UC Merced Applied Math Colloquium (September 10, 2026, UC Merced)
Melvin Leok, UCSD
Geometric adjoint sensitivity analysis with applications to neural ODEs and PDE constrained optimization
Adjoint systems are widely used to inform control, optimization, and design in systems described by ODEs or DAEs. At the level of PDEs, advection equations and mean field games also have the structure of adjoint systems, and all adjoint systems have a Hamiltonian structure. We utilize symplectic and presymplectic geometry to investigate the properties of adjoint systems associated with ODEs and DAEs, respectively. We show that the adjoint-variational quadratic conservation laws, which are critical to adjoint sensitivity analysis, arise from (pre)symplecticity of such adjoint systems. We develop structure-preserving numerical methods for such systems using Galerkin Hamiltonian variational integrators which admit discrete analogues of these quadratic conservation laws. This can be used to train neural networks arising from time-discretizations of neural ODEs, even ones based on implicit-in-time discretization. Finally, we investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary PDE has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels.

UC Merced Scientific Computing and Data Science Seminar  (November 7,  2025, UC Merced)
Yingda Cheng, Virginia Tech
Two numerical algorithms for Tucker tensor 
In this talk, we present two algorithms associated with Tucker tensor format. The first is to obtain the Tucker tensor based on a new cross approximation we developed, called Cross^2-DEIM. This method samples a few fibers (proportionate to the multi-linear rank) in each mode in a FSTD2 fashion. We use DEIM index selection for both the main and complement index sets. It is shown to be more efficient in computing the Tucker tensor format than existing cross approximations. The second method is a solver for nonlinear tensor equations in Tucker format by Anderson Acceleration (AA). This is an extension of our prior results of low rank AA. We show the the method works well for benchmark problems, such as Bratu problem and Allen-Cahn equations. This is joint work with Daniel Appelo (VT).

UC Merced Applied Math Colloquium  (November 6, 2025, UC Merced)
Daniel Appelö, Virginia Tech
Kraus is King:  High-Order Completely Positive and Trace Preserving (CPTP) Low Rank Method for Open Quantum Computing Systems 
In this talk, we will:  1. Introduce the most basic concepts in quantum computing.  2. Briefly highlight examples of quantum algorithms where the skills of a numerical analyst can be of use.  3. Describe one type of quantum computing hardware (a transmon) and how it is modeled. 4. Show how to design high order accurate methods that exploit low rank structure in the density matrix while respecting the essential structure of the Lindblad equation. Our methods preserve complete positivity and are trace preserving.

UC Merced Scientific Computing and Data Science Seminar (September 12, 2025, UC Merced)
Lukas Einkemmer, University of Innsbruck
Higher-order structure preserving low-rank methods for kinetic problems
Low-rank methods have proven their utility as a complexity reduction technique for kinetic equations, both in the collisionless and collisional regimes (see, e.g., the recent review article https://doi.org/10.1016/j.jcp.2025.114191). Since the resulting low-rank factors are lower-dimensional, such methods can overcome the famous curse of dimensionality. This is usually the most severe constraint for performing kinetic simulations in practice. In their classic form, these methods, however, do not conserve any of the invariants or underlying conservation laws. In this talk, we will present our recent work on developing structure-preserving dynamical low-rank methods of arbitrary order.

Tutorial on modeling physical problems with AI using PINNs and PhysicsNeMo (September 10, 2025, SFU)
Charles Cheung, NVIDIA AI Technology Center HK
Modeling physical problems with AI using PINNs and PhysicsNeMo
In this tutorial, we will walk through the basic of AI methodology such as Physics Informed Neural Network (PINNs), Neural Operator, etc for solving physical problems. i.e., PDE problem. We will introduce PhysicsNeMo, an SDK for training PINNs and other AI model. A few cases study such as Simulating the Projectile Motion ODE and Forecasting Weather using Navier Stoke equation will be discussed.

PIMS Marsden Memorial Lecture (October 24, 2024, UC Merced)
Anil Hirani, University of Illinois at Urbana-Champaign
A Friendly Introduction to Calculus and Geometry on Meshes and Graphs
I will begin with some memories of how Jerry Marsden was as an advisor. In addition to the clarity and creativity of his mathematical thought, what has remained in my memory are his generosity with ideas, kindness as a human being, and his hands-on approach in the many research discussions we had. I will next introduce discrete exterior calculus (DEC) which got its start with Jerry. The remainder of the talk will be about our recent generalization of DEC to vector bundle valued forms using which I will demonstrate the basic ideas of differential geometry on simplicial complexes. I will describe all the ideas using simple examples to make the talk accessible.