Advanced Course

1. What is scientific machine learning?

2. Why use scientific machine learning?

3. Examples of scientific machine learning

4. The role of mathematics in scientific machine learning

5. The role of computer science in scientific machine learning

6. Limitations of SciML.

Links to Lectures: 

• general introduction to SciML

• detailed course outline

1. Brief recall of the mathematical foundations of scientific machine learning

   1. Linear algebra

   2. Calculus

   3. Differential equations

   4. Optimization

   5. Probability theory

Link to Lecture

2. Machine learning techniques for scientific applications (see Basic Course for details)

   1. Regression

   2. Classification

   3. Clustering

   4. Surrogate models and dimensionality reduction

   5. The use of machine learning in scientific applications

   6. The challenges of applying machine learning to scientific applications

Links to Lectures: 

• general principles, 

• supervised and unsupervised learning.

Links to Examples:

• Link to Examples (all)

• Link to Examples (pytorch)

Links to CodeLabs:

• Link to CodeLab (setup)

• Link to CodeLab (pytorch)

• Link to CodeLab (ML with pytorch)

1. 1. Differentiable programming with autograd and PyTorch

   2. Gradients, adjoints and inverse problems

   3. Neural networks for scientific machine learning

   4. Physics-informed neural networks

   5. The use of automatic differentiation in scientific machine learning

   6. The challenges of applying automatic differentiation to scientific applications

Link to Lecture

Links to Examples:

• Link to Examples (all)

• Link to Examples (opt)

• Link to Examples (ad)

Link to CodeLab (optimization and AD)

• Direct problems

• Inverse problems

  • Linear regression

  • Parameter identification

  • Differential-equation based inverse problems

    • PINN and PNO

    • PCL

    • others (U-NET, NWP, etc.)

Link to Lecture

Links to Examples:

• Link to Examples (all)

• Link to Examples (SciML)

Link to CodeLab

1. Applications of scientific machine learning

   1. Fluid dynamics

   2. Materials science

   3. Biology

   4. Medicine

   5. The challenges of applying scientific machine learning to different scientific domains

2. Case studies in scientific machine learning

   1. Solving partial differential equations with neural networks

   2. Predicting protein structures with deep learning

   3. Diagnosing diseases with machine learning

   4. Epidemiology with machine learning

   5. The use of case studies to illustrate the power of scientific machine learning

   6. The challenges of applying scientific machine learning to real-world problems

Link to Lecture.

1. Inference Cycle

2. SSL and LLMs

3. Bias in machine learning models.

4. Fairness in machine learning.

5. Transparency in machine learning.

6. Trustworthiness, explainability.

7. The ethical challenges of using scientific machine learning.

8. The responsible use of scientific machine learning.

Link to Lecture.

• Review of: 

  • 3DVar

  • 4DVar

  • EnsVar

• Practical examples and exercises

Lecture Link

Links to Examples:

• Link to Examples (all)

• Link to Examples (variational DA)

Link to CodeLab

• Review of:

  • Basic filters (KF)

  • Ensemble filters (EnKF)

  • Nonlinear filters (EKF, UKF, PF)

• Practical examples and exercises

Lecture Link

Links to Examples:

• Link to Examples (all)

• Link to Examples (statistical DA)

Link to CodeLab

Applying SciML to Data Assimilation

Examples of the use of SciML in Data Assimilation

More details coming soon...