My research is mainly about adaptive strategies for approximating, optimizing, and inverting functions (e.g., numerical simulators) under severely limited evaluation budgets. This recent but very active field of applied mathematics is at a crossroad between functional approximation, numerical optimization, computer experiments, and machine learning. In the past few years, I have been focusing on the following topics:
- Kriging-based optimization and inversion algorithms: design, properties, and implementation
- Functional approximation, especially within the theory of Reproducing Kernel Hilbert Spaces
- Gaussian Random fields: model selection, estimation of covariance parameters
- Positive-definite kernels: incorporation of prescribed mathematical properties
- Applications with hydrogeologists, mechanical engineers, and nuclear criticality safety specialists
A publication list as well as further documents are available here.