Neural Surrogate Modeling

Numerical site-response predictions often deviate from observations, yet correcting these discrepancies is difficult because records are limited in both sensor coverage and number of events. This study proposes the Transfer-Enabled Forced Latent Autoencoder for Response Equations (FLARE-T) to improve these predictions by learning and calibrating low-dimensional latent dynamics that connect the base acceleration input to acceleration outputs at multiple depths. FLARE-T learns a low-dimensional response manifold and input-driven dynamics from dense finite-element simulations. It then trains a sparse encoder to map simulated sensor responses into the learned coordinates and uses limited records to calibrate the dynamics within them. A short response window initializes each prediction, while the complete base motion drives the response. The framework was evaluated using a layered-soil centrifuge test and the Lotung field vertical array. Test-set results show that FLARE-T improved multi-depth acceleration histories and 5%-damped pseudoacceleration response spectra relative to the original finite-element models, reducing errors at every evaluated sensor for motions of different intensities and, at Lotung, for both horizontal components. Two Lotung source models with different constitutive parameters achieved comparable test-set accuracy, indicating reduced dependence on precise prior calibration. FLARE-T therefore provides a data-efficient means of combining dense numerical response information with limited field records to improve future site-response predictions.

A learned simulator can reproduce its training conditions accurately yet fail in two distinct ways once those conditions change. Over long rollouts, small errors accumulate until the trajectory drifts away from physically plausible behavior; under an intervention on a physical parameter, the model may continue to follow the law seen during training rather than the intervened one. We show that these two failures require different structural remedies. Evolving a learned energy with a symplectic integrator preserves the geometry of the conservative dynamics and keeps rollouts bounded and physically meaningful for up to $100\times$ the training horizon, while equal-capacity predictors, an energy-regularized predictor, and a tuned neural ODE diverge. By contrast, encoding the physical coupling through an explicit linear factorization enables the model to follow a never-seen sign of that coupling, whereas an unrestricted parameterization remains locked to the training law. Crucially, the two mechanisms are separable: removing the structure responsible for long-horizon stability leaves counterfactual transfer intact, while removing the factorized coupling destroys counterfactual transfer without eliminating stability. This double dissociation, established with matched controls that remove or replace one structural component at a time, persists beyond the headline three-body system and remains visible when the physical state must be inferred from pixels rather than provided directly. The result is a concrete design principle for physical world models: long-horizon stability and changed-law generalization arise from distinct structural commitments, and each can be imposed deliberately without requiring the other.

Wildfire spread is traditionally predicted using physics-based simulators, which are physically interpretable but whose cost increases with each additional ensemble member. We ask how well deep learning surrogates can reproduce these simulations at a fraction of this cost, training them on 10,584 fire spread simulations at 2m resolution for the Rectoret region in Catalonia, Spain. Four architectures are compared: a patch-based U-Net, a transfer-learned ResNet-50, a physics-informed network constrained by the wind-driven advection equation and a Swin-Unet transformer. Among the terrain and vegetation variables, only surface fuel load predicts burn probability with any strength (r = 0.27) and including it lowers prediction error by 21%. The remaining variables correlate weakly and are highly duplicative. Next, an experiment with saliency, occlusion and rotation demonstrates the models' learning. Convolutional models rely primarily on distance from the current fire front, while Swin-Unet assigns more weight to fuel and terrain, a finding also noted in an unrelated wildfire dataset. When applied without retraining to the second region, Pedriza, all three convolutional models still predict fire spread, losing accuracy by a small but systematic margin.

