Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems 

Abstract

Operator learning provides an efficient surrogate framework for solving high-dimensional partial differential equations, particularly in many-query applications such as real-time prediction and parameter studies. However, existing methods often face accuracy limitations when handling complex boundaries, long-term dynamics, and inverse problems. In this talk, I will introduce the Starter-Iterator Neural Operator (SINO), which reformulates the initialization and iterative refinement strategies of classical numerical methods within a neural-operator framework. Its frequency-domain starter captures globally stable features, while its time-domain iterator progressively reduces local solution residuals. Experiments on the Navier–Stokes equations, acoustic wave equations, super-resolution imaging, and weather forecasting demonstrate strong accuracy, generalization, and robustness. 

Our Speaker

Yuping Duan received her Ph.D. in Computational Mathematics from Nanyang Technological University, Singapore, in 2012. She worked as a Research Scientist at A*STAR’s Institute for Infocomm Research from 2012 to 2015 and joined Tianjin University as a professor in 2016. Since 2023, she has been with the School of Mathematical Sciences at Beijing Normal University. Her research interests include variational image processing, PDE-inspired deep learning, and AI for Science. She has published in journals and conferences including ACM Comput. Surv., IEEE TPAMI, IEEE TIP, IEEE TMI, IEEE TVCG, SIAM J. Imaging Sci., Inverse Probl., CVPR, and AAAI, etc.