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.
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.
arXiv:2602. 03670v2 Announce Type: replace-cross Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning.
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.
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.
The paper introduces DissipNet, a deep discrete‑time recurrent neural network that enforces dissipativity through structural weight constraints and a specialized training algorithm. By design, the network learns dissipative dynamics while maintaining stability, as formally verified using Lyapunov theory. Compared to standard RNNs and Physics‑Informed Neural Networks, DissipNet offers explicit stability guarantees and demonstrates improved performance across several modeling tasks.
arXiv:2603. 28707v3 Announce Type: replace-cross Abstract: We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics.
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.
arXiv:2606. 08956v1 Announce Type: new Abstract: Scientists have historically relied on mathematical models based on differential equations to relate system inputs -- forces, fluxes, or heat sources -- to outputs, such as displacement, velocity, concentration, and temperature.
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
arXiv:2602. 14885v2 Announce Type: replace-cross Abstract: Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows.
arXiv:2510. 16084v3 Announce Type: replace Abstract: Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks.
arXiv:2509. 24627v2 Announce Type: replace Abstract: Embedding physical intuition into network architectures allows the learning of dynamics that enforce fundamental properties, such as energy conservation laws, thereby leading to physically-plausible predictions.