Physics-informed neural networks for a highly nonlinear dynamic system

Abstract The micromachined beam fixed at both ends is an essential component of electrostatically-actuated Micro-Electro-Mechanical System (MEMS) based switches. The pull-in voltage and the response time are some of the most important parameters of this system. With physics-based approaches, the challenge of modelling and producing simplified representations comes from the strong nonlinearities involved and the interaction of more than one physical field. Data-driven methods based on recurrent neural networks can be used to obtain simplified, yet accurate models for predicting the minimum gap dynamics for different applied voltages. However, the solution of these black-box models lacks physical connection and can contradict the physical laws. Here, we propose using a hybrid approach, namely a physics-informed machine learning model, and we show the benefits of incorporating initial and boundary conditions into the training process in terms of accuracy without compromising the learning and simulation times. Our neural network models incorporating physics-based constraints are ten times more accurate than the classical neural network architectures for the same problem.