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CD Technical Meeting (ML12): Model order reduction method for Hamiltonian dynamics using deep learning
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Europe/London
Description
Machine Learning, Uncertainty Quantification and Data Science
Many mathematical models of physical processes pose significant challenges for numerical simulation due to their high dimensionality and complexity. This is particularly the case in nuclear fusion, where such models are very demanding in terms of computational time and resources. The issue becomes even more critical when repeated or real-time evaluations are required, as in optimization or control applications. To overcome these limitations, reduced-order models (ROMs) can be developed to provide fast approximations of the full systems, at the cost of some loss in accuracy. When dealing with Hamiltonian systems, it is essential to preserve their underlying geometric structure in the reduction process. In this work, we introduce the fundamentals of symplectic model reduction, based on the symplectic Galerkin projection, and extend this framework by replacing linear approximations with neural networks. The proposed approach is illustrated on a particle-in-cell (PIC) model of the Vlasov–Poisson equation.
