arXiv AI
One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEs
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
Related stories
arXiv Machine Learning
Jun 16
ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
arXiv Machine Learning
Aug 14
Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv Machine Learning
Sep 22
Learning Physics from an Imperfect Ancestor
arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
arXiv Machine Learning
Aug 26
Physics-Integrated Operator Learning via Gaussian Splatting Representations
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
arXiv Machine Learning
Jun 24
Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training
arXiv:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.
arXiv Machine Learning
Sep 1
Learning PDE Time-Stepping with Neural Cellular Automata
arXiv:2608.30328v1 Announce Type: new Abstract: Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditio...