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]
Upcoming Talks:
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 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.
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.
Past Talks:
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.