Cover Image

Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Pförtner, Marvin, Steinwart, Ingo, Hennig, Philipp, Wenger, Jonathan
Format:	Preprint
Published:	2022
Subjects:	Machine Learning Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Flexible and Efficient Probabilistic PDE Solvers through Gaussian Markov Random Fields
by: Weiland, Tim, et al.
Published: (2025)

Computation-Aware Kalman Filtering and Smoothing
by: Pförtner, Marvin, et al.
Published: (2024)

Scaling up Probabilistic PDE Simulators with Structured Volumetric Information
by: Weiland, Tim, et al.
Published: (2024)

Affine Tracing: A New Paradigm for Probabilistic Linear Solvers
by: Hegde, Disha, et al.
Published: (2026)

Parallel-in-Time Probabilistic Numerical ODE Solvers
by: Bosch, Nathanael, et al.
Published: (2023)

Gaussian Processes and Reproducing Kernels: Connections and Equivalences
by: Kanagawa, Motonobu, et al.
Published: (2025)

Mode-Shape Expansion Using Physics-Constrained Gaussian Process Regression
by: Ghahari, Farid
Published: (2026)

Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers
by: Zhang, Enrui, et al.
Published: (2022)

Learning Neural PDE Solvers with Convergence Guarantees
by: Hsieh, Jun-Ting, et al.
Published: (2019)

Scalable Bayesian Inference for Nonlinear Conservation Laws
by: Weiland, Tim, et al.
Published: (2026)

Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers
by: Zhou, Hang, et al.
Published: (2024)

CodePDE: An Inference Framework for LLM-driven PDE Solver Generation
by: Li, Shanda, et al.
Published: (2025)

Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers
by: Chen, Chuqi, et al.
Published: (2024)

PDE Solvers Should Be Local: Fast, Stable Rollouts with Learned Local Stencils
by: Cheng, Chun-Wun, et al.
Published: (2025)

Linearization Turns Neural Operators into Function-Valued Gaussian Processes
by: Magnani, Emilia, et al.
Published: (2024)

Neural Parameter Regression for Explicit Representations of PDE Solution Operators
by: Mundinger, Konrad, et al.
Published: (2024)

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter
by: Wu, Yuhan, et al.
Published: (2026)

Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation
by: Zhang, Rui, et al.
Published: (2023)

Better Neural PDE Solvers Through Data-Free Mesh Movers
by: Hu, Peiyan, et al.
Published: (2023)

Sketching Low-Rank Plus Diagonal Matrices
by: Fernandez, Andres, et al.
Published: (2025)

DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training
by: Hao, Zhongkai, et al.
Published: (2024)

Bayesian Physics Informed Neural Networks for Linear Inverse problems
by: Mohammad-Djafari, Ali
Published: (2025)

Gaussian Process Regression under Computational and Epistemic Misspecification
by: Sanz-Alonso, Daniel, et al.
Published: (2023)

Deep Learning-Enhanced Preconditioning for Efficient Conjugate Gradient Solvers in Large-Scale PDE Systems
by: Li, Rui, et al.
Published: (2024)

End-to-End Mesh Optimization of a Hybrid Deep Learning Black-Box PDE Solver
by: Ma, Shaocong, et al.
Published: (2024)

Parameter Inference based on Gaussian Processes Informed by Nonlinear Partial Differential Equations
by: Li, Zhaohui, et al.
Published: (2022)

Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space
by: Yue, Xihang, et al.
Published: (2024)

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation
by: Zhang, Yi, et al.
Published: (2025)

Transolver: A Fast Transformer Solver for PDEs on General Geometries
by: Wu, Haixu, et al.
Published: (2024)

Error Analysis and Numerical Algorithm for PDE Approximation with Hidden-Layer Concatenated Physics Informed Neural Networks
by: Qian, Yianxia, et al.
Published: (2024)

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models
by: Yang, Jianan, et al.
Published: (2026)

Learning from Linear Algebra: A Graph Neural Network Approach to Preconditioner Design for Conjugate Gradient Solvers
by: Trifonov, Vladislav, et al.
Published: (2024)

Sample Path Regularity of Gaussian Processes from the Covariance Kernel
by: Da Costa, Nathaël, et al.
Published: (2023)

Constructing Gaussian Processes via Samplets
by: Neugebauer, Marcel
Published: (2024)

Bayesian Quadrature: Gaussian Processes for Integration
by: Mahsereci, Maren, et al.
Published: (2026)

Calibrated Computation-Aware Gaussian Processes
by: Hegde, Disha, et al.
Published: (2024)

Solving All Regression Models For Learning Gaussian Networks Using Givens Rotations
by: Alipourfard, Borzou, et al.
Published: (2019)

DeltaPhi: Physical States Residual Learning for Neural Operators in Data-Limited PDE Solving
by: Yue, Xihang, et al.
Published: (2024)

LieSolver: A PDE-constrained solver for IBVPs using Lie symmetries
by: Klausen, René P., et al.
Published: (2025)

Preconditioned Additive Gaussian Processes with Fourier Acceleration
by: Wagner, Theresa, et al.
Published: (2025)