Calculating disequilibrium chemistry in exoplanet atmospheres remains a significant computational bottleneck in atmospheric retrievals. The increasing observational precision from facilities such as JWST and the Ariel mission requires including disequilibrium chemistry in these analyses. Previous studies have demonstrated that neural networks can emulate kinetic chemistry, although their spatial inductive bias does not align with the topology of chemical reaction networks. This study introduces a graph neural network surrogate that represents chemical species as nodes and temperature-dependent reaction rates as edges, thereby enabling information propagation along physically meaningful chemical pathways. The model is trained on atmospheres generated using the Venot+2020 chemical scheme and Guillot temperature-pressure profiles. The GNN accurately reconstructs disequilibrium abundances across the sampled parameter space and reduces the mean abundance error by a factor of approximately 3 compared to the previous U-Net model. When applied to transmission spectra, most predictions fall within the observational precision expected for JWST and Ariel, with only about 7% of test atmospheres exceeding a 20 ppm mean spectral error. Performance variations are primarily observed in chemically transitional regimes near a carbon-to-oxygen ratio of one and at low temperatures. An evaluation of the boundary-case planet WASP-39b demonstrates effective performance under a moderate domain shift. Perturbation analysis indicates that disturbances propagate along chemical connectivity rather than spatial adjacency, confirming that the architecture captures the structure of reaction networks. These results suggest that GNN surrogates provide accurate, computationally efficient predictions of disequilibrium chemistry, facilitating integration into the atmospheric retrieval pipeline.

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.

The purpose of this paper is the identification of high-fidelity digital twin data models from numerical code outputs by non-intrusive techniques (i.e., not requiring Galerkin projection of the governing equations onto the reduced modes basis). In this paper the author defines the concept of the digital twin data model (DTM) as a model of reduced complexity that has the main feature of mirroring the original process behavior. The significant advantage of a DTM is to reproduce the dynamics with high accuracy and reduced costs in CPU time and hardware for settings difficult to explore because of the complexity of the dynamics over time. This paper introduces a new framework for creating efficient digital twin data models by combining two state-of-the-art tools: randomized dynamic mode decomposition and deep learning artificial intelligence. It is shown that the outputs are consistent with the original source data with the advantage of reduced complexity. The DTMs are investigated in the numerical simulation of three shock wave phenomena with increasing complexity. The author performs a thorough assessment of the performance of the new digital twin data models in terms of numerical accuracy and computational efficiency.

Learning-based surrogates for AC optimal power flow (ACOPF) promise large speedups over classical solvers, but their operational value depends on physical feasibility as much as predictive accuracy. Physics-aware objectives such as the augmented Lagrangian (AL) improve constraint satisfaction at additional per-step cost, yet how this trade-off behaves with scale is uncharacterized. We sweep model and dataset sizes under both MSE and AL training, and characterize how constraint violation changes with network size across grids. Both objectives improve as power laws, but at different rates: MSE is governed primarily by model capacity, while AL is balanced across both. Violation grows roughly twice as fast with network size under MSE as under AL. On matched hardware, AL reduces violation by nearly $30\times$ for an order of magnitude more training time, with negligible added memory. The training objective determines not only where a surrogate lands but how its quality evolves with scale.

Optimal transport gives structured data a geometry, but exact evaluation is costly in large pairwise analyses that exploit relationships among distances. Learned surrogates are faster, but need not preserve this metric structure. We develop a Deep Sets surrogate for OT between variable-size weighted point clouds that enforces non-negativity, exchange symmetry, and zero self-distance, leaving the triangle inequality unconstrained. Applied to the Energy Mover's Distance between collider events in a particle physics application, the Metric-Aware Particle Flow Network achieves percent-level mean absolute percentage error while significantly improving inference throughput over other exact and approximate methods surveyed. The architectural constraints are found to improve properties that are not explicitly enforced: across $10^6$ held-out event triplets, triangle-inequality violations fall from 199 for a matched unconstrained network to 2, and the maximum from 149.5 to 5.8 GeV. These results demonstrate that targeted inductive biases can yield fast neural surrogates with substantially improved geometric fidelity.

Transient glacier simulations with higher-order ice flow require the repeated solution of a nonlinear problem as the geometry evolves. In the online mode of the Instructed Glacier Model, the velocity field is represented by a neural network whose weights are warm-started from the previous time step and updated with a few optimizer iterations. We show that supplying the network with inexpensive input fields derived from low-order ice-flow balances improves this online solver. Unlike residual-based physics-informed neural networks, which incorporate physics through governing-equation penalties in the loss, our approach leaves the governing energy objective unchanged, adding physical structure through the network inputs. Across three real-world glacier configurations, the enriched solver is markedly more robust to solver settings. On the two alpine cases, it also improves the tuned accuracy--runtime trade-off, reducing surface-velocity errors by factors of two to four at fixed runtime and reaching few-percent relative errors with only $10^4$--$10^5$ trainable parameters, far fewer than comparable raw-input baselines. A 300-year Aletsch simulation then completes in under one minute, and the larger Valais domain in about two minutes, on a single GPU---a budget once reserved for much simpler shallow-ice models. Gains are smaller for the fast marine-terminating glacier, where nonlocal stress coupling favors larger or spectral networks. More broadly, the results suggest that enriching a neural solver's inputs with reduced-order physics can make repeated higher-order solves much cheaper, with no training data and no offline training.

