CSE DSI Machine Learning Seminar with Lu Lu (Statistics, Yale)

Learning neural operators accurately, efficiently, reliably, and in one shot

As an emerging paradigm in scientific machine learning, deep neural operators pioneered by us can learn nonlinear operators of complex dynamic systems via neural networks. In this talk, I will present the vanilla deep operator network (DeepONet) and several extensions of DeepONet, such as DeepONet with Fourier decoder layers and manifold operator learning. I will demonstrate their effectiveness on diverse multiphysics and multiscale 3D problems, such as geological carbon sequestration, full waveform inversion, and topology optimization. Deep learning models are usually limited to interpolation scenarios, and I will quantify the extrapolation complexity and develop a complete workflow to address the challenge of extrapolation for deep neural operators. Moreover, I will present the first operator learning method that requires only one PDE solution, i.e., one-shot learning, by introducing a new concept of local solution operator based on the principle of locality of PDEs. I will also present the first systematic study of federated scientific machine learning (FedSciML) for approximating functions and solving PDEs with data heterogeneity. Lastly, I will present FunDiff, a novel framework of diffusion models over function spaces for physics-informed generative modeling.

Lu Lu is an Assistant Professor in the Department of Statistics and Data Science at Yale University. Prior to joining Yale, he was an Assistant Professor in the Department of Chemical and Biomolecular Engineering at the University of Pennsylvania from 2021 to 2023, and an Applied Mathematics Instructor in the Department of Mathematics at Massachusetts Institute of Technology 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 in Mechanical Engineering, Economics, and Computer Science 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. His broad research interests focus on multiscale modeling and high performance computing for physical and biological systems. He has received the Department of Energy Early Career Award and MIT Technology Review Innovators under 35 Asia Pacific.