Neural PDE Solvers

PDE: Partial Differential Equation

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23 papers in the last four weeks, up 109% on the four weeks before. 0.2% of all new papers.

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Latest papers 166

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Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow
May 9, 2026Hanru Bai, Yuncheng Zhou, Difan ZouFlow Matching Neural PDE Solvers
1Fudan University · 2The University of Hong Kong.
Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency
May 8, 2026Yuxiang Luo, Andrew PerraultNeural PDE Solvers System Identification
Department of Computer Science and Engineering The Ohio State University
AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training
May 8, 2026Binghang Lu, Runyu Zhang, Changhong Mou +2Neural PDE Solvers Constrained Optimization
Purdue University · Massachusetts Institute of Technology · Utah State University +1
When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains
May 8, 2026Brandon Yee, Pairie Koh, Jack Rodriguez +1Neural PDE Solvers PDE Solving
Physics Lab, Yee Collins Research Group
Sparse Random-Feature Neural Networks with Krylov-Based SVD for Singularly Perturbed ODE
May 8, 2026Kevin Kurian Thomas Vaidyan, Siddharth RoutNeural PDE Solvers Singular Value Decomposition
Institute of Applied Mathematics University of British Columbia Vancouver, BC V6T 1Z4
Learned Lagrangian Models of PDEs via Euler-Lagrange Residual Minimization
May 8, 2026Lyra Zhornyak, Eric Forgoston, M. Ani HsiehNeural PDE Solvers PDE Surrogate Modeling
University of Pennsylvania · Montclair State University
INEUS: Iterative Neural Solver for High-Dimensional PIDEs
May 7, 2026Jean-Loup Dupret, Davide Gallon, Patrick CheriditoNeural PDE Solvers PDE Solving
Department of Mathematics and RiskLab, ETH Zurich, Switzerland · Applied Mathematics: Institute for Analysis and Numerics, University of Münster, Germany
Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations
May 6, 2026Zhangyong Liang, Huanhuan GaoNeural PDE Solvers PDE Solving
National Center for Applied Mathematics Tianjin University Tianjin, 300072, China · School of Mechanical and Aerospace Engineering, Jilin University Jilin University Changchun, 130025, China
Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
May 5, 2026Diego MarcondesNeural PDE Solvers PDE Solving
Posterior-First Neural PDE Simulation: Inferring Hidden Problem State from a Single Field
May 5, 2026Wenshuo Wang, Fan ZhangNeural PDE Solvers PDE Surrogate Modeling
School of Future Technology, South China University of Technology, China · State Key Laboratory of Ocean Sensing & Ocean College, Zhejiang University, China · Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, USA
Isotropic Fourier Neural Operators
May 4, 2026Michael F. StaddonFourier Neural Operator Neural PDE Solvers
Independent Researcher
Mesh Based Simulations with Spatial and Temporal awareness
May 2, 2026Paul Garnier, Vincent Lannelongue, Elie HachemGraph Neural Networks Neural PDE Solvers
1CEMEF - Mines Paris PSL
PILIR: Physics-Informed Local Implicit Representation
May 1, 2026Jianfeng Li, Feng Wang, Ke TangNeural PDE Solvers Implicit Neural Representations
School of Computer Science, Wuhan University · School of Computer Science and Technology, Southern University of Science and Technology
A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions
Apr 30, 2026Matteo Raviola, Benjamin PeherstorferNeural PDE Solvers PDE Solving
EPFL, Lausanne, Switzerland · Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networks
Apr 29, 2026Beomchul Park, Minsu Koh, Heejo Kong +1Neural PDE Solvers Meta-Learning
Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Republic of Korea · Department of Brain and Cognitive Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Republic of Korea
Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Regimes
Apr 27, 2026Zhangyong LiangNeural PDE Solvers Gradient Interference
National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China.
Shared-kernel Wavelet Neural Networks for Poisson Image Reconstruction
Apr 27, 2026Yuanhao Gong, Tan Tang, Qianyan LiuNeural PDE Solvers Image Reconstruction
Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework
Apr 27, 2026You Yang, Fei WangNeural PDE Solvers PDE Operator Learning
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China. · School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China.
Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen
Apr 24, 2026Leszek Siwik, Maciej Sikora, Natalia Leszczyńska +7Neural PDE Solvers Air Quality Prediction
AGH University of Krakow, Faculty of Computer Science, Al. Mickiewicza 30, Kraków, 30-059, Poland · Medical University of Silesia-Katowice, Faculty of Medical Sciences, ul. Poniatowskiego 15, Katowice, 40-055, Poland · The University Centre in Svalbard, Longyearbyen, Box 156 N-9171, Longyearbyen, Norway +4
A Green-Integral-Constrained Neural Solver with Stochastic Physics-Informed Regularization
Apr 23, 2026Mohammad Mahdi Abedi, David Pardo, Tariq AlkhalifahNeural PDE Solvers PDE Solving
University of the Basque Country (UPV/EHU), Department of Mathematics, Spain · Basque Center for Applied Mathematics (BCAM), Bilbao, Spain · Ikerbasque, Basque Foundation for Science, Bilbao, Spain +1
CO $_2$ sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)
Apr 22, 2026Askold Vilkha, Tomasz Służalec, Marcin Łoś +1Neural PDE Solvers PDE Solving
AGH University of Krakow, Faculty of Computer Science, Al. Mickiewicza 2026 30, Kraków, 30-059, Poland
Virtual boundary integral neural network for three-dimensional exterior acoustic problems
Apr 19, 2026Jiahao Li, Qiang Xi, Ilia Marchevskiy +1Neural PDE Solvers PDE Solving
College of Mechanics and Engineering Science, Hohai University, Nanjing 211100, China · Department of Applied Mathematics, Bauman Moscow State Technical University, Moscow 105005, Russia
FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation
Apr 18, 2026Yilong Dai, Yiming Sun, Yiheng Chen +3Flow Matching Neural PDE Solvers
University of Alabama · University of Pittsburgh
PINNACLE: An Open-Source Computational Framework for Classical and Quantum PINNs
Apr 17, 2026Shimon Pisnoy, Hemanth Chandravamsi, Ziv Chen +4Neural PDE Solvers PDE Surrogate Modeling
†Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa, Israel. · ‡Corresponding author. · §The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering, Technion Israel Institute of Technology, Haifa, Israel. +2
A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws
Apr 17, 2026Jiamin Jiang, Shanglin Lv, Jingrun ChenGraph Neural Networks Neural PDE Solvers
School of Artificial Intelligence and Data Science and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China · School of Mathematical Sciences, University of Science and Technology of China, China · School of Mathematical Sciences and Suzhou Institute for Advanced Research, University of Science and Technology of China, and Suzhou Big Data & AI Research and Engineering Center, China
G-PARC: Graph-Physics Aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics on Unstructured Meshes
Apr 16, 2026Jack T. Beerman, Tyler J. Abele, Mehdi Taghizadeh +6Neural PDE Solvers PDE Surrogate Modeling
School of Data Science, University of Virginia, Charlottesville, VA 22903, United States · Department of Engineering Systems and Environment, University of Virginia, Charlottesville, VA 22903, United States · Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22903, United States +1
Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains
Apr 10, 2026Zhangyong Liang, Huanhuan GaoNeural PDE Solvers PDE Solving
National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China. · School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China.
Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation
Apr 9, 2026Andrew Qing He, Wei Cai, Sihong ShaoNeural PDE Solvers
*Department of Mathematics, Southern Methodist University, Dallas, TX, USA. · †School of Mathematical Sciences, Peking University, Beijing, China.
Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNs
Mar 31, 2026Zhangyong Liang, Huanhuan GaoNeural PDE Solvers Physics-Informed ML
National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China · School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China
Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach
Mar 23, 2026Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos +1Dynamical Systems Neural PDE Solvers
Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, 21218, MD, USA · Dept. of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, 21218, MD, USA · School of Chemical Engineering, National Technical University of Athens, 9 Iroon Polytechniou Street, Athens, 15772, Greece +2