The Hohenberg-Kohn theorem establishes that, in principle, the ground state (GS) charge density contains all GS information of a many-electron system, such that all GS observables can be expressed as functionals of the GS charge density. Conventional Kohn-Sham density functional theory requires iterative solution of the self-consistent-field equations at substantial computational cost, motivating the development of deep learning surrogates for electronic structure calculations and, in turn, accelerating computer-aided materials design. Here, we propose AIDEN, an Atomic-Interaction Density Equivariant Network for solving real-space charge density. AIDEN separates the element-dependent one-center density from environment-induced density redistribution and represents the latter through complementary atom- and edge-centered tensor correlations. A continuous low-rank Gaussian decoder then reconstructs the density at arbitrary spatial coordinates while reusing atomic encodings independently of the evaluation grid. AIDEN achieves state-of-the-art accuracy on periodic crystal benchmarks while remaining competitive for molecular systems, and further demonstrates zero-shot transferability across several structurally distinct out-of-distribution case studies. Furthermore, AIDEN provides substantially faster inference than both baseline models and full SCF calculations, enabling efficient charge density reconstruction for large-scale electronic structure calculations.

Modeling the Martian nightside thermosphere remains challenging due to sparse in situ sampling and strong coupling among transport, magnetic, and seasonal processes. Purely data-driven models can produce non-physical artifacts, such as density inversions, in poorly sampled altitude regimes. We present a multi-task physics-informed neural network that simultaneously predicts the base-10 logarithmic densities of four neutral species (O, CO$_2$, N$_2$, and Ar) using more than a decade of MAVEN/NGIMS observations (MY 32-38, 2014-2025). A shared backbone learns a common representation of the nightside thermospheric state and branches into species-specific output heads. A weak monotonicity prior is incorporated via automatic differentiation by penalizing positive vertical gradients in logarithmic density. Experiments using an orbit-disjoint train/validation/test split show that physics-informed regularization substantially reduces non-physical inversions while preserving predictive skill and slightly improving it in the best-performing configuration, as measured by RMSE, MAE, and $R^2$. The resulting model provides a computationally efficient surrogate for nightside thermospheric reconstruction with improved vertical consistency.

Although the impact resistance of concrete has been studied extensively, a framework linking mesoscale heterogeneity to full-field stress-tensor prediction has been lacking. Data were generated with a full-scale aggregate-resolved LS-DYNA model (projectile diameter 45 mm, mass 2.13 kg, target diameter 500 mm x thickness 200 mm, mesh 10 mm), verified against published penetration experiments (Frew 2006, Hanchak 1992, Forrestal 1996) by configuration similarity. The dataset contains six-component stress-tensor fields on the X-Z mid-plane for 400 cases (4 impact velocities x 100 aggregate seeds). Three contributions are reported. First, case-by-case verification of the terminal penetration state delimited the rest-state validity of penetration depth and anchored reliable observables to rigid-body motion and field-level stress evolution. Second, a field-level graph neural operator surrogate learned the time-varying stress-field evolution and evaluated cross-velocity leave-one-out extrapolation. Third, the full-scale, aggregate-resolved, cross-velocity, per-seed database was established as a reproducible resource. Cases at 100, 135 and 200 m/s still moved at window end (negative velocity, i.e. rebound), and only one 165 m/s case arrested. Penetration depth is therefore not reported as a rest-state scalar except for the single arrested case (69.33 mm); nose-node depth differences were confirmed as numerical artifacts of displacement integration after erosion. The single-step relative L2 error was 0.6977, reported honestly; autoregressive rollout from frame 11 to 39 took about 144 ms, a speedup of about 3.6x10^3 to 4.3x10^3 relative to single-core LS-DYNA, reported as application value. Validation is bounded by configuration similarity and field-level self-consistency; the framework is a simulation-trained decision-support method within the studied parameter space.

