| Date | Speaker | Topic |
|---|---|---|
| T Jan 21 (2:30pm-3:30pm) (JCC 574, Math Library) |
Xue Wang (Shandong U.) |
Title: The parameter-robust preconditioner for Stokes-Darcy coupled problem. Abstract: In this talk, we consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element spaces, we establish unified well-posedness results for the coupled system under various boundary condition scenarios. Using the operator preconditioning framework, we develop a parameter-robust preconditioner that avoids the use of fractional operators. Numerical experiments employing both H(div)-conforming and nonconforming finite-element methods are presented to confirm the theoretical findings and demonstrate the robustness of the proposed block preconditioners with respect to the physical parameters and mesh size. |
| M Jan 27 |
Organizational Meeting |
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| M Feb 3 | Kyle McKee (MIT) |
Title: “Circulation and Transport in Hele-Shaw Flows”
Abstract:
Viscously-dominated flow between two closely-spaced plates is described by two-dimensional potential flow according to the standard Hele-Shaw approximation. When driven exclusively by pressure, the class of realizable potential flows is highly restricted: only flows with exactly zero circulation are possible. For example, the Hele-Shaw experiments presented in Van Dyke’s famous Album of Fluid Motion clearly illustrate this zero-circulation restriction. In the present work, we demonstrate how the Hele-Shaw cell can be used to capture flows with circulation – by using a conducting fluid and applying a constant magnetic field normal to the plates. We describe the physical picture and experimentally re-create canonical Hele-Shaw flows from Album of Fluid Motion now with arbitrary amounts of circulation induced by electromagnetic effects. The experimental flows are well described by our accompanying theoretical model. In the second part of this talk, I will segue into a related investigation of transport (advection-diffusion) in multiply-connected potential flows. By constructing a suitable conformal mapping, which is computed using recently developed methods (the AAA algorithm), we simplify the governing equations. We then formulate a boundary-integral solution to the governing equations in the mapped domain, where the exact Green’s function is known. Distinct scalings for the rate of transport (Nusselt number) under various boundary conditions are revealed.
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| M Feb 24 | Tyler Maunu (Brandeis) |
Title: “Subspace Langevin Monte Carlo“
Abstract:
Sampling from high-dimensional distributions poses significant computational challenges. We introduce Subspace Langevin Monte Carlo (SLMC), a novel and efficient sampling method that generalizes block-coordinate Langevin Monte Carlo while enabling efficient implementation of preconditioned Langevin algorithms. Our method can be viewed as a natural extension of subspace descent techniques from Euclidean space to Wasserstein space. The advantage of SLMC is its superior adaptability and computational efficiency compared to traditional Langevin Monte Carlo (LMC). Using coupling arguments, we establish error guarantees for SLMC and demonstrate its practical effectiveness through experiments on sampling from ill-conditioned distributions.
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| M Mar 3 | Tudor Manole (MIT) |
Title: “Central Limit Theorems for Smooth Optimal Transport Maps“
Abstract:
One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law in R^d onto any other given law. A large body of recent work has studied the question of estimating Brenier maps on the basis of random samples. In this talk, we derive the first such estimator which is both computationally tractable and achieves the optimal rate of convergence toward its population counterpart. We also show that this estimator enjoys a pointwise central limit theorem. This result provides a first step toward the question of performing uncertainty quantification for Brenier maps. Our proofs hinge upon a quantitative linearization of the Monge-Ampere equation governing the optimal transport problem, which may be of independent interest.
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| M Mar 10 | SeongHee Jeong (FSU) |
Title: “Optimal control for Darcy’s flow in a heterogeneous porous media” Abstract: |
| M Mar 31 | Mahya Ghandehari (U Del) | Title: Consistency of graph signal processing on large networks
Abstract: The emerging field of Graph Signal Processing (GSP) aims to develop analysis and processing techniques for data that is represented on graphs. Signal analysis on graphs relies heavily on the notion of graph Fourier transform, which is usually defined as the expansion of a signal with respect to an eigenbasis of the associated shift operator. An important question in this field is to develop a common scheme for signal analysis that can be applied to graphs that are similar in structure. The notion of similarity of graphs is beautifully captured by the recent theory of Graph Limit Theory. In this talk, we discuss how defining a graphon Fourier transform allows us to produce consistent graph signal processing for any graph sampled from the graphon. We also briefly discuss GSP on atypical samples of certain graphon using the Large Deviation Principle. |
| M Apr 14 | Yves Atchade (BU) |
Title: Assessing the importance of input variables in black-box models Abstract: Over the last two decades or so, deep learning models have produced powerful prediction algorithms that are now used in virtually every area of human activities. Despite their impressive performances, the “black-box” nature of these models remains a challenge and a significant limitation to their trustworthiness. In this work we advocate the use of posterior predictive distributions, a cornerstone of Bayesian statistics, as a new inferential framework for assessing the importance of input variables. Our framework is particularly useful in scientific applications where single-decision explanation methods often lack robustness and reproducibility. We illustrate the method with a black-box model for rainfall prediction in West Africa. |