stress-sensitive unconventional reservoirs is governed by a nonlinear trade-off between pressure-driven flow and stress-induced degradation of fracture conductivity and matrix permeability. While higher drawdown improves short-term production, it accelerates permeability loss and reduces long-term recovery. Identifying optimal, time-varying control strategies requires repeated evaluations of fully coupled flow-geomechanics simulators, making conventional optimization computationally expensive. We propose a deep learning-based surrogate optimization framework for high-dimensional well control. Unlike prior approaches that rely on predefined control parameterizations or generic sampling, our method treats well control as a continuous, high-dimensional problem and introduces a problem-informed sampling strategy that aligns training data with trajectories encountered during optimization. A neural network proxy is trained to approximate the mapping between bottomhole pressure trajectories and cumulative production using data from a coupled flow-geomechanics model. The proxy is embedded within a constrained optimization workflow, enabling rapid evaluation of control strategies. Across multiple initializations, the surrogate achieves agreement with full-physics solutions within 2-5 percent, while reducing computational cost by up to three orders of magnitude. Discrepancies are mainly associated with trajectories near the boundary of the training distribution and local optimization effects. This framework shows that combining surrogate modeling with problem-informed sampling enables scalable and reliable optimization for high-dimensional, simulator-based problems, with broader applicability to PDE-constrained systems.

Real-time monitoring of inverter-based microgrids is essential for stability, fault response, and operational decision-making. However, electromagnetic transient (EMT) simulations, required to capture fast inverter dynamics, are computationally intensive and unsuitable for real-time applications. This paper presents a data-driven surrogate modeling framework for fast prediction of microgrid behavior using convolutional neural networks (CNN) and Light Gradient Boosting Machine (LightGBM). The models are trained on a high-fidelity EMT digital twin dataset of a microgrid with ten distributed generators under eleven operating and disturbance scenarios, including faults, noise, and communication delays. A sliding-window method is applied to predict important system variables, including voltage magnitude, frequency, total active power, and voltage dip. The results show that model performance changes depending on the type of variable being predicted. The CNN demonstrates high accuracy for time-dependent signals such as voltage, with an $R^2$ value of 0.84, whereas LightGBM shows better performance for structured and disturbance-related variables, achieving an $R^2$ of 0.999 for frequency and 0.75 for voltage dip. A combined CNN+LightGBM model delivers stable performance across all variables. Beyond accuracy, the surrogate models also provide major improvements in computational efficiency. LightGBM achieves more than $1000\times$ speedup and runs faster than real time, while the hybrid model achieves over $500\times$ speedup with near real-time performance. These findings show that data-driven surrogate models can effectively represent microgrid dynamics. They also support real-time and faster-than-real-time predictions. As a result, they are well-suited for applications such as monitoring, fault analysis, and control in inverter-based power systems.

For neural surrogates of time-dependent partial differential equations (PDEs), storage and memory budgets require training data to be obtained by coarsening and quantizing very-high-resolution numerical simulations. Fine-scale information can thus be lost before it reaches the model. We analyze this effect in periodic incompressible Navier-Stokes: quantization spreads error evenly over the retained modes, so the finest retained band, which holds the least energy, is the most corrupted, and velocity and vorticity are distorted differently under the same operator. Building on this analysis, we propose Derived-Field Optimization (DerivOpt), which chooses which primitive and derived fields to carry from a supplied library, and how many bits each receives, by exactly minimizing a closed-form posterior risk under a calibrated channel model. This optimization problem always has an optimum and requires no knowledge of the governing equation. On PDEBench, DerivOpt not only lowers the pooled rollout nRMSE but also substantially reduces the fine-band error. These gains are already present in the predictor-free input state and add to those of a multiscale architecture. Which fields are carried, and at what precision, is thus an optimizable design variable upstream of the predictor that determines how much information a fixed budget leaves recoverable.

