Neural Conjugate Flows: Physics-informed architectures with flow structure
This work addresses the challenge of efficient and interpretable modeling of ODE dynamics for researchers in physics-informed machine learning, offering a novel architecture with proven theoretical properties.
The paper tackles the problem of approximating and extrapolating latent dynamics of ordinary differential equations (ODEs) by introducing Neural Conjugate Flows (NCF), a neural network architecture with exact flow structure, which trains up to five times faster than other flow-based architectures and shows computational gains in numerical experiments.
We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous group, but are also universal approximators for flows of ordinary differential equation (ODEs). Furthermore, topological properties of these flows can be enforced by the architecture in an interpretable manner. We demonstrate in numerical experiments how this topological group structure leads to concrete computational gains over other physics informed neural networks in estimating and extrapolating latent dynamics of ODEs, while training up to five times faster than other flow-based architectures.