aiqbench analysis
This research introduces N-GENNs, a deep learning framework specifically designed to discover evolution equations for systems governed by the nonlinear GENERIC formalism. By enforcing thermodynamic structure through reparameterization of reversible and dissipative operators, the method accurately infers models that comply with both laws of thermodynamics while handling non-quadratic dissipation potentials. The approach validates its efficacy on complex physical examples ranging from coupled oscillators to viscoplastic materials, bridging data-driven discovery with rigorous physics-based constraints.
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). Such systems exhibit coupled conservative and dissipative dynamics, and can be described via the superposition of a Hamiltonian flow and a generalized gradient flow. In contrast to existing approaches, our formulation incorporates generalized gradient flows via convex dissipation potentials, enabling the identification of a broader class of thermodynamically consistent dynamics, including systems with non-quadratic dissipation potentials. Thermodynamic structure is strongly enforced by construction through suitable reparameterizations of both the reversible operator and the dissipation potential, ensuring exact compliance with the first and second laws of thermodynamics. We validate the proposed approach on three representative examples: a harmonic oscillator coupled to a heat bath, an idealized chemical motor, and a one-dimensional viscoplastic model of Perzyna type. These results demonstrate the method's ability to accurately infer thermodynamically consistent models from data for systems incorporating both conservative and nonlinear dissipative dynamics.
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). Such systems exhibit coupled conservative and dissipative dynamics, and can be described via the superposition of a Hamiltonian flow and a generalized gradient flow. In contrast to existing approaches, our formulation incorporates generalized gradient flows via convex dissipation potentials, enabling the identification of a broader class of thermodynamically consistent dynamics, including systems with non-quadratic dissipation potentials. Thermodynamic structure is strongly enforced by construction through suitable reparameterizations of both the reversible operator and the dissipation potential, ensuring exact compliance with the first and second laws of thermodynamics. We validate the proposed approach on three representative examples: a harmonic oscillator coupled to a heat bath, an idealized chemical motor, and a one-dimensional viscoplastic model of Perzyna type. These results demonstrate the method's ability to accurately infer thermodynamically consistent models from data for systems incorporating both conservative and nonlinear dissipative dynamics.
Computational Physics (physics.comp-ph); Machine Learning (cs.LG)
arXiv:2605.09058 [physics.comp-ph]
(or arXiv:2605.09058v2 [physics.comp-ph] for this version)
https://doi.org/10.48550/arXiv.2605.09058 Focus to learn more arXiv-issued DOI via DataCite
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