Paper: Error-Conditioned Neural Solvers for PDEs (arXiv 2606.27354)

Forum topic · 小凯 · 2026-06-27

Summary

A forum post on zhichai.net introduces the paper 'Error-Conditioned Neural Solvers' by Haina Jiang, Liam Wang, and Peng-Chen Chen, published on arXiv (2606.27354) on 2026-06-27 in the computer vision field. The paper addresses a key limitation of neural surrogate models for PDEs: while they provide fast approximate mappings from PDE parameters to solutions, they treat solving as a purely statistical task and struggle to correct constraint violations or extrapolate beyond the training distribution. Existing hybrid methods enforce physical correctness by minimizing PDE residuals via gradient descent or Gauss-Newton steps, but inherit the compute cost and instability of classical optimizers. The proposed error-conditioned neural solvers combine theoretical analysis and experiments showing how neural solvers can be made capable of detecting and correcting their own errors.

Error-Conditioned Neural Solvers

Paper Overview

Field: CV
Authors: Haina Jiang, Liam Wang, Peng-Chen Chen
Published: 2026-06-27
arXiv: 2606.27354

Abstract

Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution. Recent hybrid methods promote physical correctness by targeting the PDE residual via gradient descent or Gauss--Newton steps, but inherit the compute cost and instability of the underlying classical optimizers. We show, theore...

Summary (translated from the Chinese abstract)

Neural surrogate models usually treat solving as a purely statistical task, making it hard to correct constraint violations and to extrapolate outside the training distribution. The authors propose error-conditioned neural solvers and, through theoretical analysis and experiments, demonstrate how neural solvers can be enabled to detect and correct their own errors.

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*Auto-collected on 2026-06-27.*

Original arXiv page: https://arxiv.org/abs/2606.27354