Nonconvex multi-well energies in cell-induced phase transitions give rise to fine-scale microstructures, low-regularity transition layers and sharp interfaces, all of which pose numerical challenges for physics-informed learning. Here we introduce biomimetic physics-informed neural networks (Bio-PINNs), which implement a near-to-far curriculum by progressively revealing the computational domain away from the cell boundary and combining this schedule with a deformation-uncertainty proxy that concentrates collocation points near evolving transition layers and tether-forming regions. Across single-cell and multicellular benchmarks, Bio-PINNs recover the densified phase more reliably near cell boundaries and in intercellular gaps, while capturing tether morphology more faithfully than representative ungated and residual-driven adaptive baselines.

We present a data-driven framework that extends the predictive capability of classical lifting-line theory (LLT) to a wider aerodynamic regime by incorporating higher-fidelity aerodynamic data from panel method simulations. A neural network architecture with a convolutional layer followed by fully connected layers is developed, comprising two parallel subnetworks to separately process spanwise collocation points and global geometric/aerodynamic inputs such as angle of attack, chord, twist, airfoil distribution, and sweep. Among several configurations tested, this architecture is most effective in learning corrections to LLT outputs. The trained model captures higher-order three-dimensional effects in spanwise lift and drag distributions in regimes where LLT is inaccurate, such as low aspect ratios and high sweep, and generalizes well to wing configurations outside both the LLT regime and the training data range. The method retains LLT's computational efficiency, enabling integration into aerodynamic optimization loops and early-stage aircraft design studies. This approach offers a practical path for embedding high-fidelity corrections into low-order methods and may be extended to other aerodynamic prediction tasks, such as propeller performance.

We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of constructing the diagram combinatorially, VoroFields learns a continuous, differentiable surrogate whose maximizer structure induces the partition implicitly. The Voronoi cells correspond to maximizer regions of the field, with boundaries defined by equal responses between competing sites. A hierarchical decomposition reduces the combinatorial complexity by refining only near envelope transition strata. Experiments across site families and metrics demonstrate accurate recovery of cells and boundary geometry without shape-specific constructions.

In a previous work (Elaarabi et al., 2025b), the Sequence Encoder for online dynamical system identification (Elaarabi et al., 2025a) and its combination with PINN (PINN-SE) were introduced and tested on both synthetic and real data case scenarios. The sequence encoder is able to effectively encode time series into feature vectors, which the PINN then uses to map to dynamical behavior, predicting system response under changes in parameters, ICs and BCs. Previously (Elaarabi et al., 2025b), the tests on real data were limited to simple 1D problems and only 1D time series inputs of the Sequence Encoder. In this work, the possibility of applying PINN-SE to a more realistic case is investigated: heating and early cooling of the thermo-stamping process, which is a critical stage in the forming process of continuous fiber reinforced composite materials with thermoplastic polymer. The possibility of extending the PINN-SE inputs to multimodal data, such as sequences of temporal 2D images and to scenarios involving variable geometries, is also explored. The results show that combining multiple encoders with the previously proposed method (Elaarabi et al., 2025b) is feasible, we also show that training the model on synthetic data generated based on experimental data can help the model to generalize well for real experimental data, unseen during the training phase.

