Part 1: Structure Without a Grid: Extracting and Tracking Topological Features in Continuous Models of Scientific Data
Speaker: Dr. Bei Wang Phillips (Associate Professor at University of Utah)

Part 2: Enhancing Operator Learning with Invertible Architectures and Multi-Functional Diffusion
Speaker: Dr. Shandian Zhe (Associate Professor at Kahlert School of Computing, University of Utah)

12pm-1pm MT (1pm-2pm CT)
Zoom & in person at University of Utah WEB 3780 (Evans Conference Room)!

Zoom: https://utexas.zoom.us/j/88630218251?pwd=OLbanw8MQXVnsiho5qaGjdPKxe98Ea.1
Meeting ID: 886 3021 8251 / Passcode: 684859

Part 1 Abstract: Large-scale scientific simulations — in fluid dynamics, climate, combustion, and beyond — are increasingly outpacing our ability to store, transfer, and analyze them at full resolution. A growing alternative to storing raw discretized grids is the continuous implicit model, such as multivariate functional approximation (MFA) and implicit neural representations (INRs). These represent a simulation's fields as continuous functions that can be queried at arbitrary points and differentiated exactly, with no resampling required. This talk presents a line of work building the topological data analysis toolkit needed to make such continuous representations practically useful. First, we show how to extract critical points — the maxima, minima, and saddles that organize a scalar field's structure — directly from an MFA model, without ever discretizing back to a grid. Second, we extend this to richer topological descriptors: contours (isosurfaces), Jacobi sets (the shared critical structure between two co-registered fields, useful for comparing related quantities like pressure and temperature), and ridge-valley graphs, which trace filamentary or ridge-like structure in the data. Third, we introduce a framework for tracking these topological features continuously through time or parameter space, following critical points as smooth trajectories using the model's own derivatives rather than resampling frame by frame — avoiding the aliasing artifacts that plague discrete feature tracking. Together, these methods point toward a workflow in which large-scale data is stored once as a continuous functional surrogate, and structural analysis — feature detection, comparison across fields, and evolution over time — happens directly on that surrogate, at whatever resolution the analysis demands. This work is joint with Guanqun Ma, David Lenz, Tom Peterka, Hanqi Guo, Kaiyuan Tang, and Chaoli Wang.

Bio: Dr. Bei Wang Phillips is an Associate Professor in the School of Computing, an Adjunct Associate Professor in the Department of Mathematics, and a faculty member of the Scientific Computing and Imaging (SCI) Institute at the University of Utah. She received her Ph.D. in Computer Science from Duke University. Her research integrates topological, geometric, statistical, data mining, and machine learning methods with visualization to enable scientific discovery in large and complex datasets. She is a recipient of a DOE Early Career Research Program award (2020), an NSF CAREER award (2022), and a Presidential Early Career Award for Scientists and Engineers (PECASE) in 2024.

Part 2 Abstract: Physical systems often involve complex interactions among multiple functions, making data-driven operator learning a powerful approach for developing effective surrogate models.

This talk presents our recent work on enhancing operator learning. First, we introduce invertible neural operators that address forward and inverse problems simultaneously through a mutual-regularizing, parameter-sharing framework, improving performance on both tasks. Next, we present a multi-functional diffusion framework, a versatile approach to surrogate modeling. The framework embeds neural operators within a denoising model, with noise modeled by Gaussian processes. It employs a random-mask-based, zero-regularized denoising objective, enabling flexible and efficient arbitrary conditional diffusion for multi-physics emulation.

Bio: Dr. Shandian Zhe is an Associate Professor at the Kahlert School of Computing, University of Utah. His research focuses on probabilistic machine learning, AI for science, and complex structured data analysis. Dr. Zhe's work encompasses a range of topics including physics-informed machine learning, operator learning, Gaussian process, governing PDE discovery, tensor decomposition, temporal and spatiotemporal event analysis, and foundational models. He has authored over 90 publications, the majority of which have been featured in leading machine learning/AI conferences and journals in computational physics, such as ICML, NeurIPS, AISTATS, and Journal of Computational Physics.

Dr. Zhe earned his Ph.D. from Purdue University in 2017, during which he was awarded the Google Ph.D. Fellowship in machine learning. He subsequently joined the University of Utah in 2018 and was honored with the NSF CAREER Award in 2021.