  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.
