Computational and Applied Mathematics Seminar
Spring 2026
Mondays at 2:15-3:05p.m (in-person (Room Carver 401) or ZOOM/WebEx/Teams talks)
The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the area of computational and applied mathematics.
- April 20 (Will Be Rescheduled)
Title:
Scott Hansen, Iowa State University
Abstract:
- April 27 (Virtual-ZOOM)
Title: Data-driven hyperbolic conservation laws
Lu Zhang, Rice University
Abstract: Hyperbolic conservation laws are fundamental to modeling wave propagation, fluid dynamics, and collective behavior across science and engineering. Despite their universal importance, traditional numerical solvers rely on explicitly known flux functions and parameters, which are often unavailable in realistic scenarios where only trajectory or observation data are accessible. In this talk, I will discuss our recent work in data-driven approaches for learning hyperbolic conservation laws that preserve their intrinsic physical and mathematical structures. These developments combine principles from numerical analysis, partial differential equations, and machine learning to construct models that are both predictive and faithful to the underlying conservation and stability properties of the governing equations.
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Time: Apr 27, 2026 02:15 PM Central Time (US and Canada)
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February 23
Title: Energy Transport in sub-10 nm SWCNT Bundle: From Measurements to Physics Exploration
Xinwei Wang, Mechanical Engineering, Iowa State University
Abstract: The interfacial energy transport between single-walled carbon nanotubes (SWCNTs) and the surrounding is of great science and engineering importance, but is rarely experimentally investigated. Even the few reported experimental work suffers very large uncertainties, which hinder in-depth physics understanding of the SWCNT interface energy transport. This is attributed to the very large difficulty faced in characterizing the thermal transport across a nm-wide 1D interface. This talk will cover our latest work on new technique development and characterization of the energy transport between an SWCNT bundle (<10 nm thickness) and silica substrate. Our ET-Raman technique makes it possible to simultaneously measure the thermal conductivity and interfacial thermal resistance (ITR) of the bundle with high confidence. Our study of the ITR dependence on temperature uncovers very strong phonon diffuse mismatch at the interface, which is further interpreted by our equivalent interfacial medium (EIM) theory. By studying the thermal response of the SWCNT under different modulated laser heating up to 25 MHz, we are able to distinguish the optical and acoustic phonon temperatures of SWCNTs, which is the first time to date. It uncovers very strong phonon mode-wide thermal nonequilibrium, and cryogenic temperature-suppressed energy coupling factor between optical and acoustic phonons.
- March 02
Title: Conservative cell-average-based neural network method for nonlinear conservation laws
Ty Kroells, Iowa State University
Abstract: This talk introduces the recently developed Cell-Average-Based Neural Network (CANN). The method utilizes the integral or weak formulation of partial differential equations and is inspired by finite volume schemes. The structure of the CANN network is designed to align with traditional one-step methods, with the well-trained network parameters serving as the scheme coefficients for an explicit one-step method. Unlike conventional numerical methods, the CANN approach is not constrained by small time-step CFL conditions, allowing for significantly larger time steps to be used for evolving solutions in an explicit manner. This results in a highly efficient and rapid method. We present a conservative version of the CANN method for nonlinear conservation laws. This conservative approach ensures mass conservation and effectively captures physically relevant entropy solutions, including phenomena such as contact discontinuities, shock collisions, and interactions between shocks and rarefaction waves.
- March 09 (Virtual)
Title: Data-driven modeling and topological data analysis: from cell fate dynamics to protein design
Yuchi Qiu, University of Illinois, Chicago
Abstract: Artificial intelligence (AI) is powerful in analyzing complex and noisy biological data, yet its limited interpretability hinders our understanding of intricate functions and dynamics. In this talk, we aim to address these challenges by integrating AI with data-driven modeling and topological data analysis (TDA) to investigate the dynamics and topological structure of biological systems. First, we will present our approaches for deciphering cell fate dynamics through the interplay of gene regulation and cell-cell communications. Specifically, we develop a deep learning-based unbalanced dynamic optimal transport model that reconstructs continuous cellular dynamics from time-course single-cell transcriptomic snapshots. Building on this framework, we further infer the temporal regulatory programs linking gene regulation and cell-cell communication to reconstruct signaling flows across cells. Last, we apply a TDA method, persistent Laplacian, to protein design and develop a hierarchical clustering-based active learning strategy for decision making.
