Learning symplectic model reduction based on a approximation theorem of symplectic embeddings
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. Although deep learning provides powerful tools for constructing low-dimensional surrogates from data, the intrinsic symplectic structure is easily destroyed during model reduction. As a result, a standard autoencoder may produce latent coordinates that do not support a Hamiltonian flow, leading to unstable long-time prediction. In this paper, we first establish a universal approximation theorem f
The increasing sophistication and application of AI in complex physical systems necessitate more robust and stable models, pushing research into integrating fundamental physics principles like symplectic structures into deep learning.
This research addresses a critical limitation in applying deep learning to high-dimensional Hamiltonian systems, potentially leading to more accurate, stable, and theoretically sound long-term predictions in scientific and engineering fields.
The ability to construct low-dimensional AI surrogates that preserve intrinsic physical properties like symplectic structures will reduce instability and improve reliability in modeling complex systems.
- · AI researchers in physics and engineering
- · Developers of scientific simulation software
- · Industries relying on complex system modeling
- · Practitioners using standard autoencoders for Hamiltonian systems
- · Models prone to unstable long-term predictions
Deep learning models will gain improved fidelity and stability when applied to physical systems governed by Hamiltonian dynamics.
This improved fidelity could accelerate discovery and optimization in fields like materials science, fluid dynamics, and quantum mechanics.
The integration of physical laws into AI could enable more autonomous and reliable AI agents managing complex infrastructure or scientific experiments.
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