Scientific Machine Learning

This volume gathers peer-reviewed papers from the workshop Scientific Machine Learning: Emerging Topics, held at SISSA in Trieste, Italy. The event gathered leading researchers in mathematics, algorithms, and machine learning. Its goal was to advance the synergy between data-driven models and scientific computing, promoting robust, interpretable, and scalable methods. The works reflect major trends in scientific machine learning (SciML), including optimization, physics-informed learning, neural graph/operators/ODE, transformers, and generative models. Contributions propose physics-based constrained neural networks, advancements in optimization and model reduction, and applications across power systems, chemical kinetics, and biomechanics. Topics span from hybrid models for image classification to generative compression and neural operators for high-dimensional systems. Blending theory and practice, the volume captures the diversity and innovation shaping modern SciML.

This volume is addressed to researchers and will provide readers with insight into the current state of the field, sparks new ideas, and encourages further research at the rich intersection of machine learning, mathematics, and scientific computing.

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.