- March 23 (Virtual--WebEx)
Title: Mathematical AI Models for Biological Data and Drug Design
Hongsong Feng, University of North Carolina at Charlotte
Abstract: Although artificial intelligence (AI) has transformed biological sciences in the past decade, challenges remain in AI-based drug discovery due to the intricate complexity, excessively high dimensionality, and multiscale interactions of biological systems. We address these challenges with a mathematical AI strategy. Specifically, we employ algebraic topology, geometric topology, commutative algebra, differential geometry to simplify biological complexity, reduce dimensionality, and decipher biological interactions. The strengths of our mathematical AI models are demonstrated through various benchmark biological problems, including predictions of protein flexibility, protein-ligand binding affinities, clustering of single-cell RNA sequencing data, multitarget drug generation, and more.
- April 06
Title: Mathematical ML and ML for K-12 Math: Alternating GD & Minimization (AltGDmin) for Secure Federated Low Rank Matrix Learning and MRI and CyMath
Namrata Vaswani, Electrical And Computer Engineering and Mathematics, Iowa State University
Abstract: This talk will consist of two parts. The first will describe my research on the AltGDmin algorithm for Byzantine-resilient distributed structured matrix learning. Details below. The second part will be on “ML for better K-12 Math”. Here I will talk about how we (MI-STEM professors, researchers, professionals) need to start thinking about fixing the early math skills of school students, particularly those without such support at home, in order to improve the likelihood of their choosing and succeeding in math-intensive STEM. I will briefly talk about the CyMath program that I direct at ISU and how the use of ML-enabled math learning apps such as ALEKS or Khan Academy can make this task easier to accomplish for non-teachers.
Modern distributed and federated learning systems are vulnerable to various kinds of adversarial attacks. Byzantine attacks are one of the most difficult attacks to deal with: since these are model update poisoning attacks (poison algorithm iterates of the attacked nodes), and since the adversarial nodes are omniscient and can collude. We introduce provably Byzantine-resilient and communication-efficient algorithms for solving multiple different federated low-rank (LR) matrix learning problems – LR Column-wise Sensing, LR Phase Retrieval, (Robust) LR matrix completion and Robust PCA – all of which involve solving a partly-decoupled optimization problem, and all involve dealing with data heterogeneity across nodes. These problems find important applications in parameter efficient fine-tuning of LLMs, recommender system design, multi-task representation learning for few-shot learning, federated sketching, accelerated dynamic MRI, and Fourier ptychography. Alternating GD and minimization (AltGDmin), introduced in our recent work, is a novel faster, and more communication-efficient, alternative to Alternating Minimization (AltMin) for partly-decoupled optimization problems. These are problems in which the set of optimization variables can be split into two, or more, subsets such that the optimization with respect to at least one subset, keeping the other fixed, is decoupled. We also describe Byz-AltGDmin which is a provably Byzantine-resilient modification. Finally, if time permits, we will show real-data experimental results on the advantage (speed and generality) of AltGDmin-based methods over the existing state-of-the-art within dynamic MRI.
Bio: Dr. Namrata Vaswani is a Professor of Electrical and Computer Engineering, and the Anderlik Professor of Engineering at Iowa State University. She also holds a courtesy professorship in the department of Mathematics. She received a Ph.D. in 2004 from the University of Maryland, College Park and a B.Tech. from Indian Institute of Technology (IIT-Delhi) in 1999. Her research is in statistical ML and signal processing, and in imaging (MRI and video analytics). Vaswani is also the director of the CyMath K-12 math tutoring and support program at Iowa State. She is a recipient of the IEEE Signal Processing Society (SPS) Best Paper Award (2014), the University of Maryland ECE Distinguished Alumni Award (2019), and the Iowa State Mid-Career Achievement in Research Award (2019). Vaswani is an AAAS Fellow (class of 2023) and an IEEE Fellow (class of 2019).
- April 15 (Virtual-ZOOM, 11am-12PM)
Title: Using AI Tools Effectively for Applied Mathematical Research
Xiangxiong Zhang, Purdue University
Abstract: I am not an expert in AI, and this talk is not about AI for mathematics. Rather, it is a practical account of my own experience as a computational mathematician using modern AI agent tools in day-to-day research. Current AI tools do not replace researchers, but when used correctly, they can reliably automate substantial portions of the research workflow. In this talk, I will discuss how these tools can be used effectively to assist mathematical research, based on what has worked (and not worked) in my own practice. The focus will be on practical strategies for obtaining trustworthy results, avoiding common pitfalls, and integrating AI into research in a controlled and verifiable way. I will present several examples from my own work, including using AI to prepare more efficiently for attending seminars by digesting relevant papers in advance, as well as how I collaborated with AI tools to produce a research paper. All examples will come from computational mathematics. Finally, I will briefly share my perspective on how students can use AI tools effectively for learning, emphasizing strategies that promote deeper understanding rather than superficial reliance.