Wednesday 10:00 -10:50 am, https://ucr.zoom.us/j/97606227247
Organizers : Weitao Chen / Heyrim Cho / Yat Tin Chow / Qixuan Wang / Jia Gou / Mykhailo Potomkin / Yiwei Wang / Maziar Raissi / Siting Liu
Past Organizers : Mark Alber / James Kelliher / Amir Moradifam
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
Links : Interdisciplinary Center for Quantitative Modeling in Biology (ICQMB) seminar
In Fall 2025, the PDE & Applied Math seminar will be held through Zoom or in person (Skye 268). 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. Yat-Tin Chow (yattinc@ucr.edu) and Dr. Yiwei Wang (yiweiw@ucr.edu).
Fall 2025 Schedule
Oct 01 10:00 (Wed) Organizational meeting
Oct 08 10:00 (Wed) Dr. Yifan Chen (UCLA) online
Oct 15 10:00 (Wed) Dr. Seirin Lee (Kyoto University) in-person
Oct 22 10:00 (Wed) Dr. Yiping Lu (Northwestern University) online
Oct 29 10:00 (Wed) Dr. Romit Maulik (Penn State University) online
Nov 05 10:00 (Wed) Dr. Jiequn Han (Flatiron Institute) online
Nov 12 10:00 (Wed) Dr. Rongjie Lai (Purdue University) online
Nov 19 10:00 (Wed) Dr. Truong Vu (IPAM and Michigan State) online
Nov 26 10:00 (Wed) Dr. Yuming Paul Zhang (Auburn University) In person
Dec 03 10:00 (Wed) Dr. Arash Fathi (ExxonMobil Corporate Strategic Research) online
Upcoming Talks:
Past Talks:
Oct 08, 2025, 10:00 AM - 11:00 AM PT
Dr. Yifan Chen (UCLA)
Title: Exploring high dimensions in dynamical sampling: flattening the scaling curve
Abstract: Dynamical sampling of probability distributions based on model or data (i.e., generative modeling) is a central task in scientific computing and machine learning. I'll present recent work on understanding and improving algorithms in high-dimensional settings. This includes a novel "delocalization of bias" phenomenon in Langevin dynamics, where biased methods could achieve dimension-free scaling for low-dimensional marginals while unbiased methods cannot—a finding motivated by molecular dynamics simulations. I'll also briefly mention a new unbiased affine-invariant Hamiltonian sampler that outperforms popular samplers in emcee package (routinely used in astrophysics literature) in high dimensions, and introduce the optimal Lipschitz energy criteria for design of measure transport in generative modeling of multiscale scientific data, as alternative to optimal kinetic energy in optimal transport. These examples show how dimensional scaling could be flattened, allowing efficient stochastic algorithms for high-dimensional sampling and generative modeling in relevant scientific applications.
Oct 15, 2025, 10:00 AM - 11:00 AM PT
Dr. Seirin Lee (Kyoto University)
Title: Pattern Formation in Skin Diseases and Its Application to Personalized Treatment in Dermatology
Abstract: Skin diseases typically appear as visible information-skin eruptions distributed across the body. However, the biological mechanisms underlying these manifestations are often inferred from fragmented, time-point-specific data such as skin biopsies. The challenge is further compounded for human-specific conditions like urticaria, where animal models are ineffective, leaving researchers to rely heavily on in vitro experiments and sparse clinical observations.To overcome the current limitations in understanding the pathophysiology of skin diseases, we propose a novel framework that connects the visible morphology of skin eruptions with the underlying pathophysiological dynamics in vivo, using a multidisciplinary approach that integrates mathematical modeling, in vitro experiments, clinical data, and data science. Furthermore, we will introduce an innovative methodology that combines mathematical modeling with topological data analysis and machine learning, allowing for the estimation of patient-specific parameters directly from morphological patterns of skin eruptions. This framework offers a new pathway for personalized analysis and mechanistic insight into
complex skin disorders.
