RESEARCH
Math is the new sexy.
- Uncertainty quantification --- Extreme event probability estimation (SIAM News Link)
- Establish connections between extreme event probability estimation and constrained optimization.
- Extend large deviation theory (LDT) to systems with uncertain parameters,
guide importance sampling and build asymptotic approximations using the LDT optimizers.
- Design efficient sampling algorithms to estimate the probabilities of extreme events using LDT information and machine learning methods such as normalizing flows.
- Optimization under uncertainty --- Extreme event mitigation and control
- Develop sampling-free methods for solving optimization problem over rare chance constraints.
- Develop iterative methods for optimal control mitigating the impacts of extreme events, using LDT-informed adaptive importance sampling and bilevel optimization.
- Study convergence of PDE-and-chance-constrained optimization, and its potential connection with reinforcement learning.
- PDE-constrained optimization --- Real-world applications of extreme event mitigation
- Design wave breaker for mitigating extreme tsunami hazard, optimization 2D shallow water equations.
- Design wall around lower Manhattan to prevent flooding and storm surge.
- Implement corresponding PDE-constrained optimization problems, where the PDE constraint is a system of nonlinear hyperbolic equations (2D shallow water equations).
- Scientific Computing and Software
- Implementation of 3D Biot Savart law on both CPUs (OpenMP) and GPUs (CUDA), [Git Repo Link].
- Implementation of the fast multipole method (FMM) for computing electrostatic interactions in 2D using C++, [Git Repo Link].
- Implementation of the SimCLR algorithm for self-supervised learning for image classifications using PyTorch, [Git Repo Link]
- Implementation of the online adaptive model reduction for shallow water equations, [Git Repo Link].
© Shanyin Tong