arXiv:2508.11911v2 Announce Type: replace-cross Abstract: We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) and may be augmented with linear SGS-reflector layers. This yields an exact symplectic map between full and latent phase spaces. Latent dynamics are advanced by a symplectic flow map implemented as a HenonNet. This unified neural architecture
The development builds on recent advancements in neural networks and the growing need for more efficient and accurate modeling of complex physical systems across various scientific and engineering disciplines.
This research introduces a novel, end-to-end framework for reduced-order modeling of Hamiltonian dynamics, potentially leading to significant advancements in simulating high-dimensional physical systems with greater accuracy and computational efficiency.
The ability to accurately model complex physical systems using data-driven, symplectic neural networks could revolutionize fields from climate modeling to materials science and engineering design, enabling faster development cycles and more precise predictions.
- · Scientific research institutions
- · Engineering simulation software providers
- · High-performance computing (HPC) sector
- · AI/ML researchers
- · Traditional physics-based modeling approaches
- · Companies reliant on less efficient simulation methods
Improved simulation fidelity and speed for complex physical systems across diverse domains.
Accelerated discovery and design cycles in areas like drug development, new materials, and aerospace engineering.
Potential for new scientific breakthroughs enabled by previously intractable simulation capabilities, leading to entirely new industries or solutions to global challenges.
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