PDE Surrogate Modeling

PDE: Partial Differential Equation

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32 papers in the last four weeks, up 146% on the four weeks before. 0.3% of all new papers.

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Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries
Jun 6, 2026Josiah D. Kunz, Kamal ChoudharyNeural Surrogate Modeling Graph Neural Networks
Illinois College, Jacksonville, IL, USA · Department of Materials Science and Engineering, Whiting School of Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Drifting Models for Surrogate Flow Modeling
Jun 5, 2026Chris R. Jung, Markus Dörr, Natalie Jüngling +3PDE Surrogate Modeling Conditional Generative Modeling
Center for Machine Learning (ZML) 2Institute for Flow in Additively Manufactured Porous Structures (ISAPS) Heilbronn University of Applied Sciences, 74081 Heilbronn, Germany
A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction
Jun 5, 2026Kangkang Qi, Huiyu Yang, Keqi Ding +5PDE Surrogate Modeling Computational Fluid Dynamics
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China · Shenzhen Key Laboratory of Complex Aerospace Flows, Southern University of Science and Technology, Shenzhen 518055, China · Shenzhen Tenfong Technology Co., Ltd., Shenzhen 518000, China +1
Learned Response-Field Inertia Operator for HEC-RAS 2D Water-Surface Elevation Prediction
Jun 4, 2026Edward Holmberg, Elias Ioup, Md Meftahul Ferdaus +2Neural Surrogate Modeling PDE Surrogate Modeling
Canizaro Livingston Gulf States Center for Environmental Informatics, Department of Computer Science, The University of New Orleans, New Orleans, LA 70148, USA · Center for Geospatial Sciences, Naval Research Laboratory, Mississippi, USA · Ocean Sciences Division, Naval Research Laboratory, Mississippi, USA
MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers
Jun 3, 2026Yanshun Zhao, Xiaoyu Peng, Jiamin Jiang +2Neural PDE Solvers PDE Surrogate Modeling
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China · Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China.
Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations
Jun 2, 2026Niccolò Perrone, Fanny Lehmann, Stefania Fresca +1PDE Surrogate Modeling Spectral Bias
Université Paris-Saclay, CentraleSupélec, CNRS, ENS Paris-Saclay · Laboratoire de Mécanique Paris-Saclay UMR 9026 · 8-10 rue Joliot Curie, 91190 Gif-sur-Yvette, France +5
EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs
Jun 2, 2026Sungwon Kim, Juho Song, Seungmin Shin +3Fourier Neural Operator PDE Surrogate Modeling
Graduate School of Data Science, KAIST, Daejeon, Republic of Korea · Mathematical Sciences, KAIST, Daejeon, Republic of Korea · LG Electronics, Pyeong-taek, Republic of Korea +1
Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
May 31, 2026Lennon J. Shikhman, Shane GilbertiePDE Surrogate Modeling Scientific ML
College of Computing, Georgia Institute of Technology, Atlanta, 30332, GA, USA · Department of Aerospace, Physics and Space Sciences, Florida Institute of Technology, Melbourne, 32901, FL, USA
An Exploratory Study into using Machine-Learning for Fast Step-by-step Emulation of Numerical Mechanical Thrombectomy Simulations for Ischemic Stroke
May 30, 2026Thijs StessenNeural Surrogate Modeling PDE Surrogate Modeling
University of Amsterdam · MSc Artificial Intelligence
Physics-Informed Coarsening for Multigrid Graph Neural Surrogates
May 29, 2026Amir Bazzi, David Cardinaux, Ramy Nemer +3Graph Neural Networks Neural PDE Solvers
1CEMEF, Mines Paris – PSL, Sophia Antipolis, France · 2Aubert et Duval, France · 3Transvalor, Mougins, France.
SubsurfaceGen: Procedural Generation of Field-Scale Earth Models and Seismic Data
May 28, 2026Joseph Stitt, Pratik Rathore, Madeleine Udell +1Synthetic Data Generation PDE Surrogate Modeling
Stanford University
Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor
May 28, 2026Minseo Lee, Seongmin Oh, Chaehyeon Song +5PDE Surrogate Modeling Reduced-Order Modeling
Division of Advanced Nuclear Engineering, POSTECH, 772026 Cheongam-Ro, Pohang-si, 37673, Gyeongbuk-do, Republic of Korea · Department of Quantum System Engineering, Jeonbuk National University, 567 Baekje-daero, Jeonju-si, 54896, Jeollabuk-do, Republic of Korea · Department of Nuclear Engineering, Hanyang University, Wangsimni-ro, Seongdong-gu, Seongdong-gu, 04763, Seoul, Republic of Korea +1
Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System
May 27, 2026Clement Etienam, Juntao Yang, Oleg Ovcharenko +4Fourier Neural Operator PDE Surrogate Modeling
NVIDIA Corporation
Resolution-free neural surrogates for geometric parameterization and mapping with spatially varying fields
May 27, 2026Yanwen Huang, Lok Ming Lui, Gary P. T. ChoiNeural Surrogate Modeling PDE Surrogate Modeling
