Spring 2023

M Jan 23Organizational Meeting  
M Jan 30Nisha Chandramoorthy (Georgia Tech) Learning from dynamics and the dynamics of learning

Abstract: In this talk, we take a dynamical systems approach toward two algorithmic questions that arise from complex systems in scientific and machine learning applications. 
In the first part, we discuss the computation of linear response: the derivative of statistics or long-time averages of a dynamical system with respect to its input parameters. In many ergodic chaotic systems, such as certain turbulent fluid flows, detailed climate models, etc., linear response exists but has been notoriously difficult to compute. Apart from the curse of dimensionality, this difficulty can be attributed to a defining aspect of chaos: infinitesimal perturbations along a given orbit grow in norm exponentially. In this talk, we present a new alternative for linear response computation called the space-split sensitivity (S3) algorithm. One key component of S3 is a fast computation of conditional scores – log gradients of probability measures conditioned on the unstable manifold. 
In the second half, we discuss a problem where taking the dynamical systems approach is insightful for generalization in machine learning: the performance of a learning algorithm on unseen data. We consider local descent training algorithms that do not converge to a fixed point but whose long-time averages converge. We redefine generalization and training errors, which traditionally use loss values at fixed parameters, in terms of loss statistics. We then extend classical generalization analyses to such non-converging regimes. Further, we show how training dynamics can provide clues for generalization. 

M Feb 6 Xuefeng Xu (Tufts) Convergence of Two-level Iterative Methods
Abstract: In this talk, we introduce a new and unified convergence theory for general two-level iterative methods. In the case of the Galerkin coarse solver, we establish a succinct identity for the energy norm of the error propagation operator of two-level methods. More generally, we present some convergence estimates for two-level methods with approximate coarse solvers, including both linear and nonlinear types.
M Feb 13Malbor Asllani (Florida State University)
M Feb 20Presidents’ Day (University Holiday) No seminar
M Feb 27Zhiyuan Zhang (NYU)
M Mar 6 Lilla Orr (University of Richmond)
M Mar 13Spencer Smith (Mt. Holyoke)
M Mar 20 Spring Break No seminar
M Mar 27 Paola Sebastiani (Tufts Med)
M Apr 3Youssef Marzouk (MIT)
M Apr 10Marc Hodes (Tufts ME)Adiabatic Section Flow Resistance of Axial-Groove Heat Pipes for Slowly-Varying Meniscus Curvature

Heat pipes are essential in every modern computer because they are reliable and passive devices per their reliance on capillarity, have an effective thermal conductivity 10-to-100 times that of a solid copper rod of same diameter and possess a sufficiently-high maximum heat load. We develop a semi-analytical procedure to capture the effect of slowly varying (streamwise) meniscus curvature on the flow resistance of the adiabatic section of an axial-groove heat pipe (AGHP). The relevant small parameter is the pitch of the grooves divided by the length of the adiabatic section. Prescribed are the geometry of the AGHP, its orientation with respect to the gravity vector and relevant thermophysical properties (and, by implication, the capillary pressure driving the flow). Our requisite consideration of the evaporator and condenser sections of the AGHP invoke the standard assumption that the radius of the meniscus in them is a constant equal to that of the lands between menisci. The deviation of the meniscus geometry from a circular arc (relative to an origin at the radial center of the AGHP) in the adiabatic section is captured using a boundary perturbation, where the small parameter is the protrusion angle between the arc defining a meniscus and that corresponding to the radius of an adjacent land. A local analysis ensures the singularities at the triple contact lines are resolved. Our procedure enables more accurate prediction of the components of the capillarity-limited maximum heat load in an AGHP and the corresponding thermal resistance of its adiabatic section.

Bio: Marc Hodes earned his BS, MS, and PhD degrees in Mechanical Engineering from the University of Pittsburgh, the University of Minnesota and the Massachusetts Institute of Technology, respectively. He spent 10 years at Bell Labs Research (Murray Hill, NJ) and has spent extended periods in residence at the National Institute of Standards and Technologies (NIST) and the University of Limerick. He joined the Department of Mechanical Engineering at Tufts University in 2008 where he is a Professor and the Director of Graduate Studies. His Groups’ research there has been funded by government agencies, e.g., NSF, DARPA and DoE, and industry, e.g., Huawei and Google. Research interests are in Transport Phenomena and, over the course of his career, four thematic areas have been addressed: 1) the thermal management of electronics, 2) mass transfer in supercritical fluids, 3) analysis of thermoelectric modules, and 4) momentum, heat, mass and charge transport in the presence of apparent slip. Pertinent to the latter topic, Marc runs the Red Lotus Project with Professors Darren Crowdy and Demetrios Papageorgiou in the Department of Mathematics at Imperial College London, where he is a regular, long-term Academic Visitor. Professor Hodes is the sole- or co-author of over 50 papers in archival journals on transport phenomena. Together with Dr. Georgios Karamanis, Marc spun Transport Phenomena Technologies, LLC, out of Tufts University in 2017, which is currently focused on a Phase II NSF SBIR project on conforming vapor chambers for the thermal management of electronics and various consulting projects.
M Apr 17Patriots Day (University Holiday) No Seminar
M Apr 24 Chun Liu (IIT)
M May 1 Wenjun Zhao (Brown)