MATLAB Implementation of Physics Informed Deep Neural Networks for Forward and Inverse Structural Vibration Problems

Abstract

In this work, we illustrate the implementation of physics informed neural networks (PINNs) for solving forward and inverse problems in structural vibration. Physics informed deep learning has lately proven to be a powerful tool for the solution and data-driven discovery of physical systems governed by differential equations. In spite of the popularity of PINNs, their application in structural vibrations is limited. This motivates the extension of the application of PINNs in yet another new domain and leverages from the available knowledge in the form of governing physical laws. On investigating the performance of conventional PINNs in vibrations, it is mostly found that it suffers from a very recently pointed out similar scaling or regularization issue, leading to inaccurate predictions. It is thereby demonstrated that a simple strategy of modifying the loss function helps to combat the situation and enhance the approximation accuracy significantly without adding any extra computational cost. In addition to the above two contributing factors of this work, the implementation of the conventional and modified PINNs is performed in the MATLAB environment owing to its recently developed rich deep learning library. Since all the developments of PINNs till date is Python based, this is expected to diversify the field and reach out to greater scientific audience who are more proficient in MATLAB but are interested to explore the prospect of deep learning in computational science and engineering. As a bonus, complete executable codes of all four representative (both forward and inverse) problems in structural vibrations have been provided along with their line-by-line lucid explanation and well-interpreted results for better understanding.