Research
I identify regularity, effective dimension, probabilistic structure, and computational hierarchies to develop scalable, reliable methods for simulation, estimation, prediction, and decision-making under uncertainty.
Research philosophy
My research spans mathematical problem formulation, algorithm design, and numerical analysis. I identify exploitable analytic regularity, effective low-dimensional structure, probabilistic change-of-measure opportunities, multilevel hierarchies, model or dimension reduction representations, and informative path features. These structures guide the construction of numerical and learning algorithms whose bias, variance, stability, convergence, and computational complexity can be quantified.
Scientific machine learning
Learning is part of the mathematical programme rather than a separate identity: it either improves how a stochastic problem is represented and computed, or approximates the target map directly.
A learned model identifies a transformation, reduced state, feature representation, change of probability measure, control component, or other proxy that is embedded within a conventional numerical algorithm.
The learned component has a prescribed mathematical role, while the final quantity can retain transparent error and complexity analysis.A learned model approximates a parameter, conditional distribution, forecast, quantity of interest, value function, solution operator, or control policy.
This route can improve scalability, with generalization, calibration, robustness, rare-event extrapolation, and predictive uncertainty assessed explicitly.Stochastic optimal control
I use stochastic optimal control in two related but distinct ways: as a principle for designing efficient numerical methods and as a framework for solving decision problems under uncertainty.
An auxiliary stochastic-control problem constructs adaptive changes of probability measure for efficient rare-event estimation. In path-dependent settings, the evolving system history guides simulation toward influential trajectories, while likelihood-ratio reweighting preserves the target expectation.
Control improves the numerical method.Stochastic control is also the decision problem itself. I develop numerical and data-driven methods for energy markets and power systems, including renewable-energy trading, storage, and the operation of coupled systems under uncertain prices, generation, demand, and dynamics.
Control produces the decision policy.Cross-cutting principle
Low-probability, high-consequence outcomes are easily underrepresented by standard simulation and unweighted learning. Two mathematically distinct strategies in my work redirect computational attention toward these influential regions.
A change of probability measure makes rare events occur more frequently in simulation, while likelihood-ratio reweighting preserves estimation under the original model.
Density-based weighting increases the contribution of scarce extreme observations to the empirical loss, improving attention to behavior that ordinary training data underrepresent.
The mechanisms are different, but the guiding principle is shared: allocate statistical effort according to inferential importance rather than empirical frequency alone.
Research hub
Fourier methods · Quasi-Monte Carlo · Hierarchical approximation
Central question
I recover or preserve mixed regularity through smoothing, damping, Fourier and Laplace representations, and domain transformations. I then combine these ideas with effective-dimension reduction, adaptive sparse grids, and randomized quasi-Monte Carlo to control bias, variance, and computational work for a prescribed accuracy.
Current directions
Selected work
All publicationsResearch hub
Stochastic control · Forecasting · Optimization
Central question
I combine Lagrangian relaxation for coupled hydrothermal systems, state augmentation for time delays, monotone numerical schemes for Hamilton–Jacobi–Bellman equations, and data-driven stochastic control for renewable producers trading in intraday electricity markets.
Current directions
Selected work
All publicationsResearch hub
Extreme events · Imbalanced learning · Uncertainty quantification
Central question
I use density-aware weighting, cost-sensitive objectives, and scientific machine learning to redirect statistical effort toward scarce, high-consequence observations. This supports reliable prediction of coastal storm surges and other environmental extremes, connecting predictive uncertainty with climate-risk and resilience decisions.
Current directions
Research hub
Monte Carlo · Multilevel Monte Carlo · Importance sampling · Filtering
Central question
I combine stable tau-leap discretizations and multilevel estimators with importance sampling, stochastic optimal control, and Markovian projection to reduce discretization error, variance, and effective dimension. These methods support forward simulation, filtering, parameter inference, and rare-event estimation for stochastic reaction networks arising in biochemical and biological systems.
Current directions
Selected work
All publicationsResearch hub
Path signatures · attention · imbalanced learning · learned controls · data-driven stochastic control
Central question
I use scientific machine learning both within numerical algorithms—to learn transformations, reduced representations, feature maps, changes of probability measure, and control components—and as a direct approximation tool for parameters, forecasts, value functions, and policies. Across stochastic differential equations, rare-event simulation, climate extremes, and energy markets, I connect predictive performance with calibration, robustness, generalization, and computational complexity.
Current directions
Selected work
All publicationsResearch hub
Multilevel Monte Carlo · numerical smoothing · adaptive approximation · error–cost analysis
Central question
I develop and analyse multilevel Monte Carlo, numerical smoothing, hierarchical quadrature, and adaptive sampling strategies that separate and control discretization bias, sampling variance, and computational work. This cross-cutting methodology supports probabilities, densities, option values, and other low-regularity quantities of interest across application areas.
Current directions
Selected work
All publicationsMethodological toolbox