1. Usage of neural networks in science, past and present.
2. Structure of the solution of a computational problem with machine learning: Identification of the problem; data acquisition, sorting, and processing of data and their connection with a model; correct choice of an architecture; loss function; optimization - training of the model; acceleration of training, regularization.
3. Utilization of deep learning in computational methods, architectures of neural networks: Hamiltonian neural networks, Fourier neural operator, physically informed neural networks, convolutional neural networks, graph neural networks.
4. Autoencoders and dimensionality reduction of the acquired data.
5. Identification of physical laws from experimental data.
6. Numerical computation with deep learning: Quadrature problem.
7. Physically informed neural networks (PINNs).
8. PINNs and their versions – Loss re-weighting and data resampling, optimization targets.
9. PINNs and their versions – Regularization techniques, new neural architectures, new paradigms in the training of PINNs, and future outlook.
10. PINNs and their versions – Advanced methods in the implementation of physical constraints: Loss function, optimization algorithm, architecture of the neural network.
11. Optimization algorithms in physical tasks.
12. Additional information for the course, discussion.
2. Structure of the solution of a computational problem with machine learning: Identification of the problem; data acquisition, sorting, and processing of data and their connection with a model; correct choice of an architecture; loss function; optimization - training of the model; acceleration of training, regularization.
3. Utilization of deep learning in computational methods, architectures of neural networks: Hamiltonian neural networks, Fourier neural operator, physically informed neural networks, convolutional neural networks, graph neural networks.
4. Autoencoders and dimensionality reduction of the acquired data.
5. Identification of physical laws from experimental data.
6. Numerical computation with deep learning: Quadrature problem.
7. Physically informed neural networks (PINNs).
8. PINNs and their versions – Loss re-weighting and data resampling, optimization targets.
9. PINNs and their versions – Regularization techniques, new neural architectures, new paradigms in the training of PINNs, and future outlook.
10. PINNs and their versions – Advanced methods in the implementation of physical constraints: Loss function, optimization algorithm, architecture of the neural network.
11. Optimization algorithms in physical tasks.
12. Additional information for the course, discussion.