Embark on a comprehensive exploration of the symbiotic relationship between neural networks and differential equations. This tutorial is designed to equip participants with foundational knowledge essential for comprehending the intricate interplay between these two fields. Beginning with a friendly introduction to the theory of differential equations, we seamlessly transition to a detailed examination of the motivation, mechanisms, and hands-on application of two groundbreaking architectures: Physics-Informed Neural Networks and Neural Ordinary Differential Equations. This tutorial aims at a diverse audience, ranging from first-year PhD students to seasoned and expert researchers interested in delving into this buzzing field.
Join us for an immersive experience that goes beyond theoretical discourse. By the end of the tutorial, participants will not only grasp the fundamentals of architectures combining neural networks and differential equations but will also be empowered to apply this knowledge effectively in real-world scenarios.
Link to tutorial website
Luı́s Ferrás - Assistant Professor at the Department of Mechanical Engineering (Section of Mathematics), Faculty of Engineering, University of Porto (FEUP), and a researcher at the Centre of Mathematics, University of Minho, Portugal. He received his PhD in Science and Engineering of Polymers and Composites from the University of Minho in 2012, a Ph.D. in Mathematics from the University of Chester in 2019, and was a visiting researcher at MIT in 2016 and 2017. His current research interests are numerical analysis, applied mathematics, partial and fractional differential equations, mathematical modelling, computational mechanics, computational fluid dynamics, complex viscoelastic flows, rheology, anomalous diffusion, and machine learning.
Cecı́lia Coelho - Currently pursuing a PhD in Mathematics at the University of Minho focused on enhancing the performance of real-world systems modelling (physics, biology, chemistry, finance and engineering) by exploring the symbiosis of differential equations and neural networks and the integration of expert-knowledge, in the form of explicit constraints, into neural networks.
