PDE Surrogate Modeling

PDE: Partial Differential Equation

PDE surrogate modeling studies how to approximate the mapping from physical conditions, geometry, and parameters to a PDE’s solution, reducing the cost of repeated simulations. Methods range from reduced-order models such as POD and latent dynamics to neural operators such as Fourier Neural Operators and DeepONets, as well as mesh-based graph networks, transformers, and generative models. Many approaches combine these learned models with physical structure, including conservation laws, symmetries, boundary conditions, and numerical solvers, to improve reliability and support inverse problems or design optimization. A central challenge is balancing speed with accuracy under new geometries or regimes, stable long rollouts, fine-scale fidelity, and calibrated uncertainty; whether a surrogate saves time overall depends on training and deployment costs as well as inference speed.

Latest papers

331 papers50 papers in the last four weeks, up 72% on the four weeks before. 0.3% of all new papers.

NEOPIC: A Neural Operator Framework for Particle-based Kinetic Plasma Simulations
Oct 29, 2026Sriramkrishnan Muralikrishnan, Chelsea Maria John, Jeffrey Kelling +3Physics-Based Simulation Neural Operators
Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, Germany · Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany · Chemnitz University of Technology, Chemnitz, Germany +1
A physics-informed uncertainty-aware surrogate for $p$ - $n$ junction diodes
Oct 29, 2026Suchita KulkarniPDE Surrogate Modeling Physics-Informed ML
Institute of Physics, NAWI Graz, University of Graz, Universitätsplatz 5, A-8010 Graz, Austria
Probabilistic Meshless Methods on Manifolds
Oct 29, 2026Federico Pavesi, Noémie Jaquier, Antonio CandelieriPDE Solving PDE Surrogate Modeling
Department of Economics, Management and Statistics University of Milano-Bicocca Piazza dell’Ateneo Nuovo 1, 20126 Milan, Italy · Department of Robotics, Perception and Learning KTH Royal Institute of Technology Lindstedtsvägen 24, 10044 Stockholm, Sweden
Predicting Sparse Observables in Parameterized Unsteady Flows Using Coarse-Mesh Graph Neural Networks
Oct 27, 2026Brener Ramos, William R. Wolf, Tarcísio C. D. Oliveira +1PDE Surrogate Modeling Reduced-Order Modeling
School of Mechanical Engineering, University of Campinas, Campinas, São Paulo, Brazil · Department of Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, Chicago, Illinois, USA
Application of PDE emulators for a multi-material, multi-physics simulation problem
Oct 27, 2026Diane Oyen, Morgan Jones, Adithan Kathirgamaraju +19PDE Surrogate Modeling Neural Surrogate Modeling
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Latent dynamics for reconstructing fine-scale PDE trajectories from coarse observations
Oct 24, 2026Chenhao Si, Zishan Qian, Shing-Tung Yau +2Latent Dynamics Modeling PDE Surrogate Modeling
School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China. · Institute of Statistics and Big Data, Renmin University, Beijing, China. · Beijing Key Laboratory of Topological Statistics and Applications for Complex Systems, Beijing Institute of Mathematical Sciences and Applications, Beijing, China. +1
Beyond Affine Reconstruction: Multi-Resolution Transformer DeepONets for the Radiative Transfer Equation
Oct 24, 2026Tanguy Azéma, Marc Bocquet, Fatiha Nmira +3PDE Surrogate Modeling Deep Operator Networks
CEREA, ENPC, EDF R&D, Institut Polytechnique de Paris, Île-de-France, France · EDF R&D, Chatou, France · Research Division, FM, 1165 Boston-Providence Turnpike, Norwood, MA 02062, USA +1
FG-ConvNO: A Geometry-Aware Neural Operator for Propeller CFD Prediction
Oct 24, 2026Yichen Di, Valentin Duruisseaux, Di Zhou +4Neural Operators Computational Fluid Dynamics
Tsinghua University · California Institute of Technology · University of Tennessee +1
Beyond Local Accuracy: Benchmarking the Rollout Reliability of PDE Foundation Models
Oct 22, 2026Jaewan Park, Seid Koric, Giri Krishnan +2PDE Foundation Models PDE Surrogate Modeling
National Center for Supercomputing Applications (NCSA), University of Illinois Urbana–Champaign · Georgia Institute of Technology
Scenario Generalization and Sector Transfer in Real Surface Irrigation Surrogate Modelling with Tabular Models
Oct 19, 2026Alessandro Cagiano, M. Aybars Seyhan, Fabiola Gangi +2Surrogate Modeling Spatial Generalization
Department of Computer Science, University of Milan, Milan, Italy · Digital Drop s.r.l., Milan, Italy · Department of Agricultural and Environmental Sciences, University of Milan, Milan, Italy
An Adaptive-Horizon Graph Neural Operator for coupled surrogate morphodynamic modelling
Oct 15, 2026Ying Cao, Yifan Yang, Junqiang Xia +2Graph Neural Operators PDE Surrogate Modeling
State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan, China · Coastal Marine Group, School of Science, The University of Waikato, Hamilton, New Zealand · Institute for Water and Environment (IWU), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Learnable Hodge-Laplacian Driven Mixture of Experts for Steady-PDE Surrogates on Coarse Unstructured Meshes