We address the challenge of scalable uncertainty quantification in large-scale scientific applications, where complex state-of-the-art machine learning methods are often computationally infeasible. Our primary contribution is a simple yet effective empirical Bayes method for automatically tuning the hyperparameters of a flexible, heteroscedastic Spectral-normalized Neural Gaussian Process. This approach retains the expressiveness and uncertainty-awareness of semi-Bayesian neural models while significantly reducing the computational burden by integrating hyperparameter learning directly into the training loop. We demonstrate the practical impact of our method on the task of estimating the dynamic aperture in circular particle accelerators, a fundamental problem in high-energy physics colliders and storage rings, using simulation data from the case of the Large Hadron Collider at CERN. Traditional approaches to DA estimation require extensive particle-tracking simulations, which are prohibitively time-consuming and resource-intensive. Our results show that the proposed method achieves competitive predictive performance and well-calibrated uncertainty estimates at much lower computational cost than state-of-the-art approaches. We stress that, beyond this application, the proposed empirical Bayes framework offers a general solution for training heteroscedastic neural models in situations where manual hyperparameter tuning is impractical. Accordingly, we anticipate that this framework can be applied to other domains that encounter comparable computational limitations.

Subseasonal-to-seasonal (S2S) forecasting is societally critical, supporting decision-making in sectors ranging from water and agricultural management to disaster risk reduction, energy planning, and insurance. Achieving reliable predictions at these timescales requires representing the ocean and its dynamics, but traditional physics-based Ocean General Circulation Models (OGCMs), are computationally expensive and difficult to develop and improve because of the code complexity. In this work, we propose Neptune, an end-to-end data-driven framework for global ocean and sea-ice components emulation tailored for S2S timescales, up to 60 days. Neptune combines Convolutional Neural Networks (CNNs) and Spherical Fourier Neural Operators (SFNOs) to effectively capture local features and global cross-scale interactions, thereby obtaining a coherent representation of the ocean state. Forced by prescribed daily atmospheric fields, Neptune emulates ocean state variables, from temperature and salinity, to zonal and meridional currents, from sea surface height to sea ice thickness and concentration, with daily outputs at the ocean surface and through the water column. Specifically, we propose two variants of Neptune, Neptune-1 and Neptune-025, capable of emulating the ocean state at 1° and 0.25° resolution, respectively. Evaluated against a suite of metrics, including statistics (RMSE, CRPS and ACC), physical coherency (Ocean Heat Content, Eddy Kinetic Energy and Ice Brier Score) and climate indices (ENSO and Z20 metric, IOD), Neptune successfully reproduces the spatio-temporal evolution of the oceanic fields up to 60 days, and is stable over long timescales. Neptune provides compelling evidence that end-to-end data-driven ocean emulators can become a powerful component of next-generation S2S forecasting systems, emulating ocean state at high spatio-temporal resolution.

Data-driven constitutive models for path-dependent plasticity are commonly formulated using nonlinear recurrent neural networks, whose sequential state evolution limits parallel training and whose predictions may depend on the discretization of the applied strain path. We introduce a Constitutive State Space (CSS) model that reformulates structured state-space dynamics as an incremental constitutive operator. The strain increment is decomposed into magnitude and direction: the loading direction drives the latent state-space system, while the increment magnitude enters the zero-order-hold discretization of its continuous-time linear recurrence. This mechanics-tailored construction guarantees stationarity under zero increments, strongly reduces sensitivity to strain-path resolution, and retains the parallel-scan structure of S5 for efficient training on long constitutive histories. The CSS and Minimal State Cell (MSC) architectures are compared for four multiaxial path-dependent material models including isotropic J2 plasticity, pressure-sensitive foam plasticity, and combined isotropic-kinematic hardening. CSS matches or exceeds the prediction accuracy of the MSC, including one order of magnitude lower validation losses for the plastically incompressible materials. Importantly, CSS maintains low errors across large changes in strain-path discretization, whereas the MSC error increases substantially when evaluated at coarser resolutions than used for training. CSS trains substantially faster and requires fewer strain-stress pairs to attain comparable or better accuracy. Analysis of the learned state further reveals latent structure consistent with the dimensionality of the underlying physical constitutive models. These results establish mechanics-tailored structured state-space dynamics as a computational framework for efficient and discretization-robust data-driven constitutive modeling.

