arXiv:2607. 06348v1 Announce Type: new Abstract: We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations.
By Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas, Leonid Sarieddine, David N. Spergel, Pedro Taranc\'on-\'Alvarez
Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and dimensions. Inspired by the GNN transferability l...
arXiv:2609.38916v1 Announce Type: new
Abstract: Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and...
By Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith, Soledad Villar
arXiv:2607. 13566v1 Announce Type: cross Abstract: For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy.
By Tianchi Yu, Ivan Oseledets
arXiv:2606. 06171v1 Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions.
By Cornelius Otchere, Michael Shields
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban