PDE Discovery

PDE: Partial Differential Equation

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Overview

Partial differential equation discovery studies how to infer the operators and coefficients governing spatially and temporally changing fields, helping explain physical systems and predict their behavior. Common approaches include sparse regression such as SINDy over candidate term libraries, weak-form methods that reduce noise from numerical differentiation, and symbolic or neural-symbolic methods that search for equations; newer systems also use language-model agents to propose and test hypotheses. Researchers test these methods on canonical PDE benchmarks and experimental or observational data, including sparse, noisy, multiscale, nonlocal, and geometry-varying settings. A central challenge is distinguishing a genuinely identifiable, physically meaningful law from a model that merely fits the available data, so evaluation increasingly considers stability, uncertainty, physical consistency, and performance on new conditions as well as predictive error.

Latest papers

CardsList

36 papers6 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

  1. Weak-PDE-Net: Discovering Open-Form PDEs via Differentiable Symbolic Networks and Weak Formulation

    Mar 24, 2026Xinxin Li, Xingyu Cui, Jin Qi +3PDE DiscoverySymbolic Regression

    School of Mathematical Sciences, East China Normal University, Shang Hai, 200241, China · Institute of Applied Physics and Computational Mathematics, 100094, Beijing, China · Shanghai Zhangjiang Institute of Mathematics, 201203, Shanghai, China +2

  2. Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Data

    Mar 23, 2026Xingyu Chen, Junxiu An, Jun Guo +1PDE DiscoveryGraph Neural Networks

    School of Software Engineering, Chengdu University of Information Technology, Chengdu, 610225, China · School of Statistics, Chengdu University of Information Technology, Chengdu, 610103, China · College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, 610225, China +1

  3. pADAM: A Plug-and-Play All-in-One Diffusion Architecture for Multi-Physics Learning

    Mar 17, 2026Amirhossein Mollaali, Bongseok Kim, Christian Moya +1Physics-Informed Generative ModelingPDE Surrogate Modeling

    School of Mechanical Engineering, Purdue University, West Lafayette, 47906, IN, USA. · Department of Mathematics, Purdue University, West Lafayette, 47906, IN, USA.

  4. Symbolic recovery of PDEs from measurement data

    Feb 17, 2026Erion Morina, Philipp Scholl, Martin HollerPDE DiscoveryPDE Inverse Problems

    IDea Lab - The Interdisciplinary Digital Lab at the University of Graz, Austria. · Aleph Alpha Research, Germany.

  5. Counterfactual Operator Relevance for PDE Discovery: Screening, Pruning, and Identifiability

    Jun 25, 2025Ronald KatendeCounterfactual EvaluationPDE Discovery

    Department of Mathematics Kabale University Kikungiri Hill, Katuna Road, 317, Kabale, Uganda

  6. A Neural Operator-Based Approach to Symbolic Discovery of PDEs

    Jan 14, 2025Sergei Garmaev, Olga FinkPDE DiscoverySymbolic Regression

    Intelligent Maintenance and Operations Systems Laboratory, EPFL, Lausanne, Switzerland