Massachusetts Institute of Technology

Cambridge, MA

Cross-pollinating ideas in applied mathematics

The MIT chapter of the Society for Applied and Industrial Mathematics (SIAM) welcomes undergraduate and graduate students interested in applied mathematics and computational science.

Sign up to give a seminar/talk, or join our mailing list for seminars, workshops, and more!

Recent + Upcoming

May 15, [4-5PM, 3-133]

Advancing the theory and applications of Lagrangian Coherent Structures methods for oceanic surface flows

Margaux Filippi, MIT/WHOI

Abstract: Ocean surface transport is at the core of many environmental disasters, including the spread of plastic pollution in seafood, the Deepwater Horizon oil spill and the nuclear contamination from the Fukushima Daiichi plant. Understanding and predicting flow transport, however, remains a scientific challenge, because it operates on multiple length- and time-scales that are set by the underlying dynamics. Building on the recent emergence of Lagrangian methods, this talk investigates the present-day abilities to describe and understand the organization of flow transport at the ocean surface, including the abilities to detect the underlying key structures, the regions of stirring and regions of coherence within the flow.

Postponed, TBA

An axiomatic approach to Salience Theory

Giacomo Lanzani, Economics

In this work, we offer an axiomatic foundation for the Salience model of choice under risk (Bordalo, Gennaioli, and Shleifer 2012). Since Salience Theory explains patterns of behavior that are impossible under expected utility maximization (EU), it has to relax some of the vN-M axioms. We first show that, for Salience to play a role, it is enough to weaken Transitivity. In doing so, we also provide a new axiomatization under risk to a more general class of intransitive preferences that includes Regret Theory. In this general framework, we then axiomatize the restrictions corresponding to the psychological properties of Ordering, Diminishing Sensitivity and Reflexivity imposed in the original Salience model. In doing so, we highlight that the property that brings the model outside the realm of EU is Ordering, and we characterize it as a submodularity property of the representing functional. Since the Salience Decision criterion is intransitive, the existence of an optimal choice in a set of three or more alternatives is not guaranteed. However, we use the min-max theorem to prove the existence of optimal randomization over possible alternatives. Refreshments will be provided.

Summer, TBA

Slip Instability of a Single Degree of Freedom Poroelastic System Following a Rate and State Dependent Friction Law

Maryam Alghannam, CSE

The study of single degree of freedom spring-slider systems as models of frictional slip has a long history, and has provided good insight into thedynamics of slip-weakening faults. The system of interest to this talk is represented by a slipping, poroelastic block. The poroelastic block represents a pressure-driven deformation process, where a piston is loaded vertically and compresses a spring inside a fluid-filled space. The spring is analogous to the rock skeleton, while the fluid inside the block represents fluid in the rock pores. Here we use the spring-poroslider model as an analogue of induced earthquakes and analyze conditions of unstable slip. We perform a linear stability analysis and nonlinear simulations to predict when a constant slip rate changes from stable to unstable under variable pore pressure. We find that injecting fluid into the slider at constant rate triggers stick-slip instability followed by stable sliding, which is consistent with laboratory experiments. This analysis provides an understanding of how rate and duration of fluid injection affect fault slip mode, with the aim that thisunderstanding will lead to improved design of subsurface operations that minimize or mitigate the occurrence of induced earthquakes. Refreshments will be provided.

Apr 17, 2019

PAC-Bayes Tree: Weighted Subtrees with Guarantees

Tinh Danh Nguyen, EECS

We present a weighted-majority classification approach over subtrees of a fixed tree, which provably achieves excess-risk of the same order as the best tree-pruning. Furthermore, the computational efficiency of pruning is maintained at both training and testing time despite having to aggregate over an exponential number of subtrees. We believe this is the first subtree aggregation approach with such guarantees.

Mar 28, 2019

MIT SIAM Coffee Hour + Social

Mar 21, 2019

Distinguished Seminar: Mechanics & Inverse-design of Shape-shifting Structures

Speaker: Prof. Wim van Rees, MechE

Recent progress in additive manufacturing and materials engineering has led to a surge of interest in shape­ changing plate and shell ­like structures. Such structures are typically printed in a planar configuration and, when exposed to an ambient stimulus such as heat or humidity, morph into a desired three­-dimensional shape. Viewed through the lens of differential geometry and elasticity, the application of the physical stimulus can be understood as a local change in the metric of a two dimensional surface embedded in three dimensions. In this talk I'll provide a short geometric and mechanic background to this problem, and demonstrate a numerical approach for simulating the elastic response to such a metric change for thin structures. I'll show my theoretical contributions on the inverse ­design of shape­ shifting bilayers, and discuss how these developments have led to the design and experimental realization of a 4D printed lattice that can undergo complex shape changes.

Mar 14, 2019

Seminar: Transform & Learn: From nonlinear PDEs to low-dimensional polynomial models

Elizabeth Qian, AeroAstro

This talk presents Transform & Learn, a physics-based approach to learning efficient, low-dimensional models for large-scale nonlinear systems. The proposed method starts from the physics of the problem—in the form of governing partial differential equations (PDEs)—and introduces variable transformations to arrive at a state representation in which the system admits a quadratic formulation. The system can then be parametrized by matrix operators, which can be learned from data. To make the problem computationally tractable, transformed state data are projected onto a low-dimensional global basis. The dense, low-dimensional quadratic model is then learned via a least-squares model learning procedure. We demonstrate our method on model problems in fluid dynamics and combustion applications.

