论文标题
物理学指导神经网络，用于建模非线性动力学
Physics guided neural networks for modelling of non-linear dynamics
论文作者
论文摘要
当前人工智能浪潮的成功可以部分归因于深层神经网络，事实证明，这些神经网络在学习最少的人类干预的大型数据集中非常有效。但是，由于数据效率低和对超参数的敏感性和初始化的敏感性，因此很难在复杂的动态系统上训练这些模型。这项工作表明，在DNN中的中间层中注入部分已知的信息可以提高模型的准确性，降低模型不确定性并在训练过程中提高收敛性。这些物理引导的神经网络的价值通过学习多种非线性动力学系统的动力学来证明，这些动力学由非线性系统理论中的五个众所周知的方程式表示：Lotka-Volterra，Duffing，van der Pol，Lorenz，Lorenz和Henon-Heiles Systems。
The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However, it is difficult to train these models on complex dynamical systems from data alone due to their low data efficiency and sensitivity to hyperparameters and initialisation. This work demonstrates that injection of partially known information at an intermediate layer in a DNN can improve model accuracy, reduce model uncertainty, and yield improved convergence during the training. The value of these physics-guided neural networks has been demonstrated by learning the dynamics of a wide variety of nonlinear dynamical systems represented by five well-known equations in nonlinear systems theory: the Lotka-Volterra, Duffing, Van der Pol, Lorenz, and Henon-Heiles systems.