Digital twins for radiation-based imaging and therapy are most useful when they assimilate patient data, quantify predictive uncertainty, and support clinically constrained decisions. This paper presents a modular framework for actionable digital twins in radiation-based imaging and therapy and instantiates its reproducible open-data component using the \openkbpfull{} benchmark. The framework couples PatientData, Model, Solver, Calibration, and Decision modules and formalizes latent-state updating, uncertainty propagation, and chance-constrained action selection. As an initial implementation, we build a GPU-ready PyTorch/MONAI reimplementation of the \openkbp{} starter pipeline: an 11-channel, 19.2M-parameter 3D U-Net trained with a masked loss over the feasible region and equipped with Monte Carlo dropout for voxel-wise epistemic uncertainty. To emulate the update loop on a static benchmark, we introduce decoder-only proxy recalibration and illustrate uncertainty-aware virtual-therapy evaluation using DVH-based and biological utilities. A complete three-fraction loop including recalibration, Monte Carlo inference, and spatial optimization executes in 10.3s. On the 100-patient test set, the model achieved mean dose and DVH scores of 2.65 and 1.82Gy, respectively, with 0.58~s mean inference time per patient. The \openkbp{} case study thus serves as a reproducible test bed for dose prediction, uncertainty propagation, and proxy closed-loop adaptation, while future institutional studies will address longitudinal calibration with delivered-dose logs and repeat imaging.

Air flow modeling at a local scale is essential for applications such as pollutant dispersion modeling or wind farm modeling. To circumvent costly Computational Fluid Dynamics (CFD) computations, deep learning surrogate models have recently emerged as promising alternatives. However, in the context of urban air flow, deep learning models struggle to adapt to the high variations of the urban geometry and to large mesh sizes. To tackle these challenges, we introduce Anchored Branched Steady-state WInd Flow Transformer (AB-SWIFT), a transformer-based model with an internal branched structure uniquely designed for atmospheric flow modeling. We train our model on a specially designed database of atmospheric simulations around randomised urban geometries and with a mixture of unstable, neutral, and stable atmospheric stratifications. Our model reaches the best accuracy on all predicted fields compared to state-of-the-art transformers and graph-based models. Our code and data is available at https://github.com/cerea-daml/abswift.

Discrete choice models are fundamental tools in management science, economics, and marketing for understanding and predicting decision-making. Logit-based models are dominant in applied work, largely due to their convenient closed-form expressions for choice probabilities. However, they impose restrictive assumptions on the stochastic utility component, constraining our ability to capture realistic substitution patterns. We propose an amortized inference approach that relies on a neural network emulator to approximate choice probabilities for general error distributions, including those with correlated errors. We develop a specialized neural network architecture designed to respect the invariance properties of discrete choice models. We provide group-theoretic foundations for the architecture, including a proof of universal approximation given a minimal set of invariant features. Once trained, the emulator enables rapid likelihood evaluation and gradient computation. We use Sobolev training, augmenting the likelihood loss with a gradient-matching penalty, so that the emulator learns both choice probabilities and their derivatives. We show that emulator-based maximum likelihood estimators are consistent and asymptotically normal under mild approximation conditions, and we provide sandwich standard errors that remain valid for a psuedo-true parameter even with imperfect likelihood approximation. Simulations show significant gains over the GHK simulator in accuracy and speed.

Parametric roll is a rare but high-consequence instability that can trigger abrupt regime changes in ship response, including pronounced shifts in roll statistics and tail risk. This paper develops a data-driven surrogate that learns the nonlinear, causal functional mapping from incident wave--motion time series to vessel motions, and demonstrates that the surrogate reproduces both (i) parametric roll episodes and (ii) the associated statistical shifts in the response. Crucially, the learning framework is data-source agnostic: the paired wave--motion time series can be obtained from controlled experiments (e.g., towing-tank or basin tests with wave probes and motion tracking) when a hull exists, or from high-fidelity simulations during design when experiments are not yet available. To provide a controlled severe-sea demonstration, we generate training data with a URANS numerical wave tank, using long-crested irregular seas synthesized from a modified Pierson--Moskowitz spectrum. The demonstration dataset comprises 49 random-phase realizations for each of three sea states, simulated at a fixed forward speed selected to yield encounter conditions under which parametric-roll episodes can occur. A stacked LSTM surrogate is trained on wave-elevation time series and evaluated on held-out realizations using time-domain accuracy and distributional fidelity metrics. In the most severe case, the model tracks the onset and growth of large-amplitude roll consistent with parametric excitation, and captures the corresponding changes in roll probability density functions (PDFs). We further compare loss-function choices (MSE, relative-entropy-based objectives, and amplitude-weighted variants) and show how they trade average error for improved tail fidelity relevant to operability and risk assessment.

