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

• Presenter in Mini-Symposium: Characterization and prediction of rare and extreme events in complex systems at SIAM Conference on Uncertainty Quantification (UQ22), April 12-15.
• Presenter in Scientific Computing and Numerics (SCAN) seminar at Cornell University, March 21.
• Presented in CCB Seminar at Center for Computational Biology at Simons Foundation, Jan 21.
• Presented in Applied Mathematical colloquium at APAM at Columbia University, Jan 20.

2021

• Presented in Mini-Symposium: Characterization and prediction of rare and extreme events in complex systems at SIAM conference on Computational Science and Engineering (CSE21), March 1-5.

2020

• Presented in General Session: Optimization under Rare Events at Virtual 2020 INFORMS Annual Meeting, November 7-13.
• Presented in Summer Argonne Students Symposium (SASSy), August 14.
• Attended the ICERM workshop: Computational Statistics and Data-Driven Models, April 20 - 24.
• Presenter in Mini-Symposium: Statistical Prediction and Quantification of Extreme Events in Complex Systems at SIAM Conference on Uncertainty Quantification (UQ20) in Munich, Germany, March 24-27. The conference was cancelled due to COVID-19.
• Presented in Courant modeling & simulation group meeting (MSG) in New York, NY, February 20.

2019

• Presented a poster at ICERM workshop: Mathematical Optimization of Systems Impacted by Rare, High-Impact Random Events in Providence, RI, June 24-28.

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".