提出具精确流结构的神经网络，加速动态系统建模与外推。
Neural Conjugate Flows: Physics-informed architectures with flow structure
- 基于拓扑共轭设计神经网络，天然具备连续群结构。
- 可精确逼近常微分方程流，数值实验显示计算效率提升5倍。
- 结构可解释性强，适合需要物理一致性建模的研究者。
我们提出神经共轭流（Neural Conjugate Flows, NCF），一类具备精确流结构的神经网络架构。通过利用拓扑共轭，我们证明这些网络不仅自然同构于连续群，还可作为常微分方程（ODE）流的通用近似器。此外，该架构能以可解释方式强制施加流的拓扑性质。数值实验表明，这种拓扑群结构在估计和外推ODE隐含动力学时带来显著计算优势，训练速度比其他流基架构快至五倍。
原文摘要 · Abstract (English)
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.
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