Scientific Machine Learning Workshop

This repository will contain all presentation slides, lab handouts, and lab code for the Scientific Machine Learning workshop at Cenpes.

The workshop offers an opportunity for attendees to improve their analytical and computational skills in the rapidly-developing field of scientific machine learning and data-driven model order reduction, while preparing them to work in highly interdisciplinary research and development projects. The workshop is structured as follows:

Day 1 (Braga Neto)

Morning:

• Introduction and Overview
• Deep Neural Networks
• Physics-Informed Neural Networks (PINN)

Afternoon:

• Lab 1: PINN solution of forward and inverse problems

Day 2 (Braga Neto)

Morning:

• Gaussian Process Regression
• Physics-Informed Gaussian Processes (PIGP)
• Operator Learning

Afternoon:

• Lab 2: PIGP solution of forward and inverse problems

Day 3 (Gildin)

Morning:

• Introduction to Model Order Reduction
• Physics-based MOR: Linear and Nonlinear Model Reduction
• Data-driven MOR Part 1: System Identification, SINDy, DMD

Afternoon:

• Lab 3a: Tutorial on Balanced Truncation, Krylov Subspaces, POD, POD-DEIM
• Lab 3b: POD-DEIM for reservoir simulation

Day 4 (Gildin)

Morning:

• Data-driven MOR Part 2: DMDc, OpInf, E2C0, FNO

Afternoon:

• Lab 4: Implementation of basic data-driven MOR for reservoir simulation

References

1. Braga-Neto, Fundamentals of pattern recognition and machine learning, 2nd edition, Springer, 2024.
   This textbook covers traditional Machine Learning in detail, and also has a chapter on Scientific Machine Learning.

2. Karniadakis et al., "Physics-Informed Machine Learning", Nature Review Physics, 2021.
   This is a very popular review of the area as of 2021, so it's a bit dated, but it is still a useful introduction to the field.

3. Gerón, Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, 2nd edition, O'Reilley, 2019.
   This is a code-oriented introduction to deep learning.

4. Chris Rackauckas’s MIT class “Parallel Computing and Scientific Machine Learning\ This class features parallel computing and Scientific Machine Learning topics.

5. Model Reduction and Approximation: Theory and Algorithms edited by Peter Benner, Albert Cohen, Mario Ohlberger, Karen Willcox. SIAM 2017

6. Athanasios C. Antoulas. Approximation of Large-Scale Dynamical Systems. SIAM 2006

7. Steven L. Brunton and J. Nathan Kutz. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control. 1st Edition, Cambridge University Press; 2019.

8. J. N. Kutz, S. L. Brunton, B. Brunton, J.L.Proctor. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. SIAM-Society for Industrial and Applied Mathematics, 2016

9. Nathan Kutz, Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data. 1st Edition, OUP Oxford, 2013