Marcelo Forets is an Applied Mathematician that works as Assistant Professor at Universidad de la República (Uruguay). Born in Uruguay (Montevideo, 1988), he graduated in Physics and in Electrical Engineering, then moved to France for a PhD in Mathematics and Informatics (Univ. Joseph Fourier, France) on the quantum random walk, a model of particular interest to Quantum Computing. He was a post-doc researcher at VERIMAG laboratory of Université Grenoble Alpes (France) under the supervision of Oded Maler and Goran Frehse, where he started to develop what is now the JuliaReach package ecosystem. His research has to do with developing innovative numerical tools that impact decisions regarding reliability, correctness and safety of control systems, hybrid dynamical systems, and robustness analysis of neural networks.
This minisymposium presents modern approaches to analyze a variety of mathematical systems in Julia, via set propagation techniques: dynamical systems, cyber-physical systems, probabilistic systems, and neural networks. To deploy those systems in the real world there is an increasing demand for safe and reliable models. The speakers represent a broad cross-section of work from different fields that build on set-based techniques and global optimization to address such challenges.
JuliaReach is among the best-of-breed software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from all initial states and for all admissible inputs and parameters. We explain the role of Julia's multiple dispatch to gain an unprecedented level of flexibility and expressiveness in this area. We explore diverse applications including differential equations, hybrid systems and neural network controlled systems.