Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
This work addresses the need for improved forecasting, stability, and physical realizability in data-driven modeling, representing an incremental advancement by combining existing methods.
The paper tackles the problem of discovering dynamical systems from data by unifying Sparse Identification of Nonlinear Dynamics (SINDy) with neural ordinary differential equations, resulting in a framework that learns both black-box dynamics and structure-preserving bracket formalisms, with demonstrated effectiveness in benchmarks including chaotic systems.
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees. We present here a unification of the Sparse Identification of Nonlinear Dynamics (SINDy) formalism with neural ordinary differential equations. The resulting framework allows learning of both "black-box" dynamics and learning of structure preserving bracket formalisms for both reversible and irreversible dynamics. We present a suite of benchmarks demonstrating effectiveness and structure preservation, including for chaotic systems.