arXiv Machine Learning
Do Neural PDE Solvers Learn the Right Dynamics?
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
arXiv Machine Learning
Oct 16
Same Target, Different Origins: Aligning Latent Rollout for Consistent PDE Emulation
The paper introduces Align Latent Rollout (ALR), a regularization technique for neural PDE solvers that encourages consistency across different rollout origins. ALR uses a second‑order Taylor analysis to define two objectives: zeroth‑order consistency aligning latent states at a shared target time, and first‑order consistency aligning local evolution responses to perturbations. The method can be applied to various neural PDE solvers without altering their architectures and demonstrates improved prediction accuracy and reduced discrepancies across rollout origins in multiple benchmarks.
arXiv AI
Jun 10
Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
arXiv Machine Learning
Jun 3
Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
arXiv AI
Jun 26
Error-Conditioned Neural Solvers
arXiv:2606. 27354v1 Announce Type: cross 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.
arXiv Machine Learning
Jul 2
TRIE: An Evaluation Framework for Stochastic PDE Surrogates
arXiv:2607. 00196v1 Announce Type: new Abstract: Many scientific systems exhibit uncertainty from stochastic forcing, unresolved degrees of freedom, or imperfect observations, making reliable surrogate forecasting fundamentally distributional rather than pointwise.
arXiv AI
Jul 17
LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks
arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).