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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Feature Interaction Modeling for Neural Operators
Jul 30, 2026Quan Gu, Xiaoduo Li, Hongxia LiuFeature Interaction Modeling PDE Surrogate Modeling
Independent Researcher · Taiyuan University of Technology
Learning features from Newton's algorithm: a way to accelerate nonlinear parametrized PDE solvers
Jul 30, 2026Rémy Vallot, Florian de Vuyst, Thibault Dairay +1PDE Solving PDE Surrogate Modeling
CB, Michelin · Centre Borelli UMR 9010, ENS Paris-Saclay, Université Paris-Saclay, CNRS, France · Michelin, Centre de Recherche de Ladoux, Cébazat, France +4
Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem
Jul 29, 2026Anton Myshak, Md Rezwan Bin Mizan, Ilya TimofeyevPDE Surrogate Modeling Reduced-Order Modeling
Dept. of Mathematics, University of Houston, Houston, TX 77204
Recursive transformers for semiconductor thermo-mechanical reliability
Jul 28, 2026Kart-leong LimNeural Surrogate Modeling PDE Surrogate Modeling
Institute of Microelectronics (IME), Agency for Science, Technology and Research (A*STAR), Singapore
A Physics-Informed Neural Operator for Thermal Ranking of Low-Cost Wall Materials in Hot-Dry Climates
Jul 28, 2026Muhammad Akbar Khan, Fahim Raees, Ubaida FatimaPDE Surrogate Modeling Physics-Informed Neural Operators
Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan
Physics Transformer: Tailoring Transformer for General PDE Prediction
Jul 27, 2026Guoze Sun, Rui Zhang, Jiankai Tang +4Transformer PDE Surrogate Modeling
Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China · School of Mechanics and Engineering Science, Peking University, Beijing, China
No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study
Jul 26, 2026Georg Winkler, Martin StollNeural Surrogate Modeling PDE Surrogate Modeling
Department of Mathematics, Chemnitz University of Technology, 09111, Chemnitz, Germany
Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage
Jul 26, 2026Yifu Han, Louis J. DurlofskyNeural Surrogate Modeling Uncertainty Quantification
Department of Energy Science and Engineering, Stanford University, Stanford, CA, 94305, USA
Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows
Jul 24, 2026Harish Ramachandran, Björn Kimpel, Thomas Paula +3Neural Surrogate Modeling PDE Surrogate Modeling
Technical University of Munich
Cycle-Consistent and Uncertainty-Aware Neural Surrogates for Tokamak Edge Plasmas
Jul 23, 2026Abdourahmane Diaw, Sebastian De Pascuale, Jae-Sun Park +3Neural Surrogate Modeling PDE Surrogate Modeling
Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, TN 37932, USA · DIFFER - Dutch Institute for Fundamental Energy Research, De Zaale 20, 5612 AJ Eindhoven, the Netherlands
Image Editing Models are Numerical Solvers
Jul 21, 2026Ulysse MizrahiNeural PDE Solvers PDE Solving
Tel Aviv University
Spatio-Temporal Prediction of Unsteady Airfoil Aerodynamics Using Augmented Graph Neural Ordinary Differential Equations with Exogenous Controls
Jul 17, 2026Henrik Lange, Reik Thormann, Philipp BekemeyerGraph Neural Networks PDE Surrogate Modeling
German Aerospace Center (DLR), Lilienthalpl. 7, 38108 Brunswick, Germany · Airbus Operations, Airbus Allee 1, 28199 Bremen, Germany
Accounting for Hysteresis and Eddy Currents in Finite Element Simulations of Ferromagnetic Laminated Cores using a Recurrent Neural Network
Jul 15, 2026Florent Purnode, Louis Denis, François Henrotte +2Neural Surrogate Modeling PDE Surrogate Modeling
Department of Electrical Engineering and Computer Science, University of Liege, Belgium
Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems
Jul 14, 2026Marc Haltmayer, Jaemin Seo, Yuseung Lee +3PDE Solving PDE Surrogate Modeling
Department of Artificial Intelligence, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, 06974, Republic of Korea · Computational Science and Engineering Team, Samsung Electronics, 41 Samsung-ro, Giheung-gu, Yongin-si, 17113, Republic of Korea
A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous underground
Jul 14, 2026Moke Rao, Thomas Hamacher, Smajil HalilovicNeural Surrogate Modeling PDE Surrogate Modeling
Technical University of Munich, Chair of Renewable and Sustainable Energy Systems, Germany
A multi-scale feature enhanced graph neural network for fluid dynamics prediction in complex geometries
Jul 13, 2026Li Xiao, Tianyu Li, Yiye Zou +2Graph Neural Networks PDE Surrogate Modeling
Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance
Jul 13, 2026Zixuan Shen, Bingchuan Wang, Zhi Wang +1Neural PDE Solvers PDE Surrogate Modeling
Central South University · Central South University, Changsha, Hunan 410083, China · Nanjing University +1
Entropy-Constrained Machine Learning with Residual Data Augmentation for Modeling Chemical Kinetics
Jul 10, 2026Okezzi Ukorigho, Opeoluwa OwoyeleSurrogate Modeling PDE Surrogate Modeling
Department of Mechanical and Industrial Engineering Louisiana State University, Baton Rouge, LA 70810, USA
Learning Physics-Informed Surrogate Model of Linear Elastic Displacement Fields from Geometry
Jul 10, 2026Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz +1Structural Mechanics PDE Surrogate Modeling
PROMES-CNRS, Universit´e Perpignan Via Domitia (UPVD), Perpignan, France · LAAS-CNRS, Universit´e de Toulouse (UT), Toulouse, France
PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations
Jul 9, 2026Weiheng Zhong, Jing Bi, Victor Oancea +1PDE Surrogate Modeling PDE Operator Learning
Department of Civil and Environmental Engineering, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US · Dassault Systemes Americas, Johnston, RI, US · Siebel School of Computing and Data Science, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US
Physics-Audited Agentic Discovery in Scientific Machine Learning
Jul 8, 2026Diab W. Abueidda, Bilal Ahmed, Panos Pantidis +1Neural Surrogate Modeling PDE Surrogate Modeling
Civil and Urban Engineering Department, New York University Abu Dhabi, United Arab Emirates · National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, United States of America
A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systems
Jul 7, 2026Sonal Ankush Chibire, Jenn-Terng Gau, Bo ZhangStructural Mechanics PDE Surrogate Modeling
Department of Mechanical Engineering, Northern Illinois University, 1425 W Lincoln Hwy, DeKalb, 60115, IL, USA.
PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference
Jul 6, 2026Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas +1PDE Solving PDE Surrogate Modeling
Tata Research Development and Design Center, Pune, India 411057
Generative wave propagator
Jul 5, 2026Shijun Cheng, Tariq AlkhalifahPDE Surrogate Modeling One-Step Generative Modeling
Division of Physical Science and Engineering King Abdullah University of Science and Technology Thuwal 23955-6900, Saudi Arabia
CoFINN: Conservation Flux Informed Neural Networks for Physics Problems Governed by Conservation Laws
Jul 5, 2026Adnan Harun Doğan, Mert Deniz, Hande Alemdar +1PDE Surrogate Modeling Physics-Informed ML
Dept. of Computer Engineering Middle East Technical University Ankara, Turkey · Dept. of Mechanical Engineering Middle East Technical University Ankara, Turkey
LLT: Local Linear Transformer for PDE Operator Learning
Jul 4, 2026Oded Ovadia, Eli TurkelPDE Surrogate Modeling Transformer Attention
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
Fourier Neural Operators for Rayleigh-Bénard Convection
Jul 2, 2026Chelsea Maria John, Thibaut Lunet, Sebastian Götschel +3Fourier Neural Operator PDE Surrogate Modeling
Jülich Supercomputing Centre, Jülich, Germany · Hamburg University of Technology, Hamburg, Germany
A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction
Jul 1, 2026Xin-Yang Liu, Xiantao Fan, Jian-Xun WangNeural PDE Solvers PDE Surrogate Modeling
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA · Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA
TRIE: An Evaluation Framework for Stochastic PDE Surrogates
Jun 30, 2026Bharat Srikishan, Javier E. Santos, Nikhil Muralidhar +1PDE Surrogate Modeling Probabilistic Forecasting
Stevens Institute of Technology · Los Alamos National Laboratory
SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling
Jun 30, 2026Alaina Kolli, Theodoros Xenakis, Utkarsh Utkarsh +4Constrained Generative Modeling Physics-Informed Generative Modeling
Massachusetts Institute of Technology, Cambridge, MA, USA · Norwegian University of Science and Technology, Trondheim, Norway

