Projected Neural Differential Equations for Learning Constrained Dynamics
This work addresses the need for accurate and reliable modeling of constrained dynamical systems in complex domains, representing an incremental improvement over existing neural differential equation methods.
The paper tackled the problem of learning constrained dynamics from data by introducing projected neural differential equations (PNDEs), which enforce known constraints through projection to improve generalizability and stability, resulting in outperformance of existing methods on challenging examples like chaotic systems and power grid models with fewer hyperparameters.
Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate models can enhance their generalizability and numerical stability. In this paper, we introduce projected neural differential equations (PNDEs), a new method for constraining neural differential equations based on projection of the learned vector field to the tangent space of the constraint manifold. In tests on several challenging examples, including chaotic dynamical systems and state-of-the-art power grid models, PNDEs outperform existing methods while requiring fewer hyperparameters. The proposed approach demonstrates significant potential for enhancing the modeling of constrained dynamical systems, particularly in complex domains where accuracy and reliability are essential.