Neural Surrogate Modeling

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.

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.

This article presents a deep learning-driven inverse design methodology for Doherty power amplifiers (PA) with multi-port pixelated output combiner networks. A deep convolutional neural network (CNN) is developed and trained as an electromagnetic (EM) surrogate model to accurately and rapidly predict the S-parameters of pixelated passive networks. By leveraging the CNN-based surrogate model within a blackbox Doherty framework and a genetic algorithm (GA)-based optimizer, we effectively synthesize complex Doherty combiners that enable an extended back-off efficiency range using fully symmetrical devices. As a proof of concept, we designed and fabricated two Doherty PA prototypes incorporating three-port pixelated combiners, implemented with GaN HEMT transistors. In measurements, both prototypes demonstrate a maximum drain efficiency exceeding 74% and deliver an output power surpassing 44.1 dBm at 2.75 GHz. Furthermore, a measured drain efficiency above 52% is maintained at the 9-dB back-off power level for both prototypes at the same frequency. To evaluate linearity and efficiency under realistic signal conditions, both prototypes are tested using a 20-MHz 5G new radio (NR)-like waveform exhibiting a peak-to-average power ratio (PAPR) of 9.0 dB. After applying digital predistortion (DPD), each design achieves an average power added efficiency (PAE) above 51%, while maintaining an adjacent channel leakage ratio (ACLR) better than -60.8 dBc.

This work formulates and solves optimization problems to generate input points that yield high errors between a neural network's predicted AC power flow solution and solutions to the AC power flow equations. We demonstrate this capability on an instance of the CANOS-PF graph neural network model, as implemented by the PF$Δ$ benchmark library, operating on a 14-bus test grid. Generated adversarial points yield errors as large as 3.7 per-unit in reactive power and 0.08 per-unit in voltage magnitude. When minimizing the perturbation from a training point necessary to satisfy adversarial constraints, we find that the constraints can be met with as little as an 0.04 per-unit perturbation in voltage magnitude on a single bus. This work motivates the development of rigorous verification and robust training methods for neural network surrogate models of AC power flow.

This paper presents a physics-constrained neural network framework for magnetic modeling of saturable synchronous machines, including spatial harmonics. By embedding gradient networks into the machine equations to model conservative electromagnetic behavior, the framework satisfies reciprocity and energy conservation by construction, while universally approximating any physically feasible magnetic characteristic. Unlike lookup tables and black-box neural networks, it guarantees monotonicity, invertibility, and smooth outputs, and remains highly data efficient. The method is validated using measured and finite-element method (FEM) data from a 5.6-kW permanent-magnet (PM) synchronous reluctance machine, and is demonstrated in real-time closed-loop control on an embedded platform. The results confirm accurate, physically consistent, and computationally efficient performance.

Accurate and efficient detector simulation is essential for modern collider experiments. To reduce the high computational cost, various fast machine learning surrogate models have been proposed. Traditional surrogate models for calorimeter shower modeling train separate networks for each particle species, limiting scalability and reuse. We introduce AllShowers, a unified generative model that simulates calorimeter showers across multiple particle types using a single generative model. AllShowers is a continuous normalizing flow model with a Transformer architecture, enabling it to generate complex spatial and energy correlations in variable-length point cloud representations of showers. Trained on a diverse dataset of simulated showers in the highly granular ILD detector, the model demonstrates the ability to generate realistic showers for electrons, photons, and charged and neutral hadrons across a wide range of incident energies and angles without retraining. In addition to unifying shower generation for multiple particle types, AllShowers surpasses the fidelity of previous single-particle-type models for hadronic showers. Key innovations include the use of a layer embedding, allowing the model to learn all relevant calorimeter layer properties; a custom attention masking scheme to reduce computational demands and introduce a helpful inductive bias; and a shower- and layer-wise optimal transport mapping to improve training convergence and sample quality. AllShowers marks a significant step towards a universal model for calorimeter shower simulations in collider experiments.

