Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling
Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling
复制标题
DOI：
--
复制
发表时间：
2021-09
期刊：
影响因子：
--
通讯作者：
Franck Djeumou;Cyrus Neary;É. Goubault;S. Putot;U. Topcu
中科院分区：
文献类型：
--
作者：
Franck Djeumou;Cyrus Neary;É. Goubault;S. Putot;U. Topcu
将基于物理的知识有效地包含到动力系统的深度神经网络模型中可以大大提高数据效率和泛化能力。这种先验知识可能来自物理原理（例如，守恒定律）或来自系统的设计（例如，机器人的雅可比矩阵），即使大部分的系统动态仍然未知。我们开发了一个框架，从轨迹数据中学习动力学模型，同时将先验系统知识作为归纳偏差。更具体地说，所提出的框架使用基于物理的边信息来通知神经网络本身的结构，并对模型的输出值和内部状态进行约束。它将系统的向量场表示为已知函数和未知函数的组合，后者由神经网络参数化。在模型的训练过程中，通过增广拉格朗日方法强制执行物理信息约束。我们通过实验证明了所提出的方法对各种动力系统的好处-包括具有大状态空间，非线性动力学，外力，接触力和控制输入的机器人环境的基准套件。通过在训练期间利用先验系统知识，所提出的方法学习预测系统动态比不包括先验知识的基线方法更准确两个数量级，给定相同的训练数据集。
Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation laws) or from the system's design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating a-priori system knowledge as inductive bias. More specifically, the proposed framework uses physics-based side information to inform the structure of the neural network itself, and to place constraints on the values of the outputs and the internal states of the model. It represents the system's vector field as a composition of known and unknown functions, the latter of which are parametrized by neural networks. The physics-informed constraints are enforced via the augmented Lagrangian method during the model's training. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems -- including a benchmark suite of robotics environments featuring large state spaces, non-linear dynamics, external forces, contact forces, and control inputs. By exploiting a-priori system knowledge during training, the proposed approach learns to predict the system dynamics two orders of magnitude more accurately than a baseline approach that does not include prior knowledge, given the same training dataset.