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.

Observations increasingly reveal the coupled radiative, chemical, and dynamical processes that shape exoplanet atmospheres. Interpreting these atmospheres requires models that can capture this complexity. However, multidimensional models remain fundamentally limited by computational cost, and answering key questions requires simulating the governing physical mechanisms at speeds classical methods cannot achieve. As a result, models often rely on simplifying approximations, such as equilibrium chemistry, even when those assumptions miss important effects. There is a pressing need for fast and accurate chemical kinetics solvers to model planetary atmospheres. Here we present a machine learning local-box chemical kinetics solver for exoplanet atmospheres using a residual flow-map architecture. We demonstrate that this surrogate model is several orders of magnitude faster than a classical solver, achieving microsecond-scale inference while retaining percent-level accuracy. The surrogate model covers a parameter space that spans $T=300$-$3000$ K, $P=10^{-6}$-$10^{4}$ bar, $Δt=10^{-3}$-$10^{8}$ s, and compositions ranging from $10^{-2}$ to $10^{3}$ times solar in both C/O ratio and metallicity. Our model outperforms several commonly used machine learning architectures and performs robustly under the extreme stiffness characteristic of atmospheric chemistry. The machine learning framework presented here is a flexible and efficient approach to emulating state-to-state flow-map problems that commonly arise in numerical simulations.

The proliferation of distributed energy resources (DERs) in distribution grids enables the active coordination of these assets to reduce costs and enable cleaner operations. Realizing this potential requires solving multiphase AC optimal power flow (AC-OPF) quickly across varying loads, DER availabilities, and topology reconfigurations, at much greater speed and scale than conventional nonlinear solvers. Learning-based surrogates can offer millisecond inference, yet existing methods target largely balanced transmission systems and do not scale to the multiphase, unbalanced, and reconfigurable nature of distribution feeders at utility scale. We present the Penalty + Sequential Linearized Feasibility Seeking (SLFS) algorithm, a self-supervised learning framework for multiphase distribution AC-OPF under switch-induced topology changes. Penalty+SLFS requires no labeled optimal solutions and trains directly from the AC-OPF objective and constraints through a differentiable fixed-point power flow solver, avoiding expensive label generation and admitting robust training procedures. Topology changes are handled efficiently using Sherman-Morrison-Woodbury updates of the admittance-matrix inverse, while an M-step Jacobian approximation accelerates differentiation through the power flow solver. At inference, SLFS repairs any infeasible predictions, providing feasibility guarantees with low computational overhead. On IEEE feeders ranging from 13 to 8,500 nodes, Penalty+SLFS achieves negligible optimality gaps and near-zero constraint violations, delivers up to three orders of magnitude speedups over IPOPT, and remains robust under large distributional shifts, demonstrating a viable path toward real-time, topology-aware AC-OPF for large-scale distribution grids.

Metasurfaces have revolutionized the development of photonic devices by enabling unprecedented precision in light manipulation. However, their design processes are often constrained by computationally expensive simulations and complex high-dimensional design spaces. Although deep learning has accelerated the design process by serving as a surrogate model, it remains constrained by task-specific architectures and lacks universal reasoning capabilities. This review surveys how Large Language Models (LLMs) are adding semantic interfaces, code generation, and tool orchestration to established numerical nanophotonic workflows. We first outline the development from classical neural networks to transformer-based models and their applications in nanophotonic design. We then review the emergence of LLM-related methods in nanophotonics and organize them into two operational modes: surrogate models that treat structure-spectrum mapping as a language task, and agentic systems that have been demonstrated to generate code, orchestrate selected simulation steps, and support closed-loop optimization. Furthermore, to identify future cross-disciplinary opportunities, we briefly explore applications of LLMs in research fields such as materials science and wireless communications. This review concludes by looking ahead to the next generation of multimodal foundation models with physical perception capabilities. In this vision, artificial intelligence is evolving from passive tools into active collaborators, participating in autonomous scientific discovery.

