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.

本研究提出了神经共轭流（NCF），一种具备精确流结构的神经网络架构，旨在解决传统物理信息神经网络在估计常微分方程动态时的不足。通过利用拓扑共轭，我们证明这些网络不仅与连续群自然同构，且能够以可解释的方式强制实施这些流的拓扑性质。实验表明，相较于其他基于流的架构，NCF在训练速度上可提升至五倍，同时在捕捉和外推常微分方程的潜在动态方面具有实质性的计算优势。

神经共轭流：具有流结构的物理信息架构