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Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow

Hanru Bai, Yuncheng Zhou, Difan Zou

1Fudan University · 2The University of Hong Kong.

Flow Matching Neural PDE Solvers PDE Solving MeanFlow PDE Surrogate Modeling Physics-Informed ML

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Deep learning paradigms, such as PINNs and neural operators, have significantly advanced the solving of PDEs. However, they often struggle to capture the continuous integral nature of physical systems, relying either on pointwise residuals that ignore the integral perspective or on pre-discretized temporal grids. Drawing inspiration from MeanFlow, a continuous-time integrator recently developed to efficiently solve generative ODEs, we introduce Spatio-Temporal MeanFlow, which functions as a novel PDE solver learning the finite-interval evolution of physical states. By substituting the generative velocity field with the physical PDE operator, we transform multi-step numerical integration into an efficient prediction with a freely controllable integration length. Crucially, we extend the original MeanFlow constraint from the temporal to the spatio-temporal domain, coupling time evolution with spatial consistency. This yields a unified framework naturally accommodating both time-dependent and stationary PDEs. Comprehensive experiments on benchmarks demonstrate that our approach achieves superior accuracy and inference efficiency over representative baselines. Furthermore, the proposed integral constraint enables excellent generalization to out-of-distribution initial conditions and varying spatial resolutions.

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Latest papers 166