Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems
This work addresses the challenge of reliable state variable discovery in second-order and Hamiltonian systems for fields like physics and engineering, representing an incremental improvement over existing data-driven methods.
The researchers tackled the problem of discovering state variables in dynamical systems by proposing a physics-informed neural network model that constrains the baseline approach with physical principles, resulting in improved identification of minimal, non-redundant, and interpretable state variables compared to the baseline.
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.