Short Courses

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Note: all the courses will be in Spanish

Course 1: An Introduction to physics-informed machine learning

In this course we will cover the basics of machine learning and physical modeling. In particular, we will learn about the terminology in these areas and their connections, and how to combine machine learning with physical models to get the better of both worlds. The course will culminate with practical applications of these tools in a workshop.

Date: to be defined (number of modules)

 Instructor: Francisco Sahli (PUC,Chile)

Abstract:

In this course we will cover the basics of machine learning and deep learning. In particular, we will learn about the busy terminology in these areas and its connections with statistical concepts, in addition to learning what neural networks are and how they are trained. The course will culminate with practical applications of these tools in a workshop.

Course 2: Introduction to inverse problems for data analysis

Date: to be defined (number of modules)

Instructor: Claudia Prieto (PUC), Axel Osses (U. de Chile)

Abstract:

In this course some basic concepts of inverse problems will be reviewed from the point of view of parameter identification, data assimilation and regularization. The theoretical classes will be accompanied by practical laboratories with applications related to the management of images through jupyter notebooks.

For the practical sessions you will need:

  • a Google account for using Google colab. You do not need to install python or jupyter in your computer;
  • try with this Jupyter notebook (click and press in “Open with Google Colab”): here
  • read and explore this notebook a brief introduction to python and numpy: here
  • you can import this folder to your own Google Drive acoount with the files and Jupyter notebook for the practical sessions: here

Bibliography:

  • Steven L. Brunton, J. Nathan Kutz. Data Driven Science & Engineering. Machine Learning, Dynamical Systems and Control, 2017. Available online here
  • Per Christian Hansen, Discrete Inverse Problems: Insights and Algorithms, SIAM, Philadelphia, 2010
  • Mario Bertero, Patrizia Boccaci, Christine De Mol, Introduction to Inverse Problems in Imaging, Second Ed., CRC Press, Boca Raton, London, New York, 2021
  • Andreas Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Third Ed., Applied Mathematical Sciences Vol 120, Springer Nature Switzerland, 2021

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