arXiv:2605. 13305v2 Announce Type: replace Abstract: Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons.
By Lake Yang, Antonio Malpica-Morales, Frank Ioannis Papadakis Wood, Serafim Kalliadasis
arXiv:2601. 22123v4 Announce Type: replace Abstract: Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration.
By Winfried Ripken, Michael Plainer, Gregor Lied, Thorben Frank, Oliver T. Unke, Stefan Chmiela, Frank No\'e, Klaus-Robert M\"uller
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.
By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas
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.
By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas
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.
By Katharina Friedl, No\'emie Jaquier, Alyx Liao, Danica Kragic
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.
By Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi, Peyman Tavallali, Houman Owhadi