Lunch Seminars
(Will be held at 12 noon PST in ANB 213 or on Zoom when noted)
October 7, 2025
Jinghao Cao [Caltech]
▦ Analytical and computational methods for metamaterials ▦
Metamaterials enable wave phenomena far beyond natural materials, yet their analysis requires tools that capture high-contrast resonances, time modulation, and non-Hermitian effects. I will present recent progress on the PDE analysis of these systems, highlighting asymptotic methods and spectral theory for resonant and modulated media. On the computational side, I will introduce fast Fourier-based quadrature schemes and accelerated solvers for boundary integral formulations. These approaches make large-scale simulations of complex metamaterials feasible while retaining analytical precision. Together, they bridge rigorous mathematics and scalable computation, offering predictive models for applications in acoustics, photonics, and sustainable materials design.
October 21, 2025
Yifan Chen [University of California, Los Angeles]
▦Exploring high dimensions in dynamical sampling:flattening the scaling curve ▦
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 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.
November 4, 2025
Ousmane Kodio [University of California, Santa Barbara]
▦ Pattern Formation in Soft Mechanics
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Elastic instabilities are ubiquitous in natural and engineered systems across a wide range of scales-from supercoiled DNA and folded tissues to flower petals and deployable space structures. While great progress has been made over the past two centuries in predicting the equilibrium shapes of stressed materials, the dynamics of buckling and wrinkling remain rich with theoretical and computational challenges.
In this talk, I will present our recent theoretical and experimental efforts to understand how elastic patterns evolve when driven far from equilibrium by mechanical and hydrodynamic instabilities. In the first part, I will discuss the evolution of wrinkle patterns of confined elastic membranes floating on fluid surfaces, showing how confinement slows down pattern selection and leads to departures from the self-similar behaviors familiar in fluid mechanics. In the second part, I will demonstrate how rapid quenching can trigger the emergence of nontrivial buckling modes, and how tuning external control parameters enables the targeted selection of specific patterns. This phenomenon-reminiscent of the Kibble-Zurek mechanism in continuous non-equilibrium phase transitions-opens new avenues for the dynamical design of elastic patterns.
November 18, 2025
Chris Vales [Dartmouth College]
▦Data driven dynamical closure of partial differential equations
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I present a data driven dynamical closure scheme for problems governed by partial differential equations. The scheme employs the operator theoretic framework of quantum mechanics to embed the original classical dynamics into an infinite dimensional dynamical system, using the space of quantum states to model the unresolved degrees of freedom of the original dynamics and the quantum Bayes rule to predict their contributions to the resolved dynamics. To realize the scheme numerically, the embedded dynamics is projected to finite dimension by a positivity preserving discretization, leading to a finite dimensional representation that is invariant under the dynamical symmetries of the resolved dynamics. I show numerical results of the application of the developed scheme to a closure problem for the shallow water equations, demonstrating the accurate prediction of the resolved dynamics for out of sample initial conditions.
January 20, 2026
Angxiu Ni [University of California, Irvine]
▦ TBA ▦
TBD
February 10, 2026
Nick Boffi [Carnegie Mellon University]
▦ TBA ▦
TBD
March 3, 2026
David Mordecai [University of Chicago Booth School of Business]
▦ TBA ▦
TBD
March 24, 2026
Ali Pakzad [California State University of Northridge]
▦ TBA ▦
TBD
April 14, 2026
Silvio Barandun [Massachusetts Institute of Technology]
▦ TBA ▦
TBD
Other Seminars
(Time and location vary)
December 9, 2025
• CMX Special Seminar •
ANB 105
11:00 am
Qing Qu [University of Michigan]
▦Understanding Generalization of Deep Generative Models Requires Rethinking Underlying Low-dimensional Structures
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Diffusion models represent a remarkable new class of deep generative models, yet the mathematical principles underlying their generalization from finite training data are poorly understood. This talk offers novel theoretical insights into diffusion model generalization through the lens of "model reproducibility," revealing a surprising phase transition from memorization to generalization during training, notably occurring without the curse of dimensionality. Our theoretical framework hinges on two crucial observations: (i) the intrinsic low dimensionality of image datasets and (ii) the emergent low-rank property of the denoising autoencoder within trained neural networks. Under simplified settings, we rigorously establish that optimizing the training loss of diffusion models is mathematically equivalent to solving a canonical subspace clustering problem. This insight quantifies the minimal sample requirements for learning low-dimensional distributions, scaling linearly with the intrinsic dimension. Furthermore, by investigating this under a nonlinear two-layer network, we fully explain the memorization-to-generalization transition, highlighting inductive biases in learning dynamics and the models' strong representation learning ability. These theoretical insights have profound practical implications, enabling various applications for generation control and safety, including concept steering, watermarking, and memorization detection. This work not only advances theoretical understanding but also stimulates numerous directions for many applications in engineering and science.
Meetings and Workshops
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