We present GeoTransolver, a multiscale geometry-aware physics attention transformer for Computer Aided Engineering (CAE). GeoTransolver extends the Transolver backbone with GALE (Geometry-Aware Latent Embeddings) attention, which pairs physics-aware self-attention on learned state slices with cross-attention to a shared geometry and global context computed via multi-scale ball queries (inspired by Domino) and reused in every block. Implemented and released in NVIDIA PhysicsNeMo, GeoTransolver persistently projects geometry and global parameters, into physical state spaces to anchor computations to domain structure and operating regimes. We benchmark on DrivAerML, SHIFT-SUV, and SHIFT-Wing against Domino, Transolver (PhysicsNeMo implementation), and literature-reported AB-UPT, evaluating drag/lift R2 and relative L1 errors on field variables. As an additional nonlinear structural mechanics application, we also report Transolver and GeoTransolver results on bumper-beam and full-vehicle Body-in-White (BIW) crash-dynamics benchmarks, evaluating relative L2 trajectory error and probe-level kinematic MSE. GeoTransolver delivers improved accuracy, robustness to geometry and regime shifts, and favorable data efficiency; we include DrivAerML ablations and qualitative contour and design-trend results, advancing operator learning for high-fidelity surrogates on complex, irregular, non-linear domains.

Hydrogen crossover is a critical safety and efficiency constraint in high-pressure polymer electrolyte membrane water electrolysis (PEMWE), but accurate prediction remains difficult because data are limited, transport physics are strongly coupled, and industrial operation requires reliable extrapolation beyond observed conditions. This study develops a hard-constraint physics-residual network (PR-Net) for hydrogen crossover prediction in PEMWE and compares it with a purely data-driven neural network (NN) and a soft-constraint physics-informed neural network (PINN). PR-Net embeds Henry's, Fick's, and Faraday's laws as a deterministic backbone and learns only a residual correction for unmodelled nonlinear effects. The benchmark includes 184 observations from eight peer-reviewed sources across six membrane types, covering 1-200 bar, $25-85°C$, and $0.05-5.0 A cm^{-2}$. PR-Net achieves $R^2 = 99.57 \pm 0.16$, with 9-fold lower prediction variability than NN and PINN. In pressure-axis extrapolation, PR-Net attains $R^2 = 94.02 \pm 0.92$ at 200 bar, 2.5 times beyond the training pressure range, compared with $68.06 \pm 5.52$ for PINN and $58.00 \pm 8.60$ for NN (p < 0.001). Residual analysis indicates that the learned correction captures part of the high-pressure gas-phase non-ideality and recovers a transport-regime transition near $0.23 A cm^{-2}$ between Fickian diffusion-dominated and Faradaic production-dominated transport. With a computation time of $1.08 \pm 0.34 ms$ on low-power embedded hardware, PR-Net provides a practical framework for real-time crossover monitoring, adaptive process control, and safer high-pressure green-hydrogen operation.

Climate policy analysis requires models that capture multi-gas climate effects, but such models are too slow to embed in reinforcement learning loops at scale. In collaboration with the European Environment Agency, we develop a multi-agent reinforcement learning (MARL) framework that integrates a higher-fidelity climate surrogate as the environment transition, enabling regional agents to learn policies under multi-gas dynamics. We train a recurrent surrogate on $20{,}000$ multi-gas emission pathways to emulate CICERO-SCM. The surrogate achieves near-simulator accuracy (global-mean temperature RMSE $\approx\!4\!\times \!10^{-4}\,\mathrm{K}$) with $\sim\!1000\times$ faster one-step inference and yields $>\!100\times$ end-to-end MARL training speed-up. We show policy agreement with the simulator in tractable settings and propose a replay- and rank-consistency test (Kendall's $τ$) for assessing policy fidelity when simulator-in-the-loop training is infeasible. This enables large-scale multi-agent policy experiments while retaining high-fidelity multi-gas climate response.

The ability to model mechanics of soft materials under flowing conditions is key in designing and engineering processes and materials with targeted properties. This generally requires solution of internal stress tensor, related to the deformation tensor through nonlinear and history-dependent constitutive models. Traditional numerical methods for non-Newtonian fluid dynamics often suffer from prohibitive computational demands and poor scalability to new problem instances. Developments in data-driven methods have mitigated some limitations but still require retraining across varied physical conditions. In this work, we introduce Rheological Operator Transformer (RheOFormer), a generative operator learning method leveraging self-attention to efficiently learn different spatial interactions and features of complex fluid flows. We benchmark RheOFormer across a range of different viscometric and non-viscometric flows with different types of viscoelastic and elastoviscoplastic mechanics in complex domains against ground truth solutions. Our results demonstrate that RheOFormer can accurately learn both scalar and tensorial nonlinear mechanics of different complex fluids and predict the spatio-temporal evolution of their flows, even when trained on limited datasets. Its strong generalization capabilities and computational efficiency establish RheOFormer as a robust neural surrogate for accelerating predictive complex fluid simulations, advancing data-driven experimentation, and enabling real-time process optimization across a wide range of applications.

