报告题目：Operator Learning Based Continuous Modeling for Data Science

报 告 人：赵熙乐 教授（电子科技大学）

负 责 人：张枫

报告时间：2025年12月22日（星期一）下午16:00-17:00

报告地点：数学大楼报告厅四（912）

参加人员：教师、研究生、本科生

报告摘要：Recently, continuous tensor representations, as an  alternative to classical discrete tensor representations, have emerged and attracted growing attention, which can represent data on meshgrid and beyond meshgrid. However, the potential of continuous tensor representations is still locked, as the interactions (i.e., mode-$n$ product) between the core tensor and factor matrices are essentially discrete and linear. To break this bottleneck, we define continuous mode-$n$ operators to genuinely capture continuous and nonlinear interactions. Specifically, we start from a continuous core tensor function instead of a discrete core tensor, and then cleverly leverage neural operators to directly map  the continuous core tensor function to the target continuous tensor function. Building upon the continuous mode-$n$ operators, we suggest a neural operator-based continuous tensor representation (termed as NO-CTR), which can faithfully represent complex real-world data. Theoretically, we establish that NO-CTR possesses a universal approximation capability for arbitrary continuous tensor functions defined on compact domains. To examine the capability of NO-CTR, we develop an NO-CTR-based multi-dimensional data completion framework. Extensive experiments, including on meshgrids data (multi-spectral images and color videos), on meshgrid data with different resolutions (Sentinel-2 images), and beyond meshgrid data (point clouds), demonstrate the superiority of  NO-CTR.

报告人简介：赵熙乐，电子科技大学教授/博导，中国工业与应用数学学会副秘书长。入选国家高层次青年人才、四川省学术和技术带头人、四川省杰青。第一/通讯在权威期刊SIAM系列(SIIMS和SISC)和IEEE系列(TPAMI、TIP、TSP、TKDE等)、Inverse Problems及顶会CVPR等发表研究工作。研究成果获四川省自然科学一等奖、四川省科技进步一等奖、江西省自然科学二等奖、华为火花奖、华为技术合作成果转化奖。主持国自然面上项目、中俄数学挑战基金项目、华为项目。