论文标题
使用动力学约束统一物理系统在神经颂歌中的归纳偏见
Unifying physical systems' inductive biases in neural ODE using dynamics constraints
论文作者
论文摘要
能量保护是许多物理现象和动态系统的核心。在过去的几年中，旨在预测使用神经网络动态系统运动的轨迹，同时遵守节能法则，旨在预测动态系统运动的运动轨迹。这些作品中的大多数都是受哈密顿和拉格朗日力学等经典力学以及神经普通微分方程的启发。尽管这些作品已被证明在特定领域中分别很好地工作，但缺乏一种统一的方法，该方法通常不适用，而无需对神经网络体系结构进行重大更改。在这项工作中，我们旨在通过提供一种简单的方法来解决这个问题，该方法不仅可以应用于能源支持系统，还可以应用于耗散系统，通过在损失函数中以正规化项的形式包括不同情况下的不同电感偏见。所提出的方法不需要更改神经网络体系结构，并且可以构成验证新思想的基础，因此表明有望在这个方向上加速研究。
Conservation of energy is at the core of many physical phenomena and dynamical systems. There have been a significant number of works in the past few years aimed at predicting the trajectory of motion of dynamical systems using neural networks while adhering to the law of conservation of energy. Most of these works are inspired by classical mechanics such as Hamiltonian and Lagrangian mechanics as well as Neural Ordinary Differential Equations. While these works have been shown to work well in specific domains respectively, there is a lack of a unifying method that is more generally applicable without requiring significant changes to the neural network architectures. In this work, we aim to address this issue by providing a simple method that could be applied to not just energy-conserving systems, but also dissipative systems, by including a different inductive bias in different cases in the form of a regularisation term in the loss function. The proposed method does not require changing the neural network architecture and could form the basis to validate a novel idea, therefore showing promises to accelerate research in this direction.