Internal variability is a dominant contributor to the uncertainty of predictions at the interannual to decadal timescale. A typical approach to separating the internal variability from forced climate responses is to generate large ensembles of simulations under different initial conditions. Due to the complexity of Earth System Models, generating these large ensembles is computationally expensive. In this work, we present ArchesClimate, a deep learning-based climate model emulator designed to reduce the cost of exploring internal variability at timescales ranging from monthly to decadal. ArchesClimate is trained on decadal hindcasts of the IPSL-CM6A-LR climate model. We train a flow matching model following ArchesWeatherGen, which we adapt to predict near-term climate. Once trained, the model generates states at a one-month lead time from the states of the two preceding months, and can be used to auto-regressively emulate climate model simulations. We show that for up to 10 years, these generations are stable and physically consistent. We also show that for several important climate variables, ArchesClimate generates simulations that are interchangeable with the IPSL model. This work suggests that climate model emulators could reduce the cost of generating large ensembles with climate models.

Accurately predicting the performance of active radio frequency (RF) circuits is essential for modern wireless systems but remains challenging due to highly nonlinear behavior and the high computational cost of traditional simulation tools. Existing machine learning (ML) surrogates often require large datasets to generalize across various topologies or are not accurate on held-out circuits. This work presents a lightweight, data-efficient, and topology-aware graph neural network (GNN) framework for predicting key performance metrics of active RF circuit classes, such as low-noise amplifiers (LNAs), mixers, voltage-controlled oscillators (VCOs), power amplifiers (PAs), and voltage amplifiers (VAs). The proposed framework employs RFIC domain-informed feature indexing to enable cross-topology adaptability by cheap encoding of functional device semantics (e.g., differential pair and varactor transistors) and efficient knowledge transfer. The surrogate model represents circuits using device-terminal graph abstractions to preserve fine-grained connectivity and transistor-level symmetry. The final model is generalized to a wide variety of classes by being trained in parallel. Experimental results demonstrate accurate modeling of multimodal and heavy-tailed RF performance distributions, achieving an average mean relative error (MRE) of 2.71% across nineteen topologies, an improvement of 3.3x and 20x faster in training over prior art, and the generalization to held-out topologies is improved by ~26.2x. Furthermore, this work shows ~36x training data efficiency compared to state-of-the-art, demonstrating its effectiveness for scalable and deployment-ready RF design automation.

Scientific machine learning uses simulation data to train surrogate models for fast physical-field prediction across geometries. Local shape editing can expand limited geometry collections, but whether its variants improve prediction on unseen geometries, and how to allocate them across sources, require controlled evaluation. We introduce AneumoBench, a dataset and benchmark linking 401 source aneurysm geometries to 9,693 locally edited descendant records, with computational fluid dynamics (CFD) fields computed on both. It contains 80,752 steady velocity-pressure cases across eight inlet conditions and 9,715 transient sequences of velocity, pressure, and wall shear stress (WSS). Each sequence contains 100 frames sampled at 0.01-s intervals from a 1-s cardiac cycle. Mesh, point, and voxel interfaces support steady field prediction and WSS forecasting from four observed frames. With family-disjoint splits, we compare source-only training, descendant training, and descendant pretraining followed by source fine-tuning across nine architectures on 79 held-out sources. Under the reported schedules, two-stage training lowers steady-field and reset-window WSS errors relative to source-only training. With the number of sampled fields and training updates fixed within each comparison, GraphSAGE benefits from descendant training and from distributing a fixed number of descendants across more sources. For WSS, reset-window gains do not consistently persist through 96-step rollout, and lower trajectory error need not improve cycle-level shear metrics or hotspot localization. These data and protocols enable researchers to compare descendant selection and training strategies on the same unseen source geometries.

This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet, PCANet, and the Fourier Neural Operator, highlighting their underlying representations, computational structures, and comparative performance. These architectures are demonstrated on three canonical PDE problems: the Poisson equation, a linear elasticity problem, and a hyperelasticity problem. To make the presentation self-contained, key foundational topics are introduced, including finite-dimensional representations of function spaces, singular-value decomposition, and sampling from infinite-dimensional function spaces. Beyond forward modeling, the review discusses the use of neural operators as surrogate models within a Bayesian inverse-problem framework, including prior specification, forward-map approximation, and posterior computation. The performance of the three neural-operator architectures is evaluated on in-distribution samples, out-of-distribution samples, and Bayesian inference tasks. The review also discusses challenges related to prediction accuracy and generalization, outlining emerging strategies such as residual-based error correction and multi-level training. The review concludes by positioning neural operators within broader scientific-computing workflows and by identifying directions for reliable, scalable operator learning.