Simulating the ALICE Zero Degree Calorimeter (ZDC) neutron detector responses at the LHC is computationally expensive, requiring complex Monte Carlo chains. We develop a generative surrogate, focusing on Normalizing Flows (NFs). Through transfer learning, we pre-train on the full imbalanced dataset and fine-tune specialized models for different particle types ($γ$, $n$, $Λ$, $K_S^0$, $Σ^+$) using two gradual-unfreezing schemes. As standard ZDC metrics like Wasserstein distance overlook conditional structure, we introduce refined metrics: conditional weighted MAE, dispersion ratio, and Jaccard co-activation error, that better capture physics-relevant input-output dependencies and response variability. Our ensemble of fine-tuned models achieves a Wasserstein distance of $1.61 \pm 0.02$, outperforming baselines across all metrics. This work provides a generalizable NF-based framework for LHC detector simulation, combining NFs, conditional fine-tuning, and physics-motivated evaluation.

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

Accurate physical-layer modeling is increasingly essential for reliable ultra-wideband operation and capacity optimization, especially under the intensified inter-channel stimulated Raman scattering (ISRS) effect. This paper proposes the link-adaptive digital twin (LA-DT) for hybrid-amplified ultra-wideband links to overcome the generalization and speed limitations of existing methods, achieving accurate modeling and robust generalized signal-to-noise ratio (GSNR) estimation across diverse links. First, to address EDFA heterogeneity, the GSNR modeling task is decomposed into three key power predictions: ASE, NLI, and signal powers before EDFA entry. Second, to enhance cross-scenario generalization, three dedicated DT models are developed using a novel neural architecture with linear modulation layers (LMLs). Third, for rapid adaptation to unseen scenarios with limited data, three domain discriminators guide few-shot fine-tuning of the LMLs. Fourth, the LA-DT explicitly accounts for Raman amplifier (RA) insertion loss, improving practical deployment reliability. Results across 35 scenarios show that LA-DT reduces RMSE for NLI, ASE, and signal power predictions to 0.151, 0.111, and 0.113 dBm with improvements of 56.0%, 58.4%, and 52.7% over the baseline,and achieves an average GSNR estimation RMSE of 0.114 dBm (55.8% improvement). For 12 unseen scenarios, the LA-DT maintains high accuracy through few-shot fine-tuning with only 20 samples per scenario, achieving an average GSNR RMSE of 0.159 dB and demonstrating strong adaptability and robustness.

Foundation models are transforming business workflows and boosting productivity, yet they remain largely absent from engineering domains such as power system analysis, where strict physical consistency must be enforced. We present GENCO (GEometric Neural Corrective Optimizer), a unified neural solver for steady-state transmission grid analysis that handles power flow (PF), optimal power flow (OPF), and state estimation (SE) within a single architecture and shared network representation. To support advances in neural power system solvers, we introduce the open-source GridFM Development Framework, which standardizes synthetic data generation and training in a low-code environment. We also release large-scale datasets with millions of PF and OPF scenarios across diverse grid topologies to support reproducible benchmarking. We evaluate GENCO on the PFDelta and OPFData benchmarks against state-of-the-art neural solvers and classical solvers, including Newton-Raphson and IPOPT, as well as on real-world Hydro-Québec SCADA data. For large-scale PF, GENCO recovers the full AC operating state, including voltage magnitudes and reactive power that DC-PF cannot provide, while matching DC-PF-level active power-balance residuals. It achieves up to 30x speedups over Newton-Raphson at only 2x the runtime of DC-PF. For OPF, it achieves up to 85x speedups over IPOPT while improving feasibility, optimality, and runtime over DC-OPF. For SE, GENCO is more robust than classical weighted least squares to noisy measurements and network parameter errors, and always returns a high-quality estimate even when weighted least squares fails to converge. Together, the unified architecture and development framework provide a new approach to large-scale steady-state grid analysis, lowering the barrier to entry for power system engineers and marking a step toward Grid Foundation Models.

