Dirac互连神经单元：在不进行约简的情况下发现物理系统中的模块性
Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reduction
浏览论文内容
中文总结 AI 辅助
提出Dirac互连神经单元（DINEs），通过微分代数方程和Dirac结构同时识别组件互连与特性，实现无需约简的模块化发现，支持子系统隔离组合及部分可观测系统，超越现有方法。
中文摘要 AI 辅助
深度学习在动力系统的数据驱动建模中已展现出显著的成功。其成功在很大程度上并非归因于神经网络的灵活性，而是归因于基于物理先验知识（如能量守恒和辛结构）的归纳偏置。然而，现有方法并未充分利用真实世界物理系统是组件间互连这一事实。一些方法要求互连结构先验已知，而另一些方法则假设系统可约简为常微分方程（ODE），仅学习约简后的ODE，从而丢弃了互连所施加的代数约束。在此，我们提出Dirac互连神经单元（DINEs），这是一种神经网络模型，将物理系统表示为微分代数方程（DAE），其代数约束由核表示中的Dirac结构给出。借助DINEs，我们同时从数据中识别组件间的互连作为Dirac结构，并将组件的特性作为神经网络进行学习。这使得我们能够将学习到的子系统保持为未约简形式，并在无需重新训练的情况下将其隔离或组合以构建新系统。此外，DINEs能够处理部分可观测系统。实验结果在现有方法无法企及的物理系统上展示了这些能力。
英文摘要
Deep learning has shown remarkable success in the data-driven modeling of dynamical systems. Much of its success is attributed not to the flexibility of neural networks but to inductive biases based on physical prior knowledge, such as energy conservation and symplecticity. However, existing methods do not fully exploit the fact that real-world physical systems are interconnections of components. Some methods require the interconnection to be known a priori, while others assume the system to be reducible to an ordinary differential equation (ODE) and learn only the reduced ODE, discarding the algebraic constraints imposed by the interconnection. Here, we propose Dirac-interconnected neural elements (DINEs), a neural network model that represents a physical system as a differential-algebraic equation (DAE), whose algebraic constraints are given by a Dirac structure in kernel representation. With DINEs, we simultaneously identify from data the interconnection among the components as a Dirac structure and learn the characteristics of the components as neural networks. This allows us to keep the learned subsystems in unreduced form and isolate or compose them to make a new system without retraining. Moreover, DINEs can handle partially observable systems. Experimental results demonstrate these capabilities on physical systems beyond the reach of existing methods.
发表机构
- Hokkaido University（北海道大学）
- Kyushu University（九州大学）
- RIKEN（理化学研究所）
- Waseda University（早稻田大学）
机构由 AI 辅助整理，请以论文原文为准。
