Speaker: Lu Lu, Department of Statistics and Data Science, Yale University; Department of Chemical and Environmental Engineering, Yale University

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

MS Teams : A MS Teams link will appear here, an hour before the talk. For best experince, please download the app.

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Fractional partial differential equation, Physics-informed neural network, Neural operator, Software

Abstract: Solving fractional partial differential equations (PDEs) can be challenging because fractional operators are nonlocal and computationally expensive. This talk will introduce scientific machine learning methods for fractional PDEs, focusing on fractional physics-informed neural networks (fPINNs) [1], which incorporate fractional PDE constraints into neural network training for forward and inverse problems; DeepONet [2], a neural operator framework for learning solution operators of families of fractional PDEs; and DeepXDE [3, 4], an open-source software library that supports PINNs, neural operators, and related methods. The goal is to present the main ideas, advantages, and practical implementation aspects of these approaches, and to show how they provide flexible tools for solving and learning fractional models. 

Biography: Lu Lu is an Assistant Professor in Departments of Statistics and Data Science and of Chemical and Environmental Engineering at Yale University. Prior to joining Yale, he was an Assistant Professor in Department of Chemical and Biomolecular Engineering at University of Pennsylvania from 2021 to 2023, and an Applied Mathematics Instructor in Department of Mathematics at MIT from 2020 to 2021. He obtained his Ph.D. degree in Applied Mathematics at Brown University in 2020, master's degrees in Engineering, Applied Mathematics, and Computer Science at Brown University, and bachelor's degrees at Tsinghua University in 2013. His current research interest lies in scientific machine learning and artificial intelligence for science, including theory, algorithms, software, and its applications to engineering, physical, and biological problems. He has received the MIT Technology Review Innovators under 35 Asia Pacific, DOE Early Career Award, Mathematics Young Investigator Award from MDPI, and Joukowsky Family Foundation Outstanding Dissertation Award.

Bibliography

[1] G. Pang, L. Lu, & G. E. Karniadakis. fPINNs: Fractional physics-informed neural networks. SIAM Journal on Scientific Computing, 41 (4), A2603–A2626, 2019.

[2] L. Lu, P. Jin, G. Pang, Z. Zhang, & G. E. Karniadakis. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature Machine Intelligence, 3 (3), 218–229, 2021.

[3] L. Lu, X. Meng, Z. Mao, & G. E. Karniadakis. DeepXDE: A deep learning library for solving differential equations. SIAM Review, 63 (1), 208–228, 2021.

[4] DeepXDE Website: https://deepxde.readthedocs.io