arXiv paper studies conformal prediction for time-dependent PDEs
Conformal prediction guarantees break down in time-dependent PDE settings, requiring discretization restrictions for coverage.
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Stories tagged #pde
HotPOT pairs PDE-specific numerical experts in one operator transformer
Across 24 matched comparisons, HotPOT cuts rollout error 50.7% on average versus MoE-POT, including a 17M model.
PaPi parallel integrator speeds neuro-spectral PDE learning
Experiments report up to two orders of magnitude faster training and inference, with some low-dimensional PDE runs under one second.
PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEs
PDE-JEPA uses masked-latent predictive pretraining with geometry alignment for parametric PDE dynamics, beating SOTA by 33.4% in-distribution and 51.4% extrapolating.
NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures
NEXT stabilizes physics-informed neuro-spectral models on stiff PDEs by integrating the linear part exactly.
Fast Learning Rates for Physics-Informed Kernel Methods
Theoretical analysis proves finite-sample learning rates for physics-informed kernel estimators, showing differential observations can improve rates from n^-1/4 to n^-1/2.
Local gradient neural operator
Researchers propose LGNO, a lightweight interpretable neural operator using learnable local stencils, matching global-operator accuracy on PDE benchmarks with fewer parameters.