The paper introduces a new class of port‑Hamiltonian neural networks that can model systems with multiple asymptotically stable equilibria. By parameterizing the Hamiltonian as a product of Bregman divergences generated by an input‑convex network, the authors overcome the limitation of previous models that could only represent a single attractor. They prove local Lyapunov stability, show that additional non‑asymptotically stable equilibria must exist, and demonstrate improved convergence on three benchmark systems.
arXiv:2609.36942v1 Announce Type: cross Abstract: Learning neural-network models of dynamical systems with safety guarantees is a fundamental requirement for their deployment in safety-critical setti...
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: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.
The paper investigates the Lyapunov solution operator, which maps a vector field to its corresponding Lyapunov function via a dissipation-based PDE. It proves that this operator is well-defined, unique, and continuous on compact subsets of the domain of attraction under exponential stability, enabling uniform approximation across families of nonlinear systems. Using Fourier Neural Operators, the authors demonstrate that a single trained operator can accurately approximate Lyapunov functions for parameterized dynamics, showcasing the potential of neural operators in stability analysis.
arXiv:2607. 28977v1 Announce Type: cross Abstract: Machine learning of Hamiltonian dynamics has driven growing interest in Hamiltonian neural networks (HNNs), which encode Hamilton's equations of motion into the learning architecture.
arXiv:2608. 19688v1 Announce Type: cross Abstract: We develop a geometric framework for learning deterministic and stochastic forced Hamiltonian systems with neural networks.
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.
arXiv:2607. 12269v1 Announce Type: new Abstract: We introduce Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), a family of parameterised quantum circuits that learn classical dynamics in a structure-preserving manner.
arXiv:2608. 00571v1 Announce Type: new Abstract: Learning solution operators for differential equations is a central problem in scientific machine learning.
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. 09929v1 Announce Type: cross Abstract: Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable.
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.