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: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: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.
arXiv:2608. 10235v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks.
arXiv:2608. 00571v1 Announce Type: new Abstract: Learning solution operators for differential equations is a central problem in scientific machine learning.
arXiv:2606. 04623v1 Announce Type: new Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics evolving on symplectic manifolds.
arXiv:2606. 04623v2 Announce Type: replace Abstract: High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics that evolve on symplectic manifolds.
arXiv:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.
The paper introduces kernel-based methods for learning Hamiltonian systems directly from trajectory data, offering both a 2‑step approach (reconstruct trajectories first, then learn the Hamiltonian) and a 1‑step approach (joint inference). Experiments on mass‑spring dynamics, a nonlinear pendulum, and the Henon‑Heiles system show that the methods achieve accurate, data‑efficient predictions, outperforming 2‑step baselines especially when data are scarce, while preserving the Hamiltonian structure. The authors also provide a priori error estimates and a general numerical framework applicable to arbitrary dynamical systems.
arXiv:2608. 19688v1 Announce Type: cross Abstract: We develop a geometric framework for learning deterministic and stochastic forced Hamiltonian systems with neural networks.
arXiv:2607. 28939v1 Announce Type: new Abstract: Structure-preserving neural networks are essential for the long-term prediction of Hamiltonian systems from data.
arXiv:2510. 01788v2 Announce Type: replace Abstract: This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes.
The paper investigates how the Brinkman penalisation method, which embeds complex domain boundary-value problems into a simple computational box, preserves a multi-conformal symplectic structure for multi-symplectic Hamiltonian PDEs under a specific compatibility condition. It demonstrates that this leads to an exact local conservation law where the multi-symplectic two-form is conserved in the fluid region and decays exponentially inside the solid. Building on these findings, the authors propose structure-preserving numerical integrators via Strang splitting and conformal symplectic neural operators that interleave exact dissipative flows with learnable multi-symplectic evolution operators, and validate their approach with numerical experiments on wave and electromagnetic scattering.