Bio: Prof. Seirin-Lee is a Professor of Mathematical Medicine at the Kyoto University Institute for Advanced Study (KUIAS) and the Graduate School of Medicine, Kyoto University. She obtained her PhD from Okayama University, Japan in 2010, having conducted part of her doctoral research at the Center for Mathematical Biology, University of Oxford, as a JSPS DC1 fellow. After postdoctoral training at the University of Tokyo and RIKEN, she was appointed Assistant Professor in 2014, Associate Professor in 2017, and Full Professor in 2020 at Hiroshima University. Since 2021, she has held her current position at Kyoto University. Her research focuses on pattern formation, mathematical medicine,
mathematical dermatology, spatial immunology, and applied mathematics. Website：https://ashbi.kyoto-u.ac.jp/bimed-math/
Oct 22, 2025, 10:00 AM - 11:00 AM PT
Dr. Yiping Lu (Northwestern University)
Title: Scaling Scientific Machine Learning: Integrating Theory and Numerics in Both Training and Inference
Abstract: Scaling scientific machine learning (SciML) requires overcoming bottlenecks at both training and inference. On the training side, we study the statistical convergence rate and limits of deep learning for solving elliptic PDEs from random samples. While our theory predicts optimal polynomial convergence for PINNs, optimization becomes prohibitively ill-conditioned as networks widen. By adapting descent strategies to the optimization geometry, we obtain scale-invariant training dynamics that translate polynomial convergence into concrete compute and yield compute-optimal configurations. On the inference side, I will introduce Simulation-Calibrated SciML (SCaSML), a physics-informed post-processing framework that improves surrogate models without retraining or fine-tuning. By enforcing physical laws, SCaSML delivers trustworthy corrections (via Feynman-Kac simulation) with approximate confidence intervals, achieves faster and near-optimal convergence rates, and supports online updates for digital twins. Together, these results integrate theory and numerics to enable predictable, reliable scaling of SciML in both training and inference. This is based on joint work with Lexing Ying, Jose Blanchet, Haoxuan Chen, Zexi Fan, Youheng Zhu, Shihao Yang, Jasen Lai, Sifan Wang, and Chunmei Wang.
Oct 29, 2025, 10:00 AM - 11:00 AM PT
Dr. Romit Maulik (Penn State University)
Title: No more adjoints: Calibrating chaotic dynamical systems with weak-form learning
Abstract: Deterministic chaos poses a major challenge in the data-driven learning of chaotic dynamical systems such as turbulent flows. When learning techniques utilize the mean-squared-error for parameterizing such systems, they suffer from instability due to the use of inaccurate adjoints and fail to capture the macroscopic properties of such systems. This results in a common failure mode - machine learning models for dynamical systems provide short-term accuracy but become unstable and unphysical at a larger time horizon. Consequently, the machine learning techniques provide suboptimal results in many fluid dynamics applications, such as the surrogate modeling of turbulent flows. In this work, we approach the learning of chaotic systems from a different perspective given by an integral formulation of the dynamics. By constructing a least-squares optimization for system identification after convolution with a time-dependent test function, backpropagation of gradients through time is avoided and an adjoint system computation is bypassed completely. We demonstrate that the proposed formulation leads to superior learning of both short-term as well as invariant properties of chaotic dynamical systems at much lower computational costs when compared to classical methods for time-series learning of fluid flows.
Nov 5, 2025, 10:00 AM - 11:00 AM PT
Dr. Jiequn Han (Flatiron Institute)
Title: Principled Adaptation of Score-Based Diffusion via Tilted Transport: Theory and Algorithms
Abstract: Score-based diffusion models have significantly advanced the generation of high-dimensional data across diverse domains by learning a denoising oracle (or score) from datasets. From a Bayesian perspective, these models provide a natural representation of data priors and shall also facilitate sampling from related distributions, such as posterior distributions in inverse problems or tilted distributions shaped by additional criteria. While many heuristic methods exist for such adaptations, they often lack the quantitative guarantees needed in scientific applications. This talk introduces recently developed techniques, grounded in the analysis of SDEs, that allow principled modifications of the initial distribution or drift to achieve such adaptations. By leveraging the rich information encoded in pretrained score models, the resulting algorithms can substantially enhance classical sampling methods such as Langevin Monte Carlo or Sequential Monte Carlo.
Nov 12, 2025, 10:00 AM - 11:00 AM PT
Dr. Rongjie Lai (Purdue University)
Title: Unsupervised In-context Operator Learning on Probability Measure Space — from optimal control to mean-field control
Abstract: Optimal control provides a principled framework for transforming dynamical models into intelligent decision-making, yet classical algorithms remain too expensive for real-time deployment in complex or uncertain environments. We begin by introducing a self-supervised operator learning approach that learns the solution operator of optimal control problems—directly mapping system conditions to optimal strategies. This perspective reframes control as operator learning, enabling instantaneous inference across scenarios while revealing scaling laws that quantify the trade-off between generalization accuracy and intrinsic problem dimension.
Building on this, we extend operator learning from single-agent optimal control to mean-field control (MFCs) on probability measure spaces. Existing methods for MFCs are often limited to single-instance solutions and demand substantial computational resources for each instance, hindering practical applicability. To address this, we develop an unsupervised in-context operator learning framework that learns the MFC solution operator without labeled supervision. The model takes MFC instances as input and outputs equilibria in a single forward pass, providing a discretization-free and scalable approach suitable for high-dimensional problems. Finally, I will discuss a generalization-error analysis of this transformer-based model on probability measure spaces, connecting the proposed framework to emerging theories of in-context learning and highlighting its broader implications and future directions.