We present SM-Net, a machine-learning model that learns a continuous spectral manifold from multiple high-resolution stellar libraries. SM-Net generates stellar spectra directly from the fundamental stellar parameters effective temperature (Teff), surface gravity (log g), and metallicity (log Z). It is trained on a combined grid derived from the PHOENIX-Husser, C3K-Conroy, OB-PoWR, and TMAP-Werner libraries. By combining their parameter spaces, we construct a composite dataset that spans a broader and more continuous region of stellar parameter space than any individual library. The unified grid covers Teff = 2,000-190,000 K, log g = -1 to 9, and log Z = -4 to 1, with spectra spanning 3,000-100,000 Angstrom. Within this domain, SM-Net provides smooth interpolation across heterogeneous library boundaries. Outside the sampled region, it can produce numerically smooth exploratory predictions, although these extrapolations are not directly validated against reference models. Zero or masked flux values are treated as unknowns rather than physical zeros, allowing the network to infer missing regions using correlations learned from neighbouring grid points. Across 3,538 training and 11,530 test spectra, SM-Net achieves mean squared errors of 1.47 x 10^-5 on the training set and 2.34 x 10^-5 on the test set in the transformed log1p-scaled flux representation. Inference throughput exceeds 14,000 spectra per second on a single GPU. We also release the model together with an interactive web dashboard for real-time spectral generation and visualisation. SM-Net provides a fast, robust, and flexible data-driven complement to traditional stellar population synthesis libraries.

Neural ODEs are increasingly used as continuous-time models for scientific and sensor data, but unconstrained neural ODEs can drift and violate domain invariants (e.g., conservation laws), yielding physically implausible solutions. In turn, this can compound error in long-horizon prediction and surrogate simulation. Existing solutions typically aim to enforce invariance by soft penalties or other forms of regularization, which can reduce overall error but do not guarantee that trajectories will not leave the constraint manifold. We introduce the invariant compiler, a framework that enforces invariants by construction: it treats invariants as first-class types and uses an LLM-driven compilation workflow to translate a generic neural ODE specification into a structure-preserving architecture whose trajectories remain on the admissible manifold in continuous time (and up to numerical integration error in practice). This compiler view cleanly separates what must be preserved (scientific structure) from what is learned from data (dynamics within that structure). It provides a systematic design pattern for invariant-respecting neural surrogates across scientific domains.

A precise spatial delivery of the radiation dose is crucial for the treatment success in radiotherapy. In the lung and upper abdominal region, respiratory motion introduces significant treatment uncertainties, requiring special motion management techniques. To address this, respiratory motion models are commonly used to infer the patient-specific respiratory motion and target the dose more efficiently. In this work, we investigate the possibility of using implicit neural representations (INR) for surrogate-based motion modeling. Therefore, we propose physics-regularized implicit surrogate-based modeling for respiratory motion (PRISM-RM). Our new integrated respiratory motion model is free of a fixed reference breathing state. Unlike conventional pairwise registration techniques, our approach provides a trajectory-aware spatio-temporally continuous and diffeomorphic motion representation, improving generalization to extrapolation scenarios. We introduce biophysical constraints, ensuring physiologically plausible motion estimation across time beyond the training data. Our results show that our trajectory-aware approach performs on par in interpolation and improves the extrapolation ability compared to our initially proposed INR-based approach. Compared to sequential registration-based approaches both our approaches perform equally well in interpolation, but underperform in extrapolation scenarios. However, the methodical features of INRs make them particularly effective for respiratory motion modeling, and with their performance steadily improving, they demonstrate strong potential for advancing this field.

