Hugging Face Trending Papers July 7, 2026

Physics-Informed Neural Embeddings of PDE Solution Families

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We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads reconstruct individual solutions associated with different initial conditions.

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arXiv Machine Learning

Jul 8

Physics-Informed Neural Embeddings of PDE Solution Families

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By Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas, Leonid Sarieddine, David N. Spergel, Pedro Taranc\'on-\'Alvarez

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arXiv AI

Jul 16

Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs

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

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arXiv Machine Learning

Jun 5

Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks

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

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arXiv Machine Learning

Jul 27

Latent PDE mapping for efficient physics-informed learning across geometries with limited data

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

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arXiv AI

Jun 3

Physics-informed diffusion models in spectral space

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By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen

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arXiv Machine Learning

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Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).

By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi

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