Abstract: Machine learning (ML) has recently significantly advanced many domains like natural language processing, computer vision, and speech processing. Since the arrival of ChatGPT in late 2022, generative models have accelerated this rate of progress. ML tools now affect all aspects of the scientific computing endeavor, and themselves can be helped with scientific computing. I will describe various related themes of research currently underway in my group at UMD: Differentiable Modeling, Implicit Representations, the Attention mechanism in Transformer architectures, and Large Audio Language Models (a recent https://youtu.be/ut1Rl-xL-Zk talk on LALMs). This talk will focus on the use of Differentiable Models and Implicit Neural Representations in scientific modeling. Scientists previously developed forward numerical models encoding domain knowledge. Making these models differentiable allows for this knowledge to be incorporated in deep learning architectures, and allows achieving more efficient computational pipelines for tasks like parameter optimization, inverse problems, and explainable models in data-sparse domains. I will talk about our recent work in human hearing (with Leslie Famularo & Nishit Anand), room acoustics (Bowen Zhi & Armin Gerami), signal processing for spatial audio (Armin Gerami), computer graphics (Meenakshi Krishnan), and inverse problems in mathematical physics (Meenakshi Krishnan and Pranav Pulijala).
Abstract: Host genetic structure can significantly alter disease transmission dynamics and long-term disease outcomes. Past work by Beck, Keener, Hoppensteadt, Feng, and others has shown that when pathogen transmission interacts with evolving host traits—such as susceptibility, recovery, or disease-induced mortality—the resulting coupled system can exhibit novel dynamics. These models demonstrated that genetic composition within a host population can shift during an epidemic, and conversely, infection pressures can reshuffle genetic frequencies, producing true feedback between genes and epidemics.
In this talk, I will discuss a specific example of this phenomenon, focusing on the interaction between Plasmodium vivax and the Duffy antigen, a host genetic trait that confers partial protection against infection.
Abstract: Quantum computing algorithms are naturally suited to simulating quantum dynamics. Many classical dynamical models, obey different physical laws and therefore take very different forms. In this talk I will present a general mapping from linear differential equations d/dt u = L(t) u into the time dependent Schrödinger equation d/dt \psi = -i H(t) \psi, enabling off-the-shelf quantum simulation algorithms to apply. The key idea is a unitary lift: embedding the problem into a slightly larger space where the evolution is unitary, then recover the original solution via a fixed linear functional. The framework has three moving parts—encode, evolve, evaluate—and it is exact whenever simple moment-matching conditions are satisfied. The second half of my talk will present stochastic and nonlinear extensions of this framework.
Abstract: Harmonic maps from a surface to a target manifold are nonlinear analogue of harmonic functions. They form a fundamental class of objects in differential geometry, but most of the time, they are very hard to describe explicitly. In recent years, people have started to study their shape under "typical", "large" or "random" constraints. In this talk, I will give a biased survey of the developments in this field, which connect geometric analysis to dynamical systems and random matrix theory.