Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems

• URL: http://arxiv.org/abs/2408.11691v1
• Date: Wed, 21 Aug 2024 15:10:50 GMT
• Title: Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems
• Authors: Félix Chavelli, Zi-Yu Khoo, Dawen Wu, Jonathan Sze Choong Low, Stéphane Bressan,
• Abstract summary: This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables.
• Score: 1.7406327893433848
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state variables or result in overparameterized state spaces. Boyuan Chen and his co-authors proposed a neural network model that estimates the degrees of freedom and attempts to discover the state variables of a dynamical system. Despite its innovative approach, this baseline model lacks a connection to the physical principles governing the systems it analyzes, leading to unreliable state variables. This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables.

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