arXiv Machine Learning June 9, 2026 By Jason Sulskis, Sathya Ravi

GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators

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arXiv:2606. 08343v1 Announce Type: new Abstract: We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

arXiv Machine Learning

22h ago

Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentials

arXiv:2605. 09058v2 Announce Type: replace-cross Abstract: We introduce Nonlinear GENERIC-Embedded Neural Networks (N-GENNs), a deep learning framework for discovering evolution equations of systems governed by the nonlinear GENERIC formalism (General Equation for Non-Equilibrium Reversible-Irreversible Coupling).

By Vojt\v{e}ch Votruba, Zequn He, Weilun Qiu, Celia Reina, Michal Pavelka

arXiv Machine Learning

5d ago

Structure-preserving uncertainty quantification for GENERIC dynamics

arXiv:2608. 12624v1 Announce Type: new Abstract: Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs.

By Zequn He, Celia Reina

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

fine-tuning

arXiv Machine Learning

Jul 22

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics

arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.

By Xizhe Wang, Xiaobin Song, Hongbo Zhao, Qingshan Jia, Qianchuan Zhao, Hao Sun, Benben Jiang

rag benchmarks

arXiv Machine Learning

Aug 5

Symplectic Neural Networks for Learning Non-Separable Hamiltonians

arXiv:2606. 27029v2 Announce Type: replace Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.

By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas

arXiv Machine Learning

Jun 26

Symplectic Neural Networks for learning Generalized Hamiltonians

arXiv:2606. 27029v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.

By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas

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Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentials

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