Scientific Machine Learning

Federico Pichi received his Ph.D. in Mathematical Analysis, Modelling and Applications at SISSA, and he is currently an assistant professor in Numerical Analysis in the mathLab group at SISSA. His research interests include projection-based and data-driven reduced order models in computational science and engineering, with applications to parametrized bifurcating problems. He also develops scientific machine learning approaches bridging numerical analysis and novel architectures.Gianluigi Rozza is a professor in numerical analysis and scientific computing at International School for Advanced Studies-SISSA, Trieste, Italy. He obtained his Ph.D. in applied mathematics at EPFL in 2005, M.Sc. in aerospace engineering at Politecnico di Milano in 2002, and post-doc at MIT. At SISSA, he is a coordinator of the SISSA mathLab group and a lecturer in the master in high-performance computing. He is the SISSA director’s delegate for Valorisation, Innovation, Technology Transfer, and Industrial Cooperation. His research is mostly focused on numerical analysis and scientific computing, developing reduced order methods. He is the author of more than 130 scientific publications (editor of six books and author of two books). He has been the advisor of 35 master theses and co-director/director of 22 Ph.D. theses since 2009. He is the principal investigator of the European Research Council Consolidator Grant (H2020) AROMA-CFD and PoC ARGOS (HE) as well as of the project FARE-AROMA-CFD funded by the Italian Government. Since 2022, he is the co-founder and scientific director of FAST Computing, a SISSA startup.Maria Strazzullo received her Ph.D. in Mathematical Analysis, Modelling and Applications at SISSA, and she is currently an assistant professor in Numerical Analysis at the Department of Mathematics of the Polytechnic of Turin. Her research focuses on reduced order models for parametric partial differential equations, with particular emphasis on optimal flow control and turbulence modeling, with the main goal of conceiving reliable and efficient methods for the simulation and control of complex systems.Davide Torlo received his Ph.D. in Mathematics at the University of Zurich, and he is currently assistant professor in Numerical Analysis at the Department of Mathematics of the University of Rome Sapienza. His interests lie chiefly in numerical methods for hyperbolic partial differential equations, including high order technique, structure preserving methods, and reduced order models. Lately, he also studied the applications of neural networks in this field.

• Chapter 1. Domain-decomposed image classification algorithms using linear discriminant analysis and convolutional neural networks.- Chapter 2. Discovering Partially Known Ordinary Differential Equations: a Case Study on the Chemical Kinetics of Cellulose Degradation.- Chapter 3. Deep Unfolding for Scientific Computing on Embedded Systems.- Chapter 4. Non-Asymptotic Analysis of Projected Gradient Descent for Physics-Informed Neural Networks.- Chapter 5. MILP Initialization for Power Transformer Dynamic Thermal Modeling with PINNs.- Chapter 6. 3D point cloud generation for surface representation.- Chapter 7. Generative Models for Parameter Space Reduction applied to Reduced Order Modelling.- Chapter 8. High-Fidelity Description of Platelet Deformation Using a Neural Operator.- Chapter 9. Nonlinear reduction strategies for data compression: a comprehensive comparison from Diffusion to Advection problems.- Chapter 10. Model Reduction for Transport-Dominated Problems via Cross-Correlation Based Snapshot Registration.