We would like to thank MathWorks for their support of the MIT Center for Computational Science and Engineering and in particular for their generous sponsorship of the Computational Science and Engineering prizes for outstanding Master’s and PhD research, respectively.
MathWorks Prize Winners
SM: Aaron Charous, “Dynamical Reduced-Order Models for High-Dimensional Systems”
Advisor: Pierre Lermusiaux
Aaron’s research focuses on reduced-order modeling for high-dimensional systems, accelerating numerical simulations of problems across computational physics. His primary applications of interest are both forward and inverse problems in computational acoustics, including seafloor mapping.
PhD: Hanzhang Qin, “Stochastic Control Through a Modern Lens: Applications in Supply Chain Analytics AND Logistical Systems”
Advisor: David Simchi-Levi
My doctoral research offers novel, interpretable, and high-performance analytical solutions to supply chain operations. My work can be broadly classified into three categories: (i) new methods for vehicle routing with stochastic demands, with flexible route assignment; (ii) sample-efficient algorithms for multistage stochastic inventory control; and (iii) novel optimization approaches to supply chain network design. My research also has involved collaborations with Alibaba, Accenture, Blue Yonder, and The Home Depot.
PhD: Ricardo Baptista, “Modeling and inference using triangular transport”
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.
PhD: Nisha Chandramoorthy, “An efficient algorithm for sensitivity analysis of statistics in chaotic systems”
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.
PhD: Chinmay Kulkarni
SM: Tony Tohme
PhD: Pablo Fernandez del Campo & Jon Paul Janet
PhD: Mojtaba Forghani Oozroody
Advisor: Nicolas Hadjiconstantinou
Micro/nano-scale solid-state heat transfer plays an important role in a number of important applications of practical interest, such as the design and fabrication of nano-electronic devices, thermoelectric materials, biosensors, drug delivery systems, etc. At the same time, modeling nanoscale heat transfer presents a number of scientific challenges, primarily because the convenient macroscopic description based on the Fourier heat conduction equation is no longer valid at these scales. As a result, alternative, higher fidelity descriptions have been developed. In order to capture the effects neglected by the Fourier description, these models treat matter at the sub-continuum level (e.g. molecular, coarse-grained molecular, kinetic) and thus require knowledge of material properties at a finer level than the continuum. While these properties can, in principle, be predicted using computational methods such as density functional theory (DFT) and molecular dynamics (MD), due to the high computational cost of these approaches and the approximations associated with their potential energy surface (PES) functions, experimental approaches remain very valuable. However, the inverse problem of extracting these material properties from so called thermal spectroscopy experiments (TSEs) remains an open problem. We have developed mathematical/computational formulations that provide solutions to the inverse problem of extracting this sub-continuum information through an optimization framework which aims at minimizing the discrepancies between the theoretical prediction of thermal behavior based on Monte Carlo (MC) simulations of the Boltzmann transport equation (BTE) and TSEs, which record the thermal response of the material of interest to some judiciously chosen thermal excitation.