Neural Conjugate Flows: Physics-informed architectures with flow structure

TL;DR

Neural Conjugate Flows are a novel neural network architecture with exact flow structure, enabling universal approximation of ODE flows, interpretable topological properties, and improved computational efficiency in modeling latent dynamics.

Contribution

The paper introduces Neural Conjugate Flows, a new architecture that incorporates flow structure and topological conjugation, offering universal approximation and interpretability.

Findings

Achieves up to five times faster training than other flow-based models.

Provides a universal approximator for ODE flows.

Enforces interpretable topological properties in neural networks.

Abstract

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.