Nov 19, 2025, 10:00 AM - 11:00 AM PT
Dr. Truong Xuan Vu (IPAM & MSU)
Title: Regularity of the data-to-solution maps of the generalized surface quasi-geostrophic equations
Abstract: We study a family of active scalar equations which interpolate between the 2D incompressible Euler equations and the (inviscid) surface quasi-geostrophic equation. We derive the entire family as the Euler–Arnold equations and show that the Eulerian data-to-solution maps fail to be uniformly continuous on bounded sets in Sobolev topology.
Nov 26, 2025, 10:00 AM - 11:00 AM PT
Dr. Yuming Paul Zhang (Auburn University)
Title: Chemotaxis Models on R^n: Global Solvability and Asymptotic Spreading Properties
Abstract: Chemotaxis models describe the movement of cells or organisms in response to chemical signals. In this talk, I will present recent results on a parabolic–parabolic chemotaxis system with a logistic source and chemical consumption. For both linear and nonlinear diffusion, we establish the global existence and boundedness of solutions that are not necessarily integrable. In the linear diffusion case, we show that the presence of chemicals typically does not slow down cell spreading and, under certain conditions, does not enhance it either. A key analytical ingredient is a new relation linking the cell density and chemical concentration. Numerical simulations further reveal a striking phase transition governed by the chemical sensitivity parameter. These are joint work with Zulaihat Hassan (PhD student) and Wenxian Shen.
Dec 03, 2025, 10:00 AM - 11:00 AM PT
Dr. Arash Fathi (ExxonMobil Technology and Engineering Company)
Title: From Bayesian inversion to decision: rapid screening and clustering of thousands of petroleum reservoir scenarios through ML-based flow diagnostics
Abstract: Petroleum reservoir development and production typically involves making costly decisions based on sparse and imperfect observations of the subsurface. A systematic framework for assessing the inherent uncertainties and deriving robust decisions from them remains a challenge for the industry.
Seismic inversion uses waves as probing agents to construct an image of the subsurface, typically with a resolution of tens of meters. Developments in generative artificial intelligence (e.g., Generative Adversarial Networks, or Diffusion Probabilistic Models) enable creation of plausible reservoir models at sub-seismic scales by training on geologic examples. These generative models, representing a prior probability distribution, may be conditioned with observations (e.g., seismic data, well-logs, drill stem test results (DST)) through Bayesian inversion. The resulting posterior distribution may then be sampled to inform a decision framework. However, thousands of samples could be required to identify modes of flow performance and to robustly assess the value of a prospective intervention with a reservoir. Such evaluations require flow simulations which remain computationally demanding; running simulations on thousands of subsurface models is untenable within the timeline in which decisions must be made.
We propose a framework to reduce thousands of posterior samples to only a few that would approximately summarize the range of flow behavior in the posterior. Having a reduced set of reservoir scenarios allows subject-matter-experts to apply the rigorous design and analysis still required to make decisions. This subset of posterior samples will comprise reservoirs with very different flow behavior, enabling practical consideration of the aspects of subsurface uncertainty which matter to decision making. We also highlight how the posterior is conditioned on observations, such as well-logs and DST.
The methods we propose efficiently work on thousands of samples. We demonstrate how we can incorporate incomplete information, such as not knowing the exact location of injector and producer wells in parts of the reservoir that has not been developed yet. Handling such circumstances is desired in realistic situations. Specifically, according to the layout of injector and producer wells, we partition the reservoir into sectors. For each sector, we evaluate the dynamic Lorenz coefficient, which is a scalar quantity that characterizes flow heterogeneity within the sector. We compute the dynamic Lorenz within a developed reservoir, where its well placement configuration is known. A static Lorenz coefficient, which also characterizes flow heterogeneity, is computed in areas for which a well placement is not known yet. The dynamic Lorenz calculation entails three-dimensional flow simulations, whereas flow simulations for static Lorenz are one-dimensional. Next, thousands of posterior samples produce thousands of low-dimensional vectors, each vector containing a few dynamic and static Lorenz coefficients corresponding to each sector, which are then clustered into a few groups. We then select the sample that is most representative of each cluster for further analysis.
We present a machine-learning-based surrogate model that can quickly and accurately predict the Lorenz coefficient given 3D porosity and permeability fields and injector/producer well positions. We also compare our fast-screening technique to full-physics flow simulations, which demonstrate the robustness and efficacy of our scheme.