My research integrates mathematical (stochastic) modeling, numerical analysis, and the development of advanced computational methods to address complex problems in engineering and science. The studied problems often exhibit challenging features such as high dimensionality, complex dynamics, low regularity, and rare events, which can adversely affect the performance of numerical methods in terms of computational cost, accuracy, robustness, and applicability. A central question in my research is how to enhance these numerical methods to achieve optimal performance (i.e., balancing efficiency and interpretability). In this respect, I focus on designing novel strategies based on smoothing techniques, dimensionality and variance reduction, improved sampling (hierarchical/adaptive/importance sampling), and machine learning. The conducted research spans theory, algorithm design, and numerical analysis.
My work is application-driven, and my research focuses include:
- Numerical and machine learning methods in quantitative finance: pricing financial derivatives and risk management.
- Optimal control and reinforcement learning for (hybrid) power systems management and trading in (renewable) energy markets.
- Forward and inverse problems in stochastic reaction networks, with applications in biochemical systems and epidemiology.
- Machine learning and data-driven methods for forecasting extreme events.
- Hierarchical approximation methods and machine learning for scientific computing.
The methodologies employed in my research encompass a range of techniques, including Monte Carlo (MC), multilevel (hierarchical) MC, Quasi-MC, (adaptive) sparse grids' quadrature, Fourier methods, stochastic optimal control, importance sampling, and machine learning.