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.

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arXiv Machine Learning

Aug 19

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

Nonlinear GENERIC-Embedded Neural Networks (N-GENNs) are a deep learning framework designed to discover evolution equations for systems governed by the nonlinear GENERIC formalism. The method incorporates generalized gradient flows through convex dissipation potentials, allowing it to capture a wider range of thermodynamically consistent dynamics, including those with non‑quadratic dissipation potentials. Thermodynamic structure is enforced by construction, ensuring compliance with the first and second laws, and the approach is validated on a harmonic oscillator with a heat bath, an idealized chemical motor, and a one‑dimensional viscoplastic Perzyna model.

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

arXiv Machine Learning

Aug 14

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

Sep 22

Learning Physics from an Imperfect Ancestor

arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...

By S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas, Somdatta Goswami

efficiency

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

One email a morning, machine-written

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