Accurate power flow analysis is critical for modern distribution systems, yet classical solvers face scalability issues, and current machine learning models often struggle with generalization. We introduce BOOST-RPF, a novel method that reformulates voltage prediction from a global graph regression task into a sequential path-based learning problem. By decomposing radial networks into root-to-leaf paths, we leverage gradient-boosted decision trees (XGBoost) to model local voltage-drop regularities. We evaluate three architectural variants: Absolute Voltage, Parent Residual, and Physics-Informed Residual. This approach aligns the model architecture with the recursive physics of power flow, ensuring size-agnostic application and superior out-of-distribution robustness. Benchmarked against the Kerber Dorfnetz grid and the ENGAGE suite, BOOST-RPF achieves state-of-the-art results with its Parent Residual variant which consistently outperforms both analytical and neural baselines in standard accuracy and generalization tasks. While global Multi-Layer Perceptrons (MLPs) and Graph Neural Networks (GNNs) often suffer from performance degradation under topological shifts, BOOST-RPF maintains high precision across unseen feeders. Furthermore, the framework displays linear $O(N)$ computational scaling and significantly increased sample efficiency through per-edge supervision, offering a scalable and generalizable alternative for real-time distribution system operator (DSO) applications.

Synthetic spectral image generation is essential for remote sensing simulation and mission design, yet physically based radiative transfer models (RTMs) remain computationally expensive. Existing learning-based emulators reduce this cost, but are mostly deterministic parameter-to-spectrum regressors with limited spatial modeling and uncertainty information. We formulate spectral image emulation as a parameter-conditioned latent-variable problem and propose a variational autoencoder (VAE)-based framework combining nonlinear spectral-image representations, fast inference, and per-pixel uncertainty estimates. The framework is instantiated at spectrum and spatial--spectral levels through two-step VAE pretraining and latent mapping. We evaluate it on PROSAIL-simulated hyperspectral vegetation cubes (211 bands) and real Sentinel-3 OLCI multispectral ocean-colour imagery (21 bands) against classical regression emulators and a deep CNN baseline. Results show that no single architecture is optimal: pixel-to-pixel models perform best on controlled hyperspectral simulations, whereas a fully convolutional VAE is more robust on noisy real observations with missing or contaminated pixels. VAE-based emulators also achieve high throughput for large-scale generation. On Sentinel-3, the spatial--spectral VAE provides predictive intervals closer to empirical errors than pixel-wise neural and classical emulators, although absolute calibration remains incomplete. A look-up-table-based retrieval experiment further shows that reconstruction fidelity alone does not ensure reliable leaf area index and chlorophyll retrieval. Emulators should therefore be evaluated in representative remote-sensing end-use scenarios, not by reconstruction metrics alone.

In engineering, uncertainty propagation aims to characterise system outputs under uncertain inputs. For interval uncertainty, the goal is to determine output bounds given interval-valued inputs, which is critical for robust design optimisation and reliability analysis. However, standard interval propagation relies on solving optimisation problems that become computationally expensive for complex systems. Surrogate models alleviate this cost but typically replace only the evaluator within the optimisation loop, still requiring many inference calls. To overcome this limitation, we reformulate interval propagation as an interval-valued regression problem that directly predicts output bounds. We present a comprehensive study of neural network-based surrogate models, including multilayer perceptrons (MLPs) and deep operator networks (DeepONet), for this task. Three approaches are investigated: (i) naive interval propagation through standard architectures, (ii) bound propagation methods such as Interval Bound Propagation (IBP) and CROWN, and (iii) interval neural networks (INNs) with interval weights. Results show that these methods significantly improve computational efficiency over traditional optimisation-based approaches while maintaining accurate interval estimates. We further discuss practical limitations and open challenges in applying interval-based propagation methods.

