Discovering interpretable Lagrangian of dynamical systems from data
This work addresses the need for interpretable models in physics and engineering by enabling automated discovery of Lagrangians and conservation laws from data, which is incremental as it builds on existing Lagrangian discovery frameworks but adds interpretability and generalization.
The authors tackled the problem of discovering interpretable Lagrangians from data for dynamical systems, proposing a machine-learning algorithm that derives them in interpretable forms and generalizes to infinite-dimensional systems, with fidelity demonstrated on examples where known Lagrangians and conserved quantities are validated.
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing equations of motion. The generalization of equation discovery techniques has huge potential; however, existing Lagrangian discovery frameworks are black-box in nature. This raises a concern about the reusability of the discovered Lagrangian. In this article, we propose a novel data-driven machine-learning algorithm to automate the discovery of interpretable Lagrangian from data. The Lagrangian are derived in interpretable forms, which also allows the automated discovery of conservation laws and governing equations of motion. The architecture of the proposed framework is designed in such a way that it allows learning the Lagrangian from a subset of the underlying domain and then generalizing for an infinite-dimensional system. The fidelity of the proposed framework is exemplified using examples described by systems of ordinary differential equations and partial differential equations where the Lagrangian and conserved quantities are known.