Wednesday 11:00 -11:50, https://ucr.zoom.us/j/97606227247
Organizers : Weitao Chen / Yat Tin Chow / Qixuan Wang / Jia Gou / Mykhailo Potomkin / Yiwei Wang / Maziar Raissi / Siting Liu / Thomas Bury
Past Organizers : Mark Alber / James Kelliher / Amir Moradifam / Heyrim Cho
Archives: Fall 2019 / Winter 2020 / Spring 2020 / Fall 2020 / Winter 2021 / Spring 2021 / Fall 2021 / Winter 2022 / Spring 2022 / Fall 2022 / Winter 2023 / Spring 2023 / Fall 2023 / Winter 2024 / Spring 2024 /Fall 2024 / Winter 2025 / Spring 2025 / Fall 2025 / Winter 2026/ Spring_2026
Links : Interdisciplinary Center for Quantitative Modeling in Biology (ICQMB) seminar
In Spring 2026, the PDE & Applied Math Seminar will be offered in hybrid format: speakers may present either via Zoom or in person in Skye 285 (Computer Lab), and a Zoom option will be available for all talks.
Specific information about the format of each talk will be provided in the email announcement and posted below. If you're interested in attending the seminar, please contact Dr. Siting Liu (sitingl@ucr.edu) and Dr. Maziar Raissi (maziarr@ucr.edu).
Spring 2026 Schedule
Apr 8, Jimmie Adriazola, Arizona State University [in person]
Apr 15, Domenico Santoro, University of Western Ontario, [in person]
Apr 22, Jiajia Yu, Duke University, [in person]
Apr 29, Ricardo Baptista, University of Toronto, [in person]
May 6, Lu Zhang, Rice University [in person]
May 13, No seminar, Colloquium talk by Dr. Alex Mogilner, New York University
May 20, Mo Zhou, UCLA [zoom only]
May 27, Paula Chen, US Naval Research Laboratory [zoom only]
Jun 3, Chunyin Siu (Alex) , Stanford University [zoom only]
Jun 10, Ziyu Chen, University of North Carolina at Chapel Hill [in person], co-host with ICQMB Center Seminar
Upcoming Talks:
June 10th, 11:00am-11:50am, zoom
Dr. Ziyu Chen, University of North Carolina at Chapel Hill
Title: Lipschitz-Regularized Probability Divergences and Applications to Generative Modeling
Abstract: Probability divergences such as the Kullback–Leibler (KL) divergence provide an information-theoretic measure of discrepancy between two probability distributions, but they require absolute continuity of one distribution with respect to the other. This assumption often fails for empirical measures or distributions supported on low-dimensional structures. In contrast, Wasserstein metrics quantify the transport cost between distributions without requiring absolute continuity, but they can break down when one of the distributions is heavy-tailed. Lipschitz-regularized divergences, introduced in Dupuis and Mao (2022) as a special class of (f, \Gamma)-divergences proposed in Birrell et al. (2022), combine f-divergences and the Wasserstein-1 metric via their variational (dual) formulations and inherit the advantages of both. In this talk, I will present key theoretical properties of Lipschitz-regularized f-divergences and demonstrate how these results lead to robust generative modeling methods under minimal assumptions on the target data distribution, including cases with heavy tails, low-dimensional structure, or fractal-like support.
Past Talks:
June 3rd, 11:00am-11:50am, zoom
Dr. Chunyin Siu, Stanford University School of Medicine
Title: Topology in Complex Systems - Random Graphs, Tensors, and Neuroscience
Abstract: Topological data analysis has emerged as a powerful framework for studying complex systems, yet fundamental questions remain about the topological signatures of different generative mechanisms and their interpretability in real-world data. In this talk, I will present results on the topology of complex systems, spanning theoretical models and biological applications.
I will begin with my work on the Betti numbers and homotopy groups of preferential attachment graphs, demonstrating that small holes dominate the topological structure. This theoretical prediction is subsequently validated in empirical network data. (https://doi.org/10.1017/apr.2024.66, joint with Gennady Samorodnitsky, Christina Lee Yu, Rongyi He; https://doi.org/10.1137/24M1693179) I will then present a theorem on the persistent diagram of positive orthogonally decomposable tensors, establishing topological properties for another class of structured mathematical objects. (In preparation)
These theoretical results provide null models against which to interpret topology in real-world complex systems. I will discuss my recent work on the topology of brain dynamics and its behavioral correlates (https://doi.org/10.64898/2026.04.30.722005, joint with Saad Pirzada, Cameron Glick, Richard Betzel, Giovanni Petri, Jeremy R Manning, Leanne Williams, Manish Saggar), as well as ongoing research characterizing the geometric shape of the space of brain functions. Together, these investigations illustrate how topological methods can bridge mathematical theory and the structure of biological complex systems.
May 27th, 11:00am-11:50am, zoom
Dr. Paula Chen, US Naval Research Laboratory
Title: Algorithms and Differential Game Representations for Exploring Nonconvex Pareto Fronts in High Dimensions
Abstract: We develop a new Hamiton-Jacobi (HJ) and differential game approach for exploring the Pareto front of (constrained) multi-objective optimization (MOO) problems. Given a preference function, we embed the scalarized MOO problem into the value function of a parameterized zero-sum game, whose upper value solves a first-order HJ equation that admits a Hopf-Lax representation formula. For each parameter value, this representation yields an inner minimizer that can be interpreted as an approximate solution to a shifted scalarization of the original MOO problem. Under mild assumptions, the resulting family of solutions maps to a dense subset of the weak Pareto front. Finally, we propose a primal-dual algorithm based on this approach for solving the corresponding optimality system. Numerical experiments show that our algorithm mitigates the curse of dimensionality (scaling polynomially with the dimension of the decision and objective spaces) and is able to expose continuous curves along nonconvex Pareto fronts in 100D in just ~100 seconds. Distribution Statement A. Approved for Public Release; Distribution is Unlimited. PR 26-0024.
