Neural PDE Solvers

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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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An Adaptive Machine Learning Framework for Fluid Flow in Dual-Network Porous Media
Mar 20, 2026V. S. Maduri, K. B. NakshatralaNeural PDE Solvers Physics-Informed ML
Department of Civil & Environmental Engineering University of Houston, Houston, Texas 77204, USA.
Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees
Mar 19, 2026Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1Neural Network Generalization Neural PDE Solvers
Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada
Neural Galerkin Normalizing Flow for Transition Probability Density Functions of Diffusion Models
Mar 19, 2026Riccardo Saporiti, Fabio NobileNormalizing Flows Neural PDE Solvers
CSQI, École Polytechnique Féderale de Lausanne, Switzerland
MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries
Mar 9, 2026Weizheng Zhang, Xunjie Xie, Hao Pan +4Neural PDE Solvers PDE Solving
Shandong University, Qingdao, China · Tsinghua University, Beijing, China · Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, China
Jacobian-Adaptive Weighting for Stability: Enhancing Long-term Rollout of Neural Partial Differential Equation Solvers via Spatially-Adaptive Regularization
Mar 4, 2026Fengxiang Nie, Yasuhiro SuzukiNeural PDE Solvers Algorithmic Stability
University of Hiroshima
Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries
Feb 4, 2026Hang Zhou, Haixu Wu, Haonan Shangguan +4Efficient Neural Network Inference Neural PDE Solvers
School of Software, BNRist, Tsinghua University, China.
Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning
Jan 1, 2026Abhisek Ganguly, Santosh Ansumali, Sauro SucciDynamical Systems Neural PDE Solvers
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore, 560064, Karnataka, India · Italian Institute of Technology, Viale Regina Elena 291, 00161 Rome, Italy · University of Roma Tre, Italy +2
PGOT: A Physics-Geometry Operator Transformer for Complex PDEs
Dec 29, 2025Zhuo Zhang, Xi Yang, Ying Miao +5Neural PDE Solvers PDE Surrogate Modeling
National University of Defense Technology · Peking University · National University of Singapore +2
Adaptive Probability Flow Residual Minimization for High-Dimensional Fokker-Planck Equations
Dec 22, 2025Xiaolong Wu, Qifeng LiaoNeural PDE Solvers PDE Solving
School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation
Nov 19, 2025Victorita Dolean, Daria Hrebenshchykova, Stéphane Lanteri +1Neural PDE Solvers PDE Solving
Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands · Atlantis project-team, Inria Research Center at Université Côte d’Azur, France · MACARON project-team, Université de Strasbourg, CNRS, Inria, IRMA, France
LieSolver: PDE-Constrained Learning for IBVPs via Lie Symmetries
Oct 29, 2025René P. Klausen, Ivan Timofeev, Jonas Naujoks +4Neural PDE Solvers PDE Solving
Department of Artificial Intelligence, Fraunhofer Heinrich Hertz Institute, Berlin, Germany · Department of Electrical Engineering and Computer Science, Technische Universität Berlin, Germany · BIFOLD Berlin Institute for the Foundations of Learning and Data, Berlin, Germany +1
Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation
Aug 29, 2025Bangti Jin, Longjun WuNeural PDE Solvers PDE Solving
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China
Accelerating Natural Gradient Descent for PINNs with Randomized Numerical Linear Algebra
May 16, 2025Ivan Bioli, Carlo Marcati, Giancarlo SangalliNeural PDE Solvers Gradient Descent
Department of Mathematics, University of Pavia, Via A. Ferrata 5, 27100 Pavia, Italy · Department of Civil Engineering and Architecture, University of Pavia, Via A. Ferrata 3, 27100 Pavia, Italy · Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes”, CNR, Via A. Ferrata 1, 27100 Pavia, Italy
DeepSPoC: A Deep Learning Based Sequential Propagation of Chaos
Aug 29, 2024Kai Du, Yongle Xie, Tao Zhou +1Stochastic Differential Equations Neural PDE Solvers
Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200438, China. · Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China. · LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing, China.
Deep learning based numerical approximation algorithms for stochastic partial differential equations
Dec 2, 2020Christian Beck, Sebastian Becker, Patrick Cheridito +2Stochastic Differential Equations Neural PDE Solvers
Department of Mathematics, ETH Zurich · School of Data Science and School of Artificial Intelligence,2025 The Chinese University of Hong Kong, Shenzhen (CUHK-Shenhen) · Applied Mathematics: Institute for Analysis and Numerics, University of Münster +1
Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equations
Date pendingMinseok Kim, Yeongjong Kim, Namkyeong Cho +1Neural PDE Solvers Stochastic Optimal Control
Department of Applied Artificial Intelligence, Seoul National University of Science and Technology, Seoul, Republic of Korea. · Department of Mathematics, Pohang University of Science and Technology, Pohang, Republic of Korea. · Department of Mathematical Finance and Big Data, Gachon University, Seongnam, Republic of Korea +1

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An Adaptive Machine Learning Framework for Fluid Flow in Dual-Network Porous Media

V. S. Maduri, K. B. Nakshatrala

Department of Civil & Environmental Engineering University of Houston, Houston, Texas 77204, USA.

Neural PDE Solvers Physics-Informed ML PDE Inverse Problems Computational Fluid Dynamics

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Porous materials -- natural or engineered -- often exhibit dual pore-network structures that govern processes such as mineral exploration and hydrocarbon recovery from tight shales. Double porosity/permeability (DPP) mathematical models describe incompressible fluid flow through two interacting pore networks with inter-network mass exchange. Despite significant advances in numerical methods, there remains a need for computational frameworks that enable rapid forecasting, data assimilation, and reliable inverse analysis. To address this, we present a physics-informed neural network (PINN) framework for forward and inverse modeling of DPP systems. The proposed approach encodes the governing equations in mixed form, along with boundary conditions, directly into the loss function, with adaptive weighting strategies to balance their contributions. Key features of the framework include adaptive weight tuning, dynamic collocation point selection, and the use of shared trunk neural architectures to efficiently capture the coupled behavior of the dual pore networks. It is inherently mesh-free, making it well-suited for complex geometries typical of porous media. It accurately captures discontinuities in solution fields across layered domains without introducing spurious oscillations commonly observed in classical finite element formulations. Importantly, the framework is well-suited for inverse analysis, enabling robust parameter identification in scenarios where key physical quantities -- such as the mass transfer coefficient in DPP models -- are difficult to measure directly. In addition, a systematic convergence analysis is provided to rigorously assess the stability, accuracy, and reliability of the method. The effectiveness and computational advantages of the approach are demonstrated through a series of representative numerical experiments.

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