Data Driven Solutions and Discoveries in Mechanics Using Physics Informed Neural Network
Stanford University CS 229 Project, Spring, 2020.
Summary
This project investigates physics-informed neural networks as solvers and inference tools for mechanics problems described by differential equations. Automatic differentiation evaluates derivatives of the network output, allowing residuals of the governing equations to enter the training objective alongside boundary conditions and observed data. The report considers both forward problems, where the solution is sought for specified model parameters, and inverse problems, where unknown parameters are inferred from observations. Predictions are compared with analytical results or finite-element calculations. The framework produces a smooth surrogate that can be differentiated with respect to coordinates and model parameters, making the same basic implementation useful for both solution and discovery tasks. The examples illustrate the potential of combining physical equations with data in neural-network models, while exploring their use as alternatives to established numerical methods for engineering mechanics.