Jan, 2019

IAP Course: Practical Computer Science for Computational Scientists

Ravikishore Kommajosyula, NSE + Ricardo Baptista, AeroAstro

The interdisciplinary nature of computational research brings in members from a variety of backgrounds in math, science, and engineering. Practical knowledge of computer science is a major factor in conducting numerical research. In this course, we present some tools, techniques, and unwritten guidelines in computer science. The following topics will be covered, with customized content to fit a computational research audience, combined with some hands-on examples: (i) writing good code, (ii) debugging and maintaining code, (iii) collaboration and modern version control, (iv) data science, and (v) improving code efficiency. Held Tuesdays and Thursdays.

Nov 28, 2018

Seminar: Teaching a Neural Network Physics to Help Design Complex Devices

Sam Raymond, CEE

Starting with the first computational weather forecasts, a ridiculously crazy idea a hundred years ago, we'll see how modern climate models work and why uncertainties in climate predictions are so high despite their sophistication. Then I'll talk about how we're trying to reduce uncertainties in climate predictions by developing a new climate model in Julia that runs on massively parallel GPU accelerators and learns from observations and high-resolution simulations.

Seminar: Reducing the Error Bars on Climate Predictions

Ali Ramadhan, EAPS

Starting with the first computational weather forecasts, a ridiculously crazy idea a hundred years ago, we'll see how modern climate models work and why uncertainties in climate predictions are so high despite their sophistication. Then I'll talk about how we're trying to reduce uncertainties in climate predictions by developing a new climate model in Julia that runs on massively parallel GPU accelerators and learns from observations and high-resolution simulations.

Nov 15, 2018

MIT SIAM Coffee Hour + Social

Oct 25, 2018

Seminar: Semiconductor Parameter Extraction (and more!) with Bayesian Inference

Rachel Kurchin, Materials Science and Engineering

Bayesian parameter estimation is a widely-used approach for model optimization in a variety of fields including astrophysics, high-energy physics, and bioinformatics. However, it has not been adopted extensively for electronic device characterization. We have developed a generalized open-source Python code, Bayesim, that accepts sets of observed data as a function of experimental conditions and modeled data as a function of those same conditions as well as a set of parameters to be fit, and outputs a probability distribution over these parameters, accounting for both experimental and model uncertainty. Because models of electronic devices are frequently computationally expensive, we adopt a deterministic and adaptive scheme for sampling the parameter space and computing model uncertainty. I will discuss applications of the code in fundamental characterization of photovoltaic materials as well as current and planned future features, and leave plenty time for discussion of how Bayesim might be useful for your application!

Sep 19, 2018

MIT SIAM / ACSES Joint Coffee Hour

Aug 9, 2018

Distinguished Speaker Seminar: Big Data vs. Big Computation

Prof. Qiqi Wang, AeroAstro

What is the future of computing? Some believe it's big data. For others, it's big computation. Supporters of big data believe that most problems can be solved by gathering huge amounts of data and applying machine learning. Those who believe in big computation, however, postulates that all phenomena in the world can be explained by solving simple physical equations with sufficient computational power. So, who is right?

Jul 30, 2018

Seminar: Iterated Pressure-Correction Projection Methods for the Unsteady Incompressible Navier-Stokes Equations

Jing Lin, MechE

In solving the unsteady incompressible Navier-Stokes equations, typical pressure-correction schemes perform only one iteration per stage or time step, and suffer from splitting errors that result in spurious numerical boundary layers and a limited order of convergence in time. In this talk, we will show that performing iterations not only reduces the effects of the splitting errors, but can also be more efficient computationally than merely reducing the time step. This iteration takes the form of the Richardson iteration applied to the pressure-Schur complement problem. Our analysis also reveals the significant role played by the rotational correction in projection methods. Moreover, we have devised stopping criteria to recover the desired order of temporal convergence, and to drive the splitting error below the time-integration error. We have also developed and implemented the iterated pressure corrections with both multi-step and multi-stage time integration schemes. Our theoretical results are validated and illustrated by numerical test cases for the Stokes and Navier-Stokes equations, using implicit-explicit (IMEX) backwards differences and Runge-Kutta time-integration solvers. It is found that iterated pressure-correction schemes can retrieve the accuracy and temporal convergence order of fully-coupled schemes and are computationally more efficient than classic pressure-correction schemes. Finally, we will draw connections between pressure-correction schemes and classic SIMPLE-based schemes for incompressible flows, which were rarely compared to each other in the literature.

May 29, 2018

Lightning Talks + Lunch

Apr 17, 2018

Distinguished Speaker Seminar: Intro to Julia

Prof. Alan Edelman, Mathematics

What makes a programming language “fast”? Alan Edelman, Professor of Applied Mathematics, gave an introduction to the Julia programming language. Julia is a high-level, high-performance dynamic programming language for numerical computing. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library.

Officers
Arkopal Dutt
Corbin Foucart
Mohammad Islam
President
Vice President
Treasurer
Nisha Chandramoorthy
Saviz Mowlavi
Rohit Supekar
Event Coordinator
Event Coordinator
Event Coordinator
Faculty Advisors
Dr. Jeremy Kepner
Prof. Alan Edelman
Lauren Milechin
MIT Lincoln Lab
MIT Mathematics
MIT EAPS
Jeff Goldblum
Jeff Goldblum
Prof. Gilbert Strang
Prof. Laurent Demanet
MIT Mathematics
MIT Mathematics