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

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

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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.

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