So, how do physics-based neural networks work?

This approach can be very simple: add the known differential equations related to physical principles into the loss function when training the neural network.

Thus, the residual of the underlying differential equation is computed using these gradients and added as an extra term in the loss function.

Source: https://benmoseley.blog/my-research/so-what-is-a-physics-informed-neural-network/

This amounts to using the following loss function (J)to train the network:

where uNN is the output of the neural network and utrue is the real measured property. This loss function presents the training of a physics-based neural network considering Newton’s law of motion.

Each loss function can we weighted (using the parameters a and b) to account for a tradeoff in the importance of a) the model accuracy and b) the model agreement with physical principles.

The physics-informed neural network is able to predict the solution with extrapolation capabilities far from the experimental data points conditions, limiting the common overfitting…