Differential Informed Auto-Encoder

If the physics formula was obtained in the form of differential equations, a physics-informed neural network can be built to solve it numerically on a global scale [5, PINN].This process could be seen as a decoder in a way that takes a sample point in the domain of the partial differential equations, and solve it to get the corresponding output of each input point. If only a small and random amount of training data was obtained, to re-sample from the domain, we need to obtain the differential relationship of the data. This process could be viewed as an encoder that encodes the inner structure of the original data.