Oct 14, 2026Stavros Nousias, Akis Nousias, Konstantinos GkrispanisPDE Surrogate Modeling Mixture-of-Experts Models
Technical University of Munich · K3Y Labs
ReAl: Refine neural operators via aligning dynamical flow
Oct 14, 2026Jing Xu, Zenglin Xu, Li Yi +2PDE Surrogate Modeling PDE Operator Learning
Shanghai Academy of AI for Science · Fudan University
Structure-preserving fidelity diagnostics for partial differential equations
Oct 12, 2026Kyriakos FlourisPDE Surrogate Modeling
MRC Biostatistics Unit, University of Cambridge, Cambridge, United Kingdom · King’s College, University of Cambridge, Cambridge, United Kingdom
Compute-optimal data scaling for neural surrogates via multi-fidelity training
Oct 12, 2026Paul Setinek, Fabian Paischer, Nils Thuerey +2Neural Surrogate Modeling PDE Surrogate Modeling
Institute for Machine Learning, JKU Linz · Mistral AI · Technical University of Munich +1
Physics-guided machine learning for saturation control across variable hydraulic conditions in heap leaching
Oct 11, 2026Sultan Alhamdan, Daniel Navia, Paulina QuintanillaPDE Surrogate Modeling Physics-Informed ML
Department of Chemical Engineering, University College London, London, United Kingdom · Department of Chemical and Environmental Engineering, Universidad Técnica Federico Santa María, Valparaíso, Chile
Comparative Study of Canvas- and Coordinate-Based Geometry-Conditioned Neural Networks for Real-Time Prediction of Indoor Environments with Varying Room Dimensions
Oct 11, 2026Shaofan Wang, Philipp GeyerPDE Surrogate Modeling
Sustainable Building Systems Group, Leibniz University Hannover, Herrenhäuser Str. 8, 30419 Hannover, Germany
An Attention-Guided Graph Neural Network Surrogate for Boundary Integral Computation in Physical Field Reconstruction
Oct 11, 2026RongZe Gao, YuWei Wu, XinRan Ji +1PDE Surrogate Modeling PDE Inverse Problems
The School of Civil and Architectural Engineering, Hainan University, HaiKou, 570000, Chain.
Energy-Guided Learning for Heat Equation with Noisy Source: Optimal Estimation and Generalization Bounds
Oct 10, 2026Zixiang Zhou, Xiaohui Chen, Shanghua TengPhysics-Informed ML PDE Solving
Department of Mathematics, University of Southern California · Thomas Lord Department of Computer Science, University of Southern California · Computing and Mathematical Sciences, California Institute of Technology
One-Way Coupling via Patchwise Adaptive Normalization in Transformer Surrogates
Oct 10, 2026Emmanuel Gottlob, Hugo Thimonier, Ludovico Buizza +3PDE Surrogate Modeling
Mistral AI · ASML The Netherlands B.V.
Learn the Dynamics, Enforce the Physics: Generative Latent Operators for High-Dimensional Beam Evolution
Oct 10, 2026Haohan Zou, Alexander Scheinker, Yuanyuan ShiLatent Dynamics Modeling Physics-Informed Generative Modeling
University of California San Diego · Los Alamos National Laboratory
SBNO : Schrödinger Bridge Neural Operator for the Forward and Inverse Problems under Missing Information
Oct 9, 2026Jaehyeon Park, Inhyeok Jeong, Noseong ParkPDE Operator Learning PDE Surrogate Modeling
SolverX · KAIST
Neural Surrogate Modeling of Ultrasonic Wave Propagation in Heterogeneous Media
Oct 9, 2026Burla Nur Korkmaz, Petro Moilanen, Ari Salmi +2Neural Surrogate Modeling PDE Surrogate Modeling
Department of Computer Science, University of Helsinki, Finland
Spatial Context or Memory? Sizing the Inputs of Neural Surrogates for Partially Observed Fields
Oct 8, 2026Ruige KongNeural Surrogate Modeling Spatiotemporal Forecasting
University of Washington, Seattle, WA, USA
Transferability of Learned States in Neural PDE Solvers
Oct 7, 2026Shunye Wang, Haochen Wen, Shuo Li Liu +3Neural PDE Solvers PDE Surrogate Modeling
University of Chicago · University of Cambridge · Princeton University +2
Conditional Flow Matching for Generation of 3D Multi-variable Instantaneous Urban Microclimate Fields
Oct 7, 2026Peng Liu, Shaoxiang Qin, Theodore Potsis +3Computational Fluid Dynamics Conditional Flow Matching
Concordia University, Centre for Zero Energy Building Studies, Department of Building, Civil and Environmental Engineering, Montreal H3G 1M8, Canada · McGill University, School of Computer Science, Montreal, H3A 0E9, Canada
Cross-Domain Pretraining for Steady-State Neural CFD Surrogates
Oct 7, 2026Anthony Zhou, Amir Barati Farimani, Shirley Ho +1Cross-Domain Generalization PDE Surrogate Modeling
Carnegie Mellon University · New York University · Polymathic AI +4
Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics
Oct 7, 2026Ridham PatelPDE Surrogate Modeling PDE Operator Learning
Indian Institute of Technology Gandhinagar, Gandhinagar, India
The Symbol of the Surrogate: Measuring Numerical Provenance in Neural PDE Solvers
Oct 7, 2026Ridham PatelPDE Surrogate Modeling
Computer Science & Engineering Indian Institute of Technology Gandhinagar Gandhinagar, India
Domain-informed Adaptive Sampling for Generalizable PINNs in Metal Additive Manufacturing via Conditional Flow Matching
Oct 6, 2026Hyeonsu Lee, Jihoon JeongAdaptive Sampling Physics-Informed ML
Wm Michael Barnes ’64 Department of Industrial and Systems Engineering Texas A&M University College Station, TX 77843, USA

