Physics-Informed Neural Networks in Julia

PINNs are an approach in deep learning to solve partial differential equations by minimizing residuum information. They require (higher-order) input-output derivatives for the MLP networks, which we will do manually in this video. Here is the code: github.com/Ceyron/machine-lea...
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Timestamps:
00:00 Introduction
00:24 What is a PINN?
00:54 Interpretation of the Poisson problem
01:32 Informing neural network of the physics
03:14 Problem with automatic differentiation
04:15 Manual differentiation of a shallow MLP
07:29 Batched Execution of the neural network
08:36 Imports
08:59 Constants
09:59 Forcing Function & Analytical Solution
10:30 Setting the random seed
10:41 Sigmoid activation function
10:52 Initialize weights & bias of the neural network
13:51 Forward/Primal pass of the network
15:02 Plot initial prediction & analytical solution
18:31 Manual input-output differentiation
23:36 Check correctness with automatic differentiation
26:13 Randomly draw collocation points
28:30 Implement forward loss function
33:11 Testing the outer autodiff call
35:49 Training loop
38:34 Loss plot
39:09 Final PINN prediction
40:03 Summary
42:35 Outro