May 20th, 11:00am-11:50am, zoom
Dr. Mo Zhou, University of California, Los Angeles
Title: Bridging Optimal Control and Machine Learning
Abstract: This talk examines the intersection of machine learning and optimal control through the development of scalable algorithms with rigorous theoretical guarantees. The first part presents learning-based frameworks for stochastic optimal control, with an emphasis on actor–critic methods that connect reinforcement learning and continuous-time control, together with their extensions to multi-agent mean-field games. The second part illustrates how control-theoretic principles can advance modern machine learning by viewing generative models as controlled probability flows, leading to an efficient and structure-preserving formulation, score-based neural ODEs and normalizing flows. Together, these results outline a unified framework in which machine learning and control mutually reinforce one another, offering new computational tools and analytical insights for scientific computing.
April 29th, 11:00am-11:50am, Skye285 & zoom
Dr. Ricardo Baptista, University of Toronto
Title: Processing Language, Images and Other Data Modalities
Abstract: A fundamental problem in machine learning is how to simultaneously deploy data from different sources, such as audio, images, text, and video, collectively known as multimodal data. In this talk, we will present a mathematical framework for studying this question, focusing primarily on text and images. We will begin by describing how large language models (LLMs) operate, addressing the challenging issue of using real-number algorithms to process language. We will then focus on the canonical problem of measuring alignment between image and text data, which is performed using contrastive learning. From a mathematical perspective, a unifying theme underlying this work is the minimization of divergences defined on spaces of probability measures. This probabilistic perspective naturally suggests generalizations, including novel loss functions and the use of alternative metrics for measuring alignment. Lastly, the proposed framework is examined through experiments in information science and a data assimilation application.
May 6th, 11:00am-11:50am, Skye285 & zoom
Dr. Lu Zhang, Rice University
Title: Data-driven hyperbolic conservation laws
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.
April 22th, 11:00am-11:50am, Skye285 & zoom
Dr. Jiajia Yu, Duke University
Title: Learning in Mean-Field Games
Abstract: Mean-field games (MFGs) study systems with a continuum of indistinguishable, non-cooperative agents, with applications ranging from physical, biological, financial, and social systems to more recent connections with reinforcement learning and generative modeling. In these models, an individual’s optimal control depends on the evolving population distribution, and a central object of interest is the mean-field Nash equilibrium (MFNE), where individual behavior is consistent with the resulting population dynamics. Computing the MFNE leads to a highly nonlinear problem and is particularly challenging in the high-dimensional settings that arise in many applications.
In this talk, I will present our recent work on developing a scalable, structure-preserving solver for MFNE. I will first highlight the structure of MFNEs through the concept of best response, and show how this perspective clarifies both the equilibrium problem and the behavior of the fictitious play algorithm. Motivated by these insights, I will introduce a Lagrangian reformulation and use flow-matching ideas from machine learning to adapt fictitious play for scalable high-dimensional computation. If time permits, I will conclude by discussing applications, recent progress, and many exciting open problems in inverse mean-field games.
This talk is based on joint work with Xiuyuan Cheng, Jian-Guo Liu, and Hongkai Zhao at Duke University, and Junghwan Lee and Yao Xie at the Georgia Institute of Technology.
April 15th, 11:00am-11:50am, Skye285 & zoom
Dr. Domenico Santoro, USP Technologies and Western University, Canada.
Title: From Equations to Infrastructure: How Applied Mathematics Supports Innovation in Water Technologies
Abstract: Water and wastewater systems are often viewed as collections of physical assets (pipes, tanks, and treatment units) but in practice they behave as complex, dynamic systems shaped by transport, reaction, and operational variability. This seminar will present how applied mathematics supports the development and deployment of real-world water technologies at USP Technologies, with a focus on bridging theory and industrial practice. Through selected case studies, the talk will illustrate how modeling tools, ranging from simplified process representations to computational fluid dynamics (CFD), are used to better understand, design, and optimize treatment systems. Examples will include sewer networks behaving as distributed reactive systems, advanced chemical treatment processes, intensified biological treatment configurations, and real-time control strategies for disinfection.
Attention will be given to how models are adapted to deal with practical constraints such as limited data, system variability, and scale-up from laboratory to full-scale applications. The seminar will also highlight the growing role of integrating mechanistic understanding with data-driven approaches to support decision-making and process optimization. The overall goal is to show how different disciplines can contribute to solving impactful engineering challenges, not only by developing models, but by making them robust, usable, and relevant in real operational environments.
April 8th, 11:00am-11:50am, Skye285 & zoom
Dr. Jimmie Adriazola, Arizona State University
Title: Probing Nonlinear Dynamics with Lax Pairs
Abstract: Many nonlinear dynamical systems of interest are not exactly integrable, yet their behavior is often strongly shaped by a geometric flow associated with a Lax pair of operators. This talk is about how to computationally probe nonlinear dynamics through that operator structure. I will discuss two complementary frameworks. The first, Sparse Identification of Lax Operators (SILO), is a data-driven method for discovering candidate Lax operators directly from observed dynamics. The second, Proximal Spectral Coordinates (PROSPECTs), uses state-dependent spectral charts associated with a proximal operator family to build reduced models that remain dynamically meaningful over long times. Together, these ideas suggest an operator-based approach to detecting hidden integrable structure and exploiting it for computation in nonlinear PDEs.