My research interests lie within two main thrusts:
Finding optimal solutions to problems represented with stochastic simulations is hard. Simulations that do not provide direct derivative information add to the challenge of designing robust and efficient simulation optimization solvers. The group tackles this challenge by (i) using adaptive sampling techniques, (ii) using variance reduction inside optimization, and (iii) informing the optimization of bias and variance of outputs. Ongoing work includes:
- Adaptive sampling stochastic optimization
- [working paper] Trust regions for expensive nonsmooth functions
- Benchmarking algorithms
- [working paper] Stochastic constraints
- Binary stochastic optimization
- [working paper] Quantum feature selection
- [working paper] Nested partitioning
Despite the unprecedented opportunities that the abundance of data brings, making reliable decisions with Big Data is computationally challenging, even with advanced computing technologies. Theories in Monte Carlo simulation and applied probability enable the utilization of distributional behavior of Big Data and a framework for interpretable prediction and prevention of high-risk events. The group’s main directions in this thrust include:
- Theoretical studies
- [working paper] Robust output analysis using nonparametric bias detection
- Applied studies
- [working paper] Spatio-temporal prediction of Electron-beam defects
- [working paper] Digital twins in additive manufacturing
- [working paper] Agricultural and coastal risk mitigations
- [working paper] Bias detection and stratification for energy expansion