2021 MIT CCSE Symposium
March 15, 2021, 1:00 PM ET
The 2021 MIT CCSE Symposium took place in a virtual format on March 15, 2021 through a combination of Zoom and Gather platforms. Many thanks to all who took part, especially our invited speakers, Prof Nick Trefethen (Oxford), Prof. Raffaele Ferrari (MIT EAPS), Prof. Wim van Rees (MIT MechE), and Prof. Bilge Yildiz (MIT NSE and DMSE). Please see below for more information; all recorded talks are available with captioning on our YouTube channel (direct links included below).
KEYNOTE
FROM THE FARADAY CAGE TO LIGHTNING LAPLACE AND HELMHOLTZ SOLVERS
Professor Nick Trefethen, University of Oxford
Click to Watch on YouTube
Abstract
We begin with the story of the Faraday cage used for shielding electrostatic fields and electromagnetic waves. Feynman in his Lectures claims the shielding is exponential with respect to the gap between wires and that it works with wires of infinitesimal radius.
In fact, the shielding is much weaker than this and requires wires of finite radius (which is why it’s hard to see into your microwave oven). How can we compute the field inside a 2D cage?
This brings us to the numerical heart of the talk. When the boundaries are smooth, series expansions (going back to Runge in 1885) converge exponentially. When there are corners and associated singularities, the new technique of lightning Laplace and Helmholtz solvers, depending on rational or Hankel functions with poles exponentially clustered near the corners, converges root-exponentially. The name “lightning” comes from the fact that this method exploits the same mathematics that makes lightning strike at sharp points. Lightning solvers and the related AAA approximation algorithm are bringing in a new era of application of rational functions and their relatives to PDEs, conformal mapping, and other numerical problems. A variant known as “log-lightning approximation” offers the prospect of even faster exponential convergence
MIT FACULTY TALKS
Improving the physics of climate (ocean) models
Raffaele Ferrari
Cecil and Ida Green Professor of Oceanography
Click to Watch on YouTube
Flow simulations for bio-inspired underwater devices
Wim van Rees
Assistant Professor of Mechanical Engineering
Click to Watch on YouTube
Electro-Chemo-Mechanical Field Effects on Electronic Properties of Functional Oxides
Bilge Yildiz
Professor of Nuclear Science and Engineering
Professor of Materials Science and Engineering
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CSE MATHWORKS RESEARCH PRIZES
Modeling and inference using triangular transport
Ricardo Baptista
Aeronautics & Astronautics – Computational Science & Engineering PhD student
Advisor: Youssef Marzouk
My research focuses on building statistical models and inference algorithms using the framework of transport maps. Triangular transport maps are deterministic transformations between random variables that can be used to characterize and sample from non-Gaussian probability distributions, such as the posteriors in Bayesian inference problems. Learning these maps from samples, however, is challenging from a function approximation perspective. In my thesis I propose methods for learning triangular maps by exploring various forms of low-dimensional structure such as conditional independence in the distribution. I then use these maps in (sequential) inference contexts to build prior-to-posterior transformations that can be used for posterior sampling. These approaches only require access to joint samples of the unknown parameters and simulated data making them applicable to inference problems where the model is only known through a data generating process — a setting where traditional likelihood-based algorithms are often inaccessible. To demonstrate the utility of these algorithms across many domains, I apply these methods in my thesis to calibrate a phase-field model from polymer science and to perform data assimilation using an atmospheric model.
An efficient algorithm for sensitivity analysis of statistics in chaotic systems
Nisha Chandramoorthy
Mechanical Engineering – Computational Science & Engineering PhD student
Advisor: Qiqi Wang
How does long-term chaotic behavior respond to small parameter perturbations? Using detailed models, chaotic systems are frequently simulated across disciplines — from climate science to astrophysics. But, an efficient computation of parametric derivatives of their statistics or long-term averages, also known as linear response, is an open problem. The difficulty is due to an inherent feature of chaos: an exponential growth over time of infinitesimal perturbations, which renders conventional methods for sensitivity computation inapplicable. More sophisticated recent approaches, including ensemble-based and shadowing-based methods are either computationally impractical or lack convergence guarantees. We propose a novel alternative known as space-split sensitivity or S3, which evaluates linear response as an efficiently computable, provably convergent ergodic average. S3 is a first step toward enabling applications of sensitivity analysis, such as optimization, control and uncertainty quantification, in the realm of chaotic dynamics, wherein these applications remain nascent.
CCSE STUDENT POSTER SESSION BEST POSTER AWARD
Neural Closure Models for Dynamical Systems
Abhinav Gupta
Mechanical Engineering – Computational Science & Engineering PhD student
Advisor: Pierre Lermusiaux
Complex dynamical systems are used for predictions in many applications. Because of computational costs, models are however often truncated, coarsened, or aggregated. As the neglected and unresolved terms along with their interactions with the resolved ones become important, the usefulness of model predictions diminishes. We develop a novel, versatile, and rigorous methodology to learn non-Markovian closure parameterizations for low-fidelity models using data from high-fidelity simulations. The new “neural closure models” augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori-Zwanzig formulation and the inherent delays in natural dynamical systems. We demonstrate that neural closures efficiently account for truncated modes in reduced-order-models, capture the effects of subgrid-scale processes in coarse models, and augment the simplification of complex biochemical models. We show that using non-Markovian over Markovian closures improves long-term accuracy and requires smaller networks. We provide adjoint equation derivations and network architectures needed to efficiently implement the new discrete and distributed nDDEs. The performance of discrete over distributed delays in closure models is explained using information theory, and we observe an optimal amount of past information for a specified architecture. Finally, we analyze computational complexity and explain the limited additional cost due to neural closure models.
Preprint: https://arxiv.org/abs/2012.13869
MIT CCSE Virtual Symposium
Monday March 15, 2021 │ 1 PM ET