Gaussian process surrogates dominate constrained multi-objective optimization because they are effective in data-scarce regimes, but their cubic scaling in training samples limits their ability to capture shared structure between objectives and constraints as problems grow in dimensionality. We show that deterministic neural network surrogates, equipped with feature tokenization and adaptive output normalization, match or exceed Gaussian process accuracy, while scaling to high-dimensional output spaces and training on all data including infeasible samples. Jointly training a single Feature Tokenizer Transformer to predict objectives, constraint satisfaction, and parameter sensitivities yields a unified gradient that simultaneously improves objective values, steers toward feasibility, and identifies the most influential parameters: a coherent search signal that disjoint per-output models cannot provide. We validate this on biophysical neural optimization problems of increasing complexity. In the hardest regime, with wide, uninformed parameter bounds where random sampling finds zero feasible solutions, descending the surrogate's learned constraint gradient steers the search into the feasible region and recovers near-optimal solutions where standard surrogate optimization and constrained Bayesian optimization find none.

Scientific machine learning is increasingly used to build surrogate models, yet most models are trained under a restrictive assumption in which future data follow the same distribution as the training set. In practice, new experimental conditions or simulation regimes may differ significantly, requiring extrapolation and model updates without re-access to prior data. This creates a need for continual learning (CL) frameworks that can adapt to distribution shifts while preventing catastrophic forgetting. Such challenges are pronounced in fluid dynamics, where changes in geometry, boundary conditions, or flow regimes induce non-trivial changes to the solution. Here, we introduce a new architecture-based approach (SLE-FNO) combining a Single-Layer Extension (SLE) with the Fourier Neural Operator (FNO) to support efficient CL. SLE-FNO was compared with a range of established CL methods, including Elastic Weight Consolidation (EWC), Learning without Forgetting (LwF), replay-based approaches, Orthogonal Gradient Descent (OGD), Gradient Episodic Memory (GEM), PiggyBack, and Low-Rank Adaptation (LoRA), within a spatial field-to-field regression setting. The models were trained to map transient concentration fields to time-averaged wall shear stress (TAWSS) in pulsatile aneurysmal blood flow. Tasks were derived from 230 computational fluid dynamics simulations grouped into four sequential and out-of-distribution configurations. Results show that replay-based methods and architecture-based approaches (PiggyBack, LoRA, and SLE-FNO) achieve the best retention, with SLE-FNO providing the strongest overall balance between plasticity and stability, achieving accuracy with zero forgetting and minimal additional parameters. Our findings highlight key differences between CL algorithms and introduce SLE-FNO as a promising strategy for adapting baseline models when extrapolation is required.

Traffic microsimulators are widely used to evaluate road network performance under various what-if" conditions. However, the behavior models controlling the actions of the actors are overly simplistic and fails to capture realistic actor-actor interactions. Deep learning-based methods have been applied to model vehicles and pedestrians as agents" responding to their surrounding environment" (including lanes, signals, and neighboring agents). Although effective in learning actor-actor interaction, these approaches fail to generate physically consistent trajectories over long time periods, and they do not explicitly address the complex dynamics that arise at traffic intersections which is a critical location in urban networks. Inspired by the World Model paradigm, we have developed an actor centric generative model using transformer-based architecture that is able to capture the actor-actor interaction, at the same time understanding the geometry to the traffic intersection to generate physically grounded trajectories that are based on learned behavior. Moreover, we test the model in a live simulation-in-the-loop" setting, where we generate the initial conditions of the actors using SUMO and then let the model control the dynamics of the actors. We let the simulation run for 40000 timesteps (4000 seconds), testing the performance of the model on long timerange and evaluating the trajectories on traffic engineering related metrics. Experimental results demonstrate that the proposed framework effectively captures complex actor-actor interactions and generates long-horizon, physically consistent trajectories, while requiring significantly fewer training samples than traditional agent-centric generative approaches. Our model is able to outperform the baseline in traffic related as well as aggregate metrics where our model beats the baseline by more than 10x on the KL-Divergence.

