Stochastic PDEs

PDE: Partial Differential Equation

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11 papers1 paper in the last four weeks, with none the four weeks before. 0.0% of all new papers.

S $^{2}$ -PINN: Stochastic Separable Physics-Informed Neural Networks
Oct 2, 2026Zhendong Li, Akwum OnwuntaStochastic PDEs Neural PDE Solvers
Industrial and Systems Engineering Dept. Lehigh University Bethlehem, PA 18015, 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
Dynamic Gaussian Processes and the Vanilla-SPDE Exchange
Jun 30, 2026Rui-Yang Zhang, Lachlan Astfalck, Edward Cripps +2Efficient Inference Gaussian Processes
School of Mathematical Sciences, Lancaster University. · School of Mathematics and Statistics, The University of New South Wales. · School of Physics, Mathematics and Computing, the University of Western Australia.
Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations
May 16, 2026Phuoc-Toan Huynh, Richard Archibald, Feng BaoUncertainty Quantification Stochastic PDEs
Department of Mathematics, Florida State University, Tallahassee, FL, USA · Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization
May 15, 2026Kai HidajatUncertainty Quantification Stochastic PDEs
Department of Applied Mathematics University of Washington Seattle, WA, USA
Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models
Apr 29, 2026Andrea Agazzi, Giuseppe Bruno, Eloy Mosig García +2Dynamical Systems Transformer
Department of Mathematics and Statistics, University of Bern (CH) · Department of Mathematics, University of Pisa (IT)
Learning noisy phase transition dynamics from stochastic partial differential equations
Mar 31, 2026Luning Sun, Van Hai Nguyen, Shusen Liu +2Stochastic PDEs PDE Surrogate Modeling
Lawrence Livermore National Laboratory, Livermore, CA, 94550,USA · The University of Texas at Austin, Austin, TX, 78712, USA
SPDE Methods for Nonparametric Bayesian Posterior Contraction and Laplace Approximation
Mar 23, 2026Enric Alberola-Boloix, Ioar Casado-TelletxeaPosterior Contraction Stochastic PDEs
Basque Center for Applied Mathematics (BCAM), Bilbao (Spain)
Symbolic Discovery of Stochastic Differential Equations with Genetic Programming
Mar 10, 2026Sigur de Vries, Sander W. Keemink, Marcel A. J. van GervenStochastic PDEs Stochastic Differential Equations
Department of Machine Learning and Neural Computing, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, the Netherlands
Wiener Chaos Expansion based Neural Operator for Singular Stochastic Partial Differential Equations
Mar 9, 2026Dai Shi, Luke Thompson, Andi Han +3Stochastic PDEs PDE Surrogate Modeling
University of Cambridge · University of Sydney · Chinese Academy of Science
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

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S $^{2}$ -PINN: Stochastic Separable Physics-Informed Neural Networks

Zhendong Li, Akwum Onwunta

Industrial and Systems Engineering Dept. Lehigh University Bethlehem, PA 18015, USA

Stochastic PDEs Neural PDE Solvers Uncertainty Quantification Physics-Informed ML

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Uncertainty quantification (UQ) for random partial differential equations (PDEs) is ubiquitous in computational science and engineering. However, classical spectral solvers for this class of problems face the curse of dimensionality, and existing neural solvers often ignore the stochastic structure that makes moments and calibration tractable. We introduce a stochastic separable physics-informed neural network, dubbed S

^{2}

-PINN, that represents the solution

u(t,\mathbf{x},\mathbf{Z})

of a random PDE with a learnable Gaussian spatial dictionary, Fourier temporal features, and a generalized polynomial chaos (gPC) stochastic basis, coupled by a low-rank Canonical Polyadic (CP) tensor decomposition core. The method is trained with a hybrid strong-form and gPC-projected residual loss. Our theoretical analysis establishes that the separable class is dense in

L^2

under mild conditions, and the projected residual corresponds exactly to a stochastic Galerkin constraint. Furthermore, we show that mini-batch projection coefficients are logarithmically dependent on the number of gPC modes, and that the orthogonality penalty controls the conditioning of the learned spatial dictionary. Using four manufactured random PDE benchmarks, we show that S

^{2}

-PINN outperforms nine baselines in terms of mean and variance accuracy, as well as calibration, while using significantly fewer parameters. Further evaluations on non-manufactured Poisson and Darcy problems, a stochastic Navier--Stokes problem, a diffusion scaling study of higher random dimensions, and two stochastic inverse problems reveal the generalization capabilities of the proposed structure. Together, these results support stochastic separability as an effective design principle for physics-informed neural UQ. The code for the experiments can be found in https://github.com/DMax1314/s2pinn