Department of Mathematics, The Chinese University of Hong Kong
Hybrid Neural World Models
May 27, 2026Pranav Lakshmanan, Paras ChopraNeural Surrogate Modeling Surrogate Modeling
Lossfunk
Adapting Automotive Aerodynamics Surrogates to New Vehicle Families via Transfer Learning
May 27, 2026Seunghwan Keum, Alok WareyPDE Surrogate Modeling Low-Rank Adaptation
General Motors Research and Development
CFDTwin: An open-source GUI and Python toolkit for POD-NN surrogate modeling of ANSYS Fluent simulations
May 26, 2026Daniel Curl, Han HuPDE Surrogate Modeling Proper Orthogonal Decomposition
Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR 72701, USA
NUCLEUS-MoE: Unified Model of Pool Boiling for Liquid Cooling
May 26, 2026Arthur Feeney, Xianwei Zou, Sheikh Md Shakeel Hassan +2Neural Surrogate Modeling PDE Surrogate Modeling
Department of Electrical Engineering and Computer Science University of California, Irvine Irvine, CA, USA
Faster Thermal Profiling of a Lunar Rover with Machine Learning Adapted Finite Difference Model
May 26, 2026Samuel Weber, Zaki Hasnain, Souma ChowdhuryPDE Solving PDE Surrogate Modeling
University at Buffalo · Department of Mechanical and Aerospace Engineering · Zij Sciences +1
APEX: Amplitude Anchors and Phase Priors for Target-Scarce Higher-Frequency Wave Prediction
May 26, 2026Yifan Sun, Lei Cheng, Sijie Chen +3PDE Surrogate Modeling Neural Operators
College of Information Science and Electronic Engineering, Zhejiang University
Guided Flow Matching for Forward and Inverse PDE Problems with Sparse Observations: Algorithm and Theory
May 25, 2026Xifeng Zhang, Jin ZhaoFlow Matching PDE Solving
School of Mathematical Science Capital Normal University Beijing, 100048, China · Academy for Multidisciplinary Studies Capital Normal University2026 Beijing, 100048, China
Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition
May 24, 2026Anuj Kumar, Josiah Bjorgaard, Nikolaos Bouklas +2Neural Surrogate Modeling PDE Surrogate Modeling
Pasteur Labs, NY, NY, USA · Cornell University, Ithaca, NY, USA · Institute for Simulation Intelligence, NY, NY, USA
A comparative study of accuracy and rollout stability of temporal surrogate models
May 24, 2026Rajarshi BiswasNeural Surrogate Modeling Long-Term Time Series Forecasting
Cargill Inc. Wayzata, MN 55391, USA
Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs
May 23, 2026Jinjin He, Zhiqi Li, Sinan Wang +1Neural PDE Solvers PDE Solving
Georgia Institute of Technology, Atlanta, GA, USA.
ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models
May 21, 2026Chengze Li, Lingwei Wei, Li Sun +7PDE Surrogate Modeling Computational Fluid Dynamics
University of Illinois Chicago · 2Beijing University of Posts and Telecommunications · 3North China Electric Power University
Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment
May 20, 2026Haozhe Jia, Pengyu Yin, Wenshuo Chen +6Physics-Informed Diffusion Models Physics-Informed Generative Modeling
The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · Shandong University, Jinan, China · Data61/CSIRO, Australia +5
Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics
May 20, 2026April Tran, Terry Haut, David Bortz +1Latent Dynamics Modeling PDE Surrogate Modeling
Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309, USA · Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, 94550, CA, USA
Physics-Informed Graph Neural Network Surrogates for Turbulent Nanoparticle Dispersion in Dental Clinical Environments
May 19, 2026Takshak Shende, Viktor PopovPDE Surrogate Modeling Physics-Informed ML
Department of Mechanical Engineering, University College London (UCL), London, United Kingdom · Ascend Technologies Ltd, Southampton, United Kingdom
Geometry-Aware Surrogate for Real-Time Hydrodynamics Estimation of Autonomous Ground Vehicles in Amphibious Environments
May 18, 2026Ammar Waheed, Luke Gallantree, Zohaib HasnainNeural Surrogate Modeling PDE Surrogate Modeling
J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77801, USA · Mounted Systems Engineering Team, Platform Systems Division, Defence Science and Technology Laboratory, Portsdown West, PO17 6AD, UK
Physics-informed convolutional neural networks for fluid flow through porous media
May 18, 2026Rafał Topolnicki, Paweł Dłotko, Maciej MatykaPDE Surrogate Modeling Physics-Informed ML
Dioscuri Center in Topological Data Analysis, Institute of Mathematics, Polish Academy of Sciences, ul. ´Sniadeckich 8, 00-656, Warsaw, Poland · Institute of Experimental Physics, Faculty of Physics and Astronomy, University of Wrocław, pl. M. Borna 9, 50-204, Wrocław, Poland · Institute of Theoretical Physics, Faculty of Physics and Astronomy, University of Wrocław, pl. M. Borna 9, Wrocław, 50-204, Poland +1