Researchers train neural simulators on uniformly sampled numerical simulation data. But under the same budget, does systematically sampled data provide the most effective information? A fundamental yet unformalized problem is how to sample training data for neural simulators so as to maximize rollout accuracy. Existing data sampling methods either tend to collapse into locally high-information-density regions, or preserve diversity but remain insufficiently model-specific, often leading to performance that is no better than uniform sampling. To address this, we propose a data sampling method tailored to neural simulators, Gradient-Informed Temporal Sampling (GITS). GITS jointly optimizes pilot-model local gradients and set-level temporal coverage, thereby effectively balancing model specificity and dynamical information. Compared with multiple sampling baselines, the data selected by GITS achieves lower rollout error across multiple PDE systems, model backbones and sample ratios. Furthermore, ablation studies demonstrate the necessity and complementarity of the two optimization objectives in GITS. In addition, we analyze the successful sampling patterns of GITS as well as the typical PDE systems and model backbones on which GITS fails.

Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress magnitudes. Convolutional architectures such as UNet tend to oversmooth high-frequency gradients, while neural operators like DeepONet exhibit spectral bias and underpredict localized extremes. Diffusion models can recover fine-scale structure but often introduce low-frequency amplitude drift, degrading physical scaling. To address these limitations, we propose a hybrid surrogate framework, cDDPM-DeepONet, that decouples stress morphology from magnitude. A conditional denoising diffusion probabilistic model (cDDPM), built on a UNet backbone, generates normalized von Mises stress fields conditioned on geometry and loading. In parallel, a modified DeepONet predicts global scaling parameters (minimum and maximum stress), enabling reconstruction of full-resolution physical stress maps. This separation allows the diffusion model to focus on spatial structure while the operator network corrects global amplitude, mitigating spectral and scaling biases. We evaluate the framework on nonlinear hyperelastic datasets with single and multiple polygonal voids. The proposed model consistently outperforms UNet, DeepONet, and standalone cDDPM baselines by one to two orders of magnitude. Spectral analysis shows strong agreement with finite element solutions across all wavenumbers, preserving both global behavior and localized stress concentrations.

We propose RHYME-XT, an operator-learning framework for surrogate modeling of spatiotemporal control systems governed by input-affine nonlinear partial integro-differential equations (PIDEs) with localized rhythmic behavior. RHYME-XT uses a Galerkin projection to approximate the infinite-dimensional PIDE on a learned finite-dimensional subspace with spatial basis functions parameterized by a neural network. This yields a projected system of ODEs driven by projected inputs. Instead of integrating this non-autonomous system, we directly learn its flow map using an architecture for learning flow functions, avoiding costly computations while obtaining a continuous-time and discretization-invariant representation. Experiments on a neural field PIDE show that RHYME-XT outperforms a state-of-the-art neural operator and is able to transfer knowledge effectively across models trained on different datasets, through a fine-tuning process.

Physics-informed machine learning surrogates are increasingly explored to accelerate dynamic simulation of generators, converters, and other power grid components. The key question, however, is not only whether a surrogate matches a stand-alone component model on average, but whether it remains accurate after insertion into a differential-algebraic simulator, where the surrogate outputs enter the algebraic equations coupling the component to the rest of the system. This paper formulates that in-simulator use as a verification and validation (V&V) problem. A finite-horizon bound is derived that links allowable component-output error to algebraic-coupling sensitivity, dynamic error amplification, and the simulation horizon. Two complementary settings are then studied: model-based verification against a reference component solver, and data-based validation through conformal calibration of the component-output variables exchanged with the simulator. The framework is general, but the case study focuses on physics-informed neural-network surrogates of second-, fourth-, and sixth-order synchronous-machine models. Results show that good stand-alone surrogate accuracy does not by itself guarantee accurate in-simulator behavior, that the largest discrepancies concentrate in stressed operating regions, and that small equation residuals do not necessarily imply small state-trajectory errors.