Research
Learning more from fewer simulations.
I develop statistical methods that turn limited simulation runs into useful predictions, uncertainty estimates, and better decisions.
My research connects Gaussian process emulation, multi-fidelity simulation, dynamic modeling, and active learning to make complex computer models more useful for scientific discovery.
Learn a response. Understand what is uncertain.
Try adding an informative run.Click below to see the emulator learn.
Why computer experiments?
Real world experiments are often too dangerous, expensive, or time consuming to perform. Testing an aircraft under extreme conditions, investigating how an infectious disease might spread, or studying the effects of a changing climate may require experiments that are difficult or impossible to conduct directly.
Computer simulations offer another way to investigate these questions. They use mathematical models and numerical algorithms to describe a system and explore how it responds to different conditions. A computer experiment studies these simulations systematically by choosing inputs, running the model, and analyzing its outputs.
Engineering
How will a design perform?
Explore airflow, heat transfer, or structural response before building a physical prototype.
Biology
How does a system function?
Investigate mechanisms and how changes in biological parameters affect a model's behavior.
Environment
What could happen under change?
Compare scenarios for climate, water resources, and other evolving environmental systems.
Simulations can be expensive, too.
A detailed simulation may take hours or days, and scientific questions rarely require just one run. Exploring unknown parameters, comparing designs, or assessing uncertainty can require many evaluations. A limited computing budget therefore raises two questions. How can we predict a simulator's behavior without running it everywhere? And which runs are worth performing?
I address these questions through statistical emulators. An emulator learns the relationship between inputs and outputs from a selected set of runs, provides fast predictions at new inputs, and quantifies uncertainty about those predictions.
Research directions
Multi-fidelity simulation · Dynamic simulators · Uncertainty quantification · Active learning and Bayesian optimization
Multi-fidelity simulation
How can models of different accuracies work together?
A coarse computational mesh or a simplified physical model can produce inexpensive approximations, while a more detailed simulation may be much more costly. Multi-fidelity methods combine these sources so that inexpensive runs help us learn where detailed simulations are most valuable.
I develop the Recursive Non-Additive model to capture nonlinear relationships across fidelity levels and the Diffusion Non-Additive model for the limiting response as a numerical precision parameter approaches zero, a target that may be too expensive to compute directly.
Dynamic simulators
How can we predict a system as it evolves over time?
Many simulators describe trajectories rather than a single output. Examples include interacting populations, oscillating mechanical systems, and the evolution of physical states. Emulating these systems requires us to account for how uncertainty at one time affects predictions at later times.
I propose approach that computes predictive means and variances analytically rather than estimating them by repeated sampling. The goal is efficient trajectory prediction with an explicit account of uncertainty.
Uncertainty quantification
What do we know, and how certain are we?
A fast prediction is most useful when we also understand its limitations. Uncertainty quantification asks how uncertain inputs, incomplete simulation data, and modeling assumptions affect the conclusions we draw.
Even a deterministic simulator can have an uncertain emulator prediction because we have observed only a finite number of runs. My research studies predictive uncertainty and its propagation.
Active learning & Bayesian optimization
Which simulation should we run next?
When each run has a cost, the choice of where to evaluate a simulator matters. Active learning uses the current emulator to select new runs, updates the model with the results, and repeats. Active learning can target improved prediction or reduced uncertainty, while Bayesian optimization targets a design or input that performs well.