Existing learning-based influence maximization frameworks rely heavily on complex neural architectures and continuous optimization over seed representations. We challenge this paradigm with SIMBA, a diffusion-model-agnostic framework pairing a lightweight neural surrogate with direct discrete search. SIMBA introduces three key components: 1) uniformly anchored node embeddings that eliminate initialization noise and encourage learning driven by graph topology and diffusion pattern, 2) a shallow two-layer graph neural network surrogate predicting final infection states, and 3) batched multi-swap simulated annealing that explores combinatorial seed space without gradients or continuous relaxation. By shifting compute from complex representation learning to effective discrete search, SIMBA drastically cuts time-to-solution while achieving superior influence spread and data efficiency. Our code is available at https://github.com/yl489/rethink-IM.

This paper presents, for the first time in power systems literature to our knowledge, analytical tools to explain the training performance of machine learning surrogate models for power system dynamics. Power system simulations are increasingly challenged by stiff and multi-timescale dynamics arising from converter-interfaced resources and fast control loops. Machine learning surrogates emerge as promising tools to handle this complexity and accelerate dynamic simulations. However, their performance remains difficult to interpret, which limits their adoption. Building on the small-signal eigenvalue analysis in power systems, this paper uses the Neural Tangent Kernel (NTK) method. NTK delivers a modal interpretation of the learning performance, identifying error modes that decay rapidly versus others that converge slowly. This connection explains how physical stiffness and timescale separation in power system dynamic models appear as optimization stiffness during Neural Network (NN) training. Based on this analysis, we develop adaptive loss-weighting strategies to improve and explain why structure-aware neural architectures, such as ActNet, perform better than vanilla NNs. We assess the proposed approach on physics-informed machine learning surrogate models of \acp{SM} and power electronic converters. The methods introduced in this paper can deliver the necessary analytical tools to interpret and improve the performance of machine learning surrogates, paving the way for the systematic, physics-aware design of NN architectures and training strategies. By moving beyond trial-and-error development, these tools reveal training dynamics and failure modes, support more reliable design decisions, and strengthen confidence in machine-learning surrogates for engineering applications.

Microwave ablation (MWA) is a promising minimally invasive treatment for liver tumors, but its therapeutic outcome strongly depends on patient-specific planning of antenna insertion trajectory, power, and treatment duration. Accurate numerical simulation can provide physically reliable ablation predictions; however, its high computational cost limits its use in optimization-based planning, where repeated forward evaluations are required. To address this issue, we propose a digital twin-based automatic planning framework that combines a neural ablation prediction model with a genetic algorithm. The model was trained on multiphysics simulation data generated from patient-specific tumor and vessel structures, antenna configurations, and treatment conditions, and was used as a fast forward model during planning. The prediction model achieved a Dice score of 95.1%, enabling accurate deep learning-based optimization. In 13 unseen planning cases, the proposed method improved ablation efficiency by 54.3% and reduced organ damage by 55.0% compared with clinician-defined planning, while slightly shortening the insertion path length by 3.3%. Most generated plans were also judged clinically applicable by MWA specialists. Furthermore, the framework enabled approximately 420-fold faster planning than numerical-simulation-based planning, demonstrating its potential as a fast digital twin for quantitative and personalized MWA treatment planning. The code is available at: https://github.com/SeonAengCho/MWA-Planning.git

We present a novel application of Neural Networks with Local Converging Inputs (NNLCI) to improve the efficiency of existing numerical methods for pricing multi-asset options. The most concise input format for NNLCI has been introduced, offering substantial convenience and efficiency. NNLCI uses a neural network to locally correct solutions from a coarse mesh and a refined mesh (relative to the coarse one), requiring only a minimal amount of high-fidelity training data. We demonstrate this approach on cash-or-nothing options under the Black-Scholes equation in one, two, and three spatial dimensions, and on single-asset down-and-out barrier call options under the Heston stochastic-volatility model (whose pricing PDE is two-dimensional in the spot price $S$ and the instantaneous variance $v$). In each case, NNLCI reduces the root-mean-square error (RMSE) of the refined-mesh numerical solution by a factor of approximately 4-12 on test sets, even when the neural network is trained on only a small subset of parameter combinations. These results demonstrate that NNLCI significantly reduces computational requirements for high-dimensional problems in real-time options trading and risk management, offering low training costs and strong generalization ability.