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Feature Interaction Modeling for Neural Operators

Quan Gu, Xiaoduo Li, Hongxia Liu

Independent Researcher · Taiyuan University of Technology

Feature Interaction Modeling PDE Surrogate Modeling PDE Operator Learning Deep Operator Networks

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Despite the many variants of DeepONet that have been proposed, query-based operator networks still struggle with shock-dominated and low-viscosity PDEs, whose sharp moving discontinuities and slowly decaying solution spectra challenge finite-dimensional separable representations. In this work, we propose \emph{Feature Interaction Modeling Operator} (FM-Operator), a point-wise query neural operator that explicitly models feature construction and interactions between sensor observations and query coordinates. Our design is motivated by a reinterpretation of the canonical DeepONet aggregation through the lens of multiplicative interactions. Specifically, the branch--trunk inner product admits the equivalent form

\boldsymbol{b}(u)^\top \boldsymbolτ(y)=\boldsymbol{1}^\top \operatorname{diag}(\boldsymbol{b}(u))\,\boldsymbolτ(y)

, revealing that the two representations interact only along corresponding latent dimensions and therefore constitute a diagonally constrained multiplicative interaction. This observation suggests that, beyond improving the individual branch and trunk networks, the structure through which function and query representations interact is itself an important inductive bias in point-wise operator learning. FM-Operator accordingly redesigns both feature construction and feature interaction, enabling structured information exchange beyond the conventional branch--trunk coupling while retaining point-wise query evaluation. Experiments across multiple PDE benchmarks demonstrate that FM-Operator consistently outperforms vanilla DeepONet and achieves clear improvements over the strong Shift-DeepONet baseline. These results suggest that explicitly designing representation construction and interaction provides a promising direction for improving the effectiveness of DeepONet-style query-based neural operators.

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