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Shanyin Tong

Courant Institute of Mathematical Sciences
New York University
251 Mercer Street
New York City, NY 10012, USA

Email: shanyin.tong@nyu.edu

My research focus is on applied and computational mathematics, in particular on uncertainty quantification, PDE-constrained optimization, optimization under uncertainty, rare events and inverse problems. The main applications driving my research are the hazard assessment of extreme tsunami waves, optimal portfolio allocations, and sesmic inversion. Currently, I am also interested in using machine learning methods in scientific computing and uncertainty quantification.

I am on the job market, please find my CV and research statements here.

EDUCATION

EXPERIENCES

  • May 2021 – August 2021 Research Scientist Intern at Amazon, Middle Mile Product & Technology.
  • June 2020 – August 2020 Summer Research Intern at Argonned National Laboratory, worked with Dr. Vishwas Rao and Dr. Anirudh Subramanyam.

RESEARCH

Math is the new sexy.

  • Extreme event probability estimation and uncertainty quantification, reported on the homepage of SIAM News (Link)
    • Established connections between extreme event probability estimations and constrained optimizations.
    • Extended large deviation theory to systems with uncertain parameters, converted the extreme event quantifications to the PDE-constrained optimizations, guided importance sampling and built asymptotic approximations using the optimizers.
    • Applied the proposed estimation methods to the tsunami hazard assessment.
    • Motivated the formulation and analysis of new classes of PDE-constrained optimization problems.
  • PDE-constrained optimization
    • Solved shallow water equations to simulate waves using the discontinuous Galerkin finite element method (DG-FEM).
    • Used adjoint methods to compute gradients for PDE-constrained optimization problem.
    • Added artificial viscosity to tackle the convergence issue when gonverning equation is a nonlinear hyperbolic conservation law and shock appears.
    • Used FEniCS to implement the inversion of slips in earthquake, currently study sensitivities of Bayesian inverse problem solutions based on this implementation, focusing on the K-L divergence between prior and posterior
  • Optimization with probabilistic constraints
    • Developed sampling-free methods for solving optimization problem over rare chance constraints.
    • Implemented the method using Julia and JuMP.
    • Verified the superiority of our methods in terms of accuracy and efficiency (accelerated by at least 5 times), comparing with the traditional sampling-based methods on the applications in engineering design, stocks investment and optimal control.
  • Computing and software
    • Implemented a 3D Biot Savart law on both CPUs (using OpenMP) and GPUs (using CUDA), [Git Repo Link].
    • Implemnted the fast multipole method (FMM) for computing electrostatic interactions in 2D using C++, [Git Repo Link].
    • Implemented the SimCLR algorithm for self-supervised learning for image classifications using PyTorch, [Git Repo Link]
    • Implemented the online adaptive model reduction for shallow water equations, [Git Repo Link].

PUBLICATIONS

My profile on Google Scholar.

  • S. Tong, E. Vanden-Eijnden, G. Stadler, Extreme event probability estimation using PDE-constrained optimization and large deviation theory, with application to tsunamis, Communications in Applied Mathematics and Computational Science 16-2 (2021), 181--225. DOI 10.2140/camcos.2021.16.181 [arXiv:2007.13930, CAMCoS Link]
  • S. Tong, E. Vanden-Eijnden and G. Stadler, Estimating earthquake-induced tsunami inundation probabilities without sampling, submitted to Geophysics Journal International (2021) [arXiv:2111.14325]
  • S. Tong, Extreme event probability estimation with application to tsunamis, SIAM News (2021) [SIAM News Link]
  • S. Tong, A. Subramanyam, V. Rao, Optimization under rare chance constraints, accepted by SIAM Journal on Optimization (2020) [arXiv:2011.06052]
  • S. Tong and G. Stadler, LDT-based reduced dimension important sampling for rare events, in preparation
  • A. Chowdhary, S. Tong, G. Stadler and A. Alexanderian, Sensitivity analysis of Bayesian inverse problem solutions, in preparation

CONFERENCES & PRESENTATIONS

2022

2021

2020

2019

2018

  • Attended the 2018 Gene Golub SIAM Summer School, Inverse Problems: Systematic Integration of Data with Models under Uncertainty in Breckenridge, CO, June 17-30. Gave a presentation on team project "Data Fitting with Soap Bubble Surfaces: A Minimal Surfaces Problem".