Oct 29, 2026J/K move · Enter open · S save

NEOPIC: A Neural Operator Framework for Particle-based Kinetic Plasma Simulations

Sriramkrishnan Muralikrishnan, Chelsea Maria John, Jeffrey Kelling, Michael Bussmann+2

Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, Germany · Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany · Chemnitz University of Technology, Chemnitz, Germany+1

Physics-Based Simulation Neural Operators PDE Surrogate Modeling

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We introduce NEOPIC, a framework for learning the field operator in particle-based methods applied to kinetic plasma simulations. Its key novelty is a neural operator that acts directly on the empirical measure of the particles, rather than on a grid, and is evaluated at the particle positions. No mesh or tree is needed and, unlike grid-based neural operators, no deposition onto a mesh takes place, so the particle noise that dominates the inputs of particle simulations is not aliased. Since it replaces only the field solve, it serves as a plug-and-play field solver for particle-based methods: it can be trained on data from particle-in-cell, particle-in-Fourier or tree codes, and combined with any time integrator, including implicit schemes. We prove that the discrete evaluation coincides with the continuous operator at any number of particles (representation equivalence) and derive an error analysis that separates sampling, learning and time-stepping errors: up to the learning error, NEOPIC has the error structure of standard Monte Carlo particle methods. We show that the particle noise in the training data acts as an implicit regularizer, which gives guidance on the number of training particles in relation to the particle numbers used at inference. A complexity analysis shows that NEOPIC is an

O(N_p)

method whose constants are set by the architecture alone, independently of any mesh or tree. Numerical experiments on electrostatic benchmarks in two and three dimensions, including Landau damping, two-stream and bump-on-tail instabilities, a cyclotron mini-app and a Penning trap, confirm the theoretical findings. A single model trained on several mini-apps generated by different reference methods captures all of them and remains stable up to twice the training time window, which points towards foundation models for fields in particle-based methods.