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.

翻译：我们提出了神经共轭流（Neural Conjugate Flows，NCF），这是一类具备精确流结构的神经网络架构。通过利用拓扑共轭，我们证明了这些网络不仅自然同构于一个连续群，而且是常微分方程（ODE）流的通用逼近器。此外，这些流的拓扑性质可以通过架构以可解释的方式强制实现。我们在数值实验中展示了这种拓扑群结构如何在估计和推断常微分方程的隐式动力学时，相比其他物理信息神经网络带来具体的计算优势，同时训练速度比基于流的其他架构快达五倍。