PINNs are a modern approach to solving (partial) differential equations (=PDEs) using neural networks based on minimizing a residuum formed with automatic differentiation. This video is a simple example of the 1D Poisson problem. Here is the code: [ Ссылка ]

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Timestamps:
00:00 Intro
01:02 What are PINNs?
01:23 1D Poisson Problem with homogeneous Dirichlet BCs
02:11 Training PINNs by residuum losses
04:28 How autodiff comes into play
06:33 Finite Differences as a reference
07:08 Considered forcing function
07:23 Imports
07:57 Constants/Hyperparameters
09:20 Defining and initializing the MLP architecture
11:38 Querying initial PINN state at some points
13:52 Computing reference solution by Finite Differences
18:07 Plot true solution and initial PINN guess
20:41 Defining PDE residuum using automatic differentiation
24:10 Total loss function
28:16 Training loop (including the third autodiff pass)
32:06 Plot Final PINN solution and discussion
34:30 Advantages of having a trained PINN
35:18 Summary
37:23 Potential improvements
37:52 Outro

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