Jun 6, 2026, cs.LGJ/K move · Enter open · S save

Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries

Josiah D. Kunz, Kamal Choudhary

Illinois College, Jacksonville, IL, USA · Department of Materials Science and Engineering, Whiting School of Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA

Neural Surrogate Modeling Graph Neural Networks Structural Mechanics PDE Surrogate Modeling Finite Element Method

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Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios. Machine learning surrogate models offer a promising alternative, yet most approaches struggle with a critical limitation: generalizing across varying geometries. This work presents a mesh graph network (MGN) for predicting von Mises stress fields in 2D structural components with arbitrary hole geometries. Unlike traditional machine learning approaches that use absolute node coordinates as features, the proposed model builds on existing MGN frameworks that encode node types (e.g., fixed boundary, free surface, hole edge), relative edge features (distance between neighbors), and global features (applied load). This architecture is inherently translation- and rotation-invariant, enabling generalization to unseen geometries without retraining. The MGN was trained on 11 plate geometries under 20 load conditions and evaluated on 7 unseen geometries and 3 unseen loads. In the most favorable case, the model achieves

R^2 \geq 0.97

on an unseen geometry and unseen load, compared to

R^2 \approx 0.01

0.86

for conventional models (Random Forest, Gradient Boosting , K-Nearest Neighbors) trained on identical data. However, even in less favorable cases, the MGN model still outperforms conventional models. This work extends the mesh-based simulation framework of Pfaff et al. (arXiv:2010.03409) to structural mechanics, demonstrating that graph neural networks can serve as efficient surrogates for finite element analysis across varying geometries.

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