Understanding and controlling complex dynamical systems often requires executing thousands of numerical simulations across vast parametric landscapes, which is time-consuming. Machine learning surrogates significantly accelerate simulation by predicting state trajectories across different initializations and parameter values. However, surrogate models are specialized to one simulation model. Modifying the underlying differential equations - e.g., adding a physiological state or altering an epidemiological contact network - renders trained models obsolete and forces computationally expensive retraining from scratch. We introduce HyperODE, a surrogate capable of operating across an entire class of approximately mass-conserving compartmental models without retraining. By mapping the structure of ordinary differential equations (ODEs) into directed hypergraphs, HyperODE decouples the functional form of system interactions from the neural network architecture. HyperODE takes a compartmental model in the form of an ODE with an arbitrary parameter distribution defined through quantiles and transforms it into a hypergraph. It outputs the distribution of the trajectories for all the states in the original ODE in the form of quantiles. We then use this surrogate to build an encoder that takes a noisy trajectory and outputs a distribution over the parameters of the original ODE, thus calibrating the model in a single pass. On families and system sizes never seen in training, HyperODE produces calibrated quantile bands in a single forward pass, with weighted-interval score and coverage on par with specialized surrogates for each structure. For inverse inference, HyperODE produces calibration from noisy state trajectories in a few milliseconds with a single shared encoder, competitive with existing methods. HyperODE extends zero-shot to ODEs that break mass conservation and to external forcing.

In stream finishing, the wear experienced by a workpiece depends strongly on its orientation within the rotating abrasive media. Determining suitable orientations to achieve uniform wear requires evaluating the wear-rate field over all feasible orientations. Although the discrete element method (DEM) accurately resolves particle interactions, simulating hundreds of feasible orientations for a new geometry is computationally expensive. We present an uncertainty-guided surrogate framework that predicts, directly from geometry, the three fields governing erosion: per-triangle normal impact velocity, tangential impact velocity, and particle impact flux. These fields are combined through the Finnie wear model to reconstruct the wear-rate distribution. The surrogate employs a deep ensemble whose disagreement estimates epistemic uncertainty, enabling an active-learning strategy that selectively performs DEM simulations for the most uncertain orientations. Trained using only $13\%$ of the $696$ feasible orientations, the surrogate achieves Spearman rank correlations of $0.93$, $0.89$, and $0.93$ for the normal impact velocity, tangential impact velocity, and particle impact flux, respectively. Moreover, the predicted uncertainty is well calibrated, reliably anticipating prediction error and the fidelity of the reconstructed wear field, which matches DEM with a Spearman rank correlation of up to $0.97$ for low-uncertainty orientations and degrades in a controlled manner as uncertainty increases.

Spatial atomic layer deposition (SALD) is a leading atmospheric-pressure, high-throughput route to industrial ALD, but design and control are limited by the cost of predicting surface coverage: high-fidelity CFD is far too slow for operating-window scans, while analytic models miss transport modulation such as the gas curtain. We present a physics-chemistry-informed neural network (PCINN), a hybrid surrogate with CFD-level accuracy at real-time speed: a query returns coverage in about 7 ms, roughly 5x10^4 times faster than a CFD solve, reaching a test R^2_log = 0.998 (leave-one-out R^2_raw = 0.974) from only 30 training cases spanning four orders of magnitude in coverage. The architecture is not a black box: a small network learns only the operating-condition to near-wall concentration closure, while the known surface kinetics is a hard-coded, trainable chemistry layer integrated along the substrate trajectory. This single-scalar bottleneck keeps it accurate under sparse data, interpretable and invertible. We add a full identifiability analysis (Fisher information, profile likelihood). The adsorption energy E_ads and desorption rate k_des are robustly identifiable; k_ads is not separately identifiable at a single temperature (only k_ads*c_wall is). Across four temperatures the prefactor nu and E_ads bind along a weakly identifiable degeneracy valley of slope 0.065 eV/decade, derived analytically as k_B T_eff ln(10) and turned into a reliability diagnostic: a seven-chemistry mismatch matrix shows it is invariant under any single-Arrhenius mismatch and shifts only when a second thermally activated process appears, so a slope departure flags unmodelled site heterogeneity. Data come from simulation with known ground truth inverted by the same kinetic form, so the study verifies pipeline self-consistency and the identifiability boundary, not real parameters.