Neural Galerkin
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Related Articles from SNS
Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundaries
Announce Type: new Abstract: One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function. Extending previous studies that solve Fokker-Planck (FP) type partial differential equations with Normalizing Flows, we propose a new Normalizing Flow architecture to learn...
When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning
arXiv:2605.19867v2 Announce Type: replace Abstract: Neural operators are increasingly used as accelerators inside classical numerical methods, but it is rarely clear which architectural ingredients matter for which application. We answer this question for one important use case: the coarse-space correction inside a two-level preconditioner for discretised linear partial differential equations.
Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer
arXiv:2408.11266v5 Announce Type: replace Abstract: Deep learning is now common across many scientific fields, including the study of partial differential equations. This article provides a brief, accessible introduction to core deep learning concepts, including neural networks, backpropagation, and the universal approximation theorem. It mainly covers how to use deep learning in solving differential equations.