Distinguished Seminar in Computational Science and EngineeringMarch 20, 2025, 12-1PM45-432 in Building 45 and Zoom WebinarMathematics of Digital Twins and Transfer LearningAlexandre Tartakovsky Professor Department of Civil and Environmental Engineering University of Illinois at Urbana-ChampaignAbstract:A digital twin for physical systems governed by partial differential equations (PDEs) is a real-time virtual replica, capable of simulating system behavior under various conditions. This talk will present the mathematical foundation for developing digital twins as surrogate models for PDE systems. We require the surrogate model to support real-time inference, be differentiable with respect to control parameters, and be adaptable to new conditions with a reasonable amount of data. We employ the KL-NN method as the surrogate model, treating the PDE state and control parameters as stochastic processes, which are decomposed into mean functions and fluctuations. The fluctuations are approximated with zero-mean truncated Karhunen–Loève expansion (KLE), enabling a reduced-order representation. A parameterized mapping then relates KLE coefficients of control parameters to KLE coefficients of the state.To adapt the KL-NN surrogate model trained under one set of conditions (source) to another set (target), we apply moment equation analysis to investigate the transferability of the KL-NN surrogate components. The analysis shows that for linear PDEs, all components of the KL-NN surrogate model can be transferred, except for the mean function, which can be learned with just one additional simulation under the target mean condition. For certain nonlinear PDE models—specifically when the variability in the random control parameters is small—the eigenfunctions can also be transferred. In these cases, the mean function and the parameters of the mapping between KLE coefficients can be retrained using “few-shot” learning. We provide examples, including linear and nonlinear time-dependent diffusion equations, demonstrating that transfer learning for the KL-NN model can be achieved with minimal solution samples under target conditions.Bio:Alexandre Tartakovsky is a Professor in the Department of Civil and Environmental Engineering at the University of Illinois Urbana-Champaign and a Lab Fellow at the Pacific Northwest National Laboratory. His research focuses on scientific machine learning, multiscale mathematics, uncertainty quantification, and Lagrangian particle methods. Dr. Tartakovsky received master’s degree in applied mathematics from Kazan State University in Russia and Ph.D. in Hydrology from the University of Arizona. Prior to joining PNNL, he was a postdoctoral research scientist at the Idaho National Laboratory.

PhDs and postdocs are often more comfortable talking about technical skills versus their non-technical experiences. In an approachable format, learn the importance of becoming an expert in yourself and strategies to communicate your stories to a target audience. We’ll discuss foundational components in a brief presentation followed by an opportunity to address your questions.This CAPD event is open to MIT PhDs, postdocs, and alumni.

MIT Free English Class is for international students, sholars, spouses. Twenty seven years ago we created a community to welcome the nations to MIT and assist with language and friendship. Join our Tuesday/Thursday conversation classes around tables inside W11-190.

Ten minutes for your mind@2:50 every day at 2:50 pm in multiple time zones:Europa@2:50, EET, Athens, Helsinki (UTC+2) (7:50 am EST) https://us02web.zoom.us/j/88298032734Atlantica@2:50, EST, New York, Toronto (UTC-4) https://us02web.zoom.us/j/85349851047Pacifica@2:50, PST, Los Angeles, Vancouver (UTC=7) (5:50 pm EST) https://us02web.zoom.us/j/85743543699Almost everything works better again if you unplug it for a bit, including your mind. Stop by and unplug. Get the benefits of mindfulness without the fuss.@2:50 meets at the same time every single day for ten minutes of quiet together.No pre-requisite, no registration needed.Visit the website to view all @2:50 time zones each day.at250.org or at250.mit.edu

Speaker: Zihong Chen (MIT)Title: Boundary Dehn twists on symplectic 4-manifold with Seifert-fibered boundaryAbstract: In this talk I will discuss the following result: the boundary Dehn twist on a symplectic filling M of a Seifert-fibered rational homology 3-sphere (negatively-oriented, equipped with its canonical contact structure) has infinite order in the smooth mapping class group of $M$ (fixing the boundary) provided $b^+ (M) > 0$. This result has applications to the monodromy of surface singularities, such as: the monodromy diffeomorphism of a weighted-homogeneous isolated hypersurface singularity of complex dimension 2 has infinite order in the smooth mapping class group of its Milnor fiber, provided the singularity is not ADE. (In turn, the ADE singularities have finite order monodromy by Brieskorn’s Simultaneous Resolution Theorem.)The proof involves studying the Seiberg—Witten equation in 1-parametric families of 4-manifolds, by a combination of techniques from Floer homology, symplectic and contact geometry. I will also explain how to use our techniques to obstruct boundary Dehn twists from factorising as products of Seidel—Dehn twists on Lagrangian 2-spheres and/or their squares, in both the smooth and/or symplectic mapping class groups.This is based on joint work with Hokuto Konno, Jianfeng Lin and Anubhav Mukherjee.

Talk Title: Cognitive tools for making the invisible visibleAbstract: In the 17th century, the Cartesian coordinate system was groundbreaking. It exposed the unity between algebra and geometry, accelerating the development of the math that took humans to the moon. It was not just another concept, but a cognitive tool that people could wield to express abstract ideas in visual form, thereby expanding their capacity to think and generate new insights about a variety of other problems. Research in my lab aims to uncover the psychological mechanisms that explain how humans have come to deploy these technologies in such innovative ways to learn, share knowledge, and create new things. In the first part of this talk, I will provide an overview of our work investigating drawing — one of humanity's most enduring and versatile tools. Across several empirical and computational studies, I’ll argue that drawing not only provides a window into how people perceive and understand the visual world, but also accelerates the ability to learn and communicate useful abstractions. In the second part of this talk, I will preview an emerging line of work in our lab investigating the cognitive foundations of data visualization — one of humanity's more recent inventions for making the invisible visible. I will close by noting the broader implications of embracing the continually expanding suite of cognitive tools for accelerating the development of new technologies for augmenting human intelligence.Bio: Judy Fan is an Assistant Professor of Psychology at Stanford University. Research in her lab aims to reverse engineer the human cognitive toolkit, especially how people use physical representations of thought to learn, communicate, and solve problems. Towards this end, her lab employs converging approaches from cognitive science, computational neuroscience, and artificial intelligence. She held a previous faculty appointment at the University of California, San Diego, earned her PhD in Psychology from Princeton University, and received her AB in Neurobiology and Statistics from Harvard College.This talk is co-sponsored by The MIT Quest for Intelligence and the Center for Brains, Minds, and Machines.Webinar Link:https://us02web.zoom.us/j/89002014229?pwd=bzZuZGh6cVhOSjJ6TlNZVHgrRnNaQT09Followed by a reception with food and drink in 3rd floor atrium