Machine Learning for Scientific Computing and Numerical Analysis

This MSc course introduces and develops advanced methods at the intersection of machine learning and scientific computing, with a special emphasis on solving and analyzing forward and inverse problems governed by partial differential equations (PDEs). Students will learn how to combine classical numerical methods with modern neural-network architectures to approximate functions, operators, and solution maps, while critically assessing stability, generalization, and interpretability.

Graduates of this course will be able to:

• Apply supervised learning techniques to PDE-based forward and inverse problems.
• Derive and implement classical and neural-network-based function approximators for high-dimensional problems.
• Design optimization strategies for scientific ML tasks, including constrained and PDE-informed settings.
• Implement operator learning frameworks and evaluate their performance across diverse PDE families.
• Formulate and solve inverse problems using data-driven, variational, or hybrid approaches.
• Assess robustness, stability, and physical consistency of ML-based solvers.

Hybrid teaching: students at Polytechnique on campus, EuroTeQ students online.