Physics guided neural networks for modelling of non-linear dynamics
This addresses the problem of low data efficiency and sensitivity in neural networks for modeling nonlinear dynamics, offering a domain-specific improvement.
The paper tackles the challenge of training deep neural networks on complex dynamical systems by injecting partially known physics information into intermediate layers, resulting in improved model accuracy, reduced uncertainty, and better convergence during training, as demonstrated on five nonlinear systems like Lorenz and Duffing equations.
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.