Scientific Machine Learning

Launch course

Course outline

Basics of Machine Learning

• Coding your own neural network with PyTorch/Tensorflow
• Feature engineering and preprocessing
• Automatic differentiation and backpropagation

Explainable AI

• Linear models and their interpretation
• Decision trees and rule-based models
• Model-agnostic explainability: LIME and SHAP

ODEs and PDEs

• Introduction to ODE and PDE Discretization Methods
• Numerical methods for solving ODEs and PDEs

Physics-Informed Neural Networks (PINNs)

• Introduction to PINNs
• Incorporating physical constraints into neural networks
• Applications and case studies
• Solving ODEs, PDEs and Inverse problems
• Operator Learning
• Neural ODEs

Differentiable Simulators:

• Overview of differentiable programming
• Importance and applications in scientific machine learning
• Differentiable wave and heat-transfer simulators
• Solving design and inverse problems

Surrogate Modeling

• Graph Neural Networks for dynamic particle simulations
• Symbolic Regression

Bayesian Machine Learning and Uncertainty Quantification

• Review of Probability
• Gaussian processes
• Bayesian neural networks
• Uncertainty quantification in engineering applications