Teacher: Adil Rasheed

In the context of Digital Twin there is a need for mathematical models that are computationally efficient, capability to model the unknown, self-evolving and above all humanly interpretable. The four desired model characteristics mentioned can be addressed by developing a new breed of modelling approach that will combine the interpretability, robust foundation and understanding of a physics-based modelling approach with the accuracy, efficiency, and automatic pattern-identification capabilities of advanced data-driven machine learning and artificial intelligence algorithms.

• Introduction to Hybrid Analysis and Modelling in the context of Digital Twin – 2 Lectures
• Numerical methods for partial and ordinary differential equations – 2 Lectures
• Interpretable data-driven models (PCA, ICA) – 2 Lectures
• More recent data-driven models (Compressed sensing, Dynamic Mode Decomposition) – 2 Lectures
• Blackbox machine learning methods (DNN, GANS, LSTM) – 3 Lectures
• Symbolic regression using Gene Expression Programming – 1 Lecture
• Equation discovery from data – 2 Lectures
• Combining physics-based modelling with data-driven modelling – 2 Lectures

5 assignments that will be based on the provided python notebook during the lectures

A project assignment where the students will have to show how they applied the concepts in the course to solve a problem of their choice. A small report with an oral presentation.

Detailed python notebook with codes and corresponding theory will be provided to the students to give them a working knowledge of the algorithms and to identify their strengths and weaknesses