arXiv AI
Jun 3

Physics-informed diffusion models in spectral space

arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.

By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen
arXiv Machine Learning
Jun 4

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning

arXiv:2407. 00809v4 Announce Type: replace Abstract: This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from functions to functions).

By Matthew Lowery, John Turnage, Zachary Morrow, John D. Jakeman, Akil Narayan, Shandian Zhe, Varun Shankar