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. Previous research focused on either facet, respectively with a potential-based architecture and with degenerate variational integrators, but new issues arise when combining both. In experiments, the learnt model is sometimes numerically unstable due to the gauge dependency of the scheme, rendering long-time simulations impossible. In this paper, we ide
This paper addresses critical stability challenges in learning physics-based dynamics, a foundational capability for the future of AI in complex systems.
Improving the accuracy and long-term stability of AI models in simulating physical systems is crucial for reliable autonomous agents and advanced scientific discovery.
This work potentially enables more robust and long-lasting simulations for AI, moving beyond short-term predictions to practical, real-world applications in engineering and science.
- · AI researchers in physics-informed ML
- · Robotics and autonomous systems developers
- · Scientific computing sector
- · Developers relying on purely black-box AI models for physical systems
- · Industries with high-cost, real-world testing of complex dynamics
Improved long-term stability in AI simulations of physical systems.
Accelerated development of AI agents capable of operating reliably in dynamic physical environments.
Reduced need for expensive physical prototypes and real-world testing in complex engineering disciplines.
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