Day 1. Setting the Stage

1.1 Machine Learning for Scientific Discovery, by S. Brunton
1.2 Motivation for Machine Learning in Fluid Dynamics, by B. Noack
1.3 F1: Theory of Learning, by B. Noack
1.4 F2: Fundamentals of Regression, by M. A. Mendez

Day 2: Machine Learning Tools

2.1 F3: Hidden Fluid Mechanics, by G. Karniadakis
2.2 F4: Bayesian Inference and Uncertainty Quantification, by O. Le Maître
2.3 F5: Predictions in Chaotic Dynamical Systems, by L. Magri
2.4 F6: Dimensionality Reduction, by M. A. Mendez

Day 3: Simulations, Experiments and Understanding

3.1 Reduced Order Models in complex flows, by S. Le Clainche
3.2 Equation- and Data-driven Reduced Order Modeling, by B. McKeon
3.3 Data-driven turbulence Modeling, by P. Cinnella
3.4 Data Enriched Experiments, by A. Ianiro

Day 4: Improving Performances

4.1 Machine Learning Control, by B.Noack
4.2 Reinforcement Learning, by O. Semeraro
4.3 Model Predictive Control, by S. Discetti
4.4 Data-Driven Modeling for Enhanced Aerodynamics, by P. Bekemeyer

Day 5: Heading into the fourth Industrial Revolution

5.1 Digital Twins: Challenges and Enablers, by O. San
5.2 The role of digital twins in the energy transformation, by A. Parente
5.3 Reduced Order Surrogate DNS of Turbulent Combustion at the Exascale, by J. H. Chen
5.4 Round Table

• Data is a valuable resource in most fields
• Machine learning is building models from data (we have been doing this for decades!)
• More data, faster computers, and better algorithms/software are transforming our capabilities
• ML is rapidly changing the industrial and scientific landscape, including in fluid mechanic

• Fluidic pinball as a benchmark problem
• The many facets of the unforced and forced wake
• Modes, manifolds and clusters — Different flavors of reduced-order modeling
• From reinforcement to machine learning control — Different strategies for stabilizing the wake
• Good practices for reduced-order modeling and control
  

• Introductory examples: What can and cannot be learned from data
• Persistent topology: Understanding from the raw data
• Avoiding overfitting: Creating models which generalize beyond the data
• Occam’s razor: The sweet spot between model complexity and available data
• Regularizers and Co: Clever guessing in the sparse data limit

• The regression landscape: parametric and nonparametric methods
• The training problem with constraints and penalties
• Linear tools: Radial Basis Functions and Gaussian Processes
• Nonlinear tools: Artificial Neural Networks and Genetic Programming
• Tutorial 1: constrained RBFs for super resolution
• Tutorial 2: collective learning for digital twins

• Discover velocity and pressure fields from passive scalars
• AIV: Artificial Intelligence Velocimetry (jets and wakes 3D flows)
• Examples in blood flow and CSF in the brain

• Uncertainty Quantification and calibration problems in simulations
• Fundamentals of Bayesian inference
• Markov Chain Monte Carlos methods for posterior sampling
• Example: Gaussian Process models
• Surrogate-Based acceleration of Bayesian inference
• Bayesian models calibration with model error

• Time series forecasting and sequential data
• Gated recurrent neural networks
• Reservoir computers
• Physics-constrained machines

• Introduction to autoencoders and manifold learning
• The PCA and the link to modal analysis
• Kernel PCA and Kernel Decompositions
• Fundamentals of ANN Autoencoders
• Manifold learning: Locally Linear Embedding and Isomaps
• Tutorial : Python implementations

• Modal decomposition to extract physical features and reduce data dimensionality
• Combining modal decomposition with deep learning strategies
• Machine learning and reduced order models based on physical principles combining numerical and experimental databases
• Applications of reduced order models to acceleratenumerical simulations and to reconstruct flow fields from sensor measurements

• Equation-driven vs. data-driven reduced order modeling
• Resolvent analysis and resolvent-based modeling for turbulent flows
• Physics-informed, input-output analysis in the machine learning framework
• Application for discovery, modeling and control

• Reminder of turbulence fundamentals and modelling approaches
• Limitations and uncertainties in turbulence models
• Machine learning techniques for data-driven turbulence modeling, review of existing approaches and pitfalls
• Ensemble methods for robust predictions

• Experimental discrete data
• Exploiting data ensembles: Reducing noise
• Exploiting multiple measurements: Data Fusion
• Data-driven enhancement of the spatial and temporal resolution in experiments

• Turbulence control problem: Engineering examples and considerations
• Control landscape and control-law representation: Tools for understanding
• Machine learning control (MLC): Automated learning of multiple-input multiple-output feedback
• Multi-scale MLC: Distributed input distributed output feedback
• Smart skin separation control: A challenging case study
  

• Introduction to MPC fundamentals
• Challenges of MPC application in fluid dynamics
• Nonlinear vs linear MPC
• Self-tuned hyperparametrization of nonlinear MPC
• Tutorial: Matlab implementation

• Potentials and limitations of Machine Learning for Industrial applications
• Data-driven shape optimization, uncertainty quantification & robust design
• Deep learning for aerodynamic data prediction
• Machine Learning for enhancing computational fluid dynamics

• Digital twin: taxonomy and terminology
• Capability levels of a digital twin
• Hybrid physics-data driven modeling
• ROM as a key enabler for digital twins

• Energy-intensive industries
• Challenges in turbulent combustion simulations
• Low-dimensional combustion manifolds
• Data-driven modelling of reacting flows
• Reduced-order models and digital twins

• DNS of turbulent combustion: opportunities and challenges
• Data-driven approach: principal component transport
• Model-drive approach: time-dependent bases for on-the-fly ROM
• Performance on HPC and data sharing