Abstract: Scientific Machine Learning (SciML) has rapidly emerged as a potent tool for tackling complex challenges posed by partial differential equations (PDEs) across diverse real-world scenarios. This surge in interest prompts a critical reevaluation of traditional numerical methods, emphasizing the imperative for more efficient and dependable approaches that seamlessly integrate both model-driven and data-driven methodologies. Within this evolving landscape, Physics-Informed Neural Networks (PINNs) have surfaced as innovative deep learning frameworks, exhibiting significant prowess in solving forward and inverse problems associated with nonlinear PDEs. Despite their remarkable effectiveness, the continuous evolution of Artificial Intelligence (AI) methodologies introduces several compelling alternatives that merit exploration, particularly in addressing more intricate and demanding applications. In this talk, we delve into the dynamic intersection of AI and SciML, exploring both theoretical advancements and practical challenges that lie at the forefront of this fascinating amalgamation. By navigating through novel territories, we aim to uncover opportunities for synergy between cutting-edge AI techniques and SciML, paving the way for enhanced solutions to the most complex problems in science and engineering.
References – Cuomo, S., Cola, V. S. D., Giampaolo, F., Rozza, G., Raissi, M., Piccialli, F. Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What’s next. Journal of Scientifc Computing, 2023 Cuomo, S., De Rosa, M., Giampaolo, F., Izzo, S., Di Cola, V. S. (2023). Solving groundwater flow equation using physics-informed neural networks. Computers \& Mathematics with Applications, 145, 106-123. Ascione, G., Cuomo, S. (2022). A sojourn-based approach to semi-Markov Reinforcement Learning. Journal of Scientific Computing, 92(2), 36.
Speaker: Salvatore Cuomo is Associate Professor of Numerical Analysis of Dept. Mathematics and Applications “R. Caccioppoli” (DMA), University of Naples Federico II (UNINA), Italy. In 2004 he received a Ph.D. in Applied Mathematics and Computer Sciences from the University of Naples Federico II, Italy. He has been Visiting Researcher Case Western Reserve University in Ohio USA in 2016 and Visiting Professor at the University of Geosciences, Beijing, China in 2019. He was a founder of Predico S.r.l. (http://www.predico.eu), an innovative Academic Spin-off, dealing with innovative AI solutions and data analysis. His research interests are in Applied Mathematics topics, more in detail: i) Numerical Approximation problems (theory, practice, and applications); ii) Multivariate Data Analysis; iii) Scientific Machine Learning. He has been involved in several research and development projects in the research areas of Scientific Computing, Data Science, Internet of Things. He is the author of numerous research papers (150+) in international conferences and international journals indexed in Scopus and WOS databases.
Recording: Novel Computational Approaches through Scientific Machine Learning