I am an applied mathematician and computational scientist working at the interface of approximation theory, compressed sensing, scientific machine learning, uncertainty quantification, and numerical analysis. My research develops mathematical and computational foundations for reliable learning from limited information, with applications to PDEs, inverse problems, imaging, generative models, and computational science.

A central theme of my work is that reliable scientific machine learning requires more than expressive model classes. It also requires principled choices of what information to collect, how to encode that information, and how to recover stable approximations from finite data. 

Research areas

• Reliable scientific machine learning from limited information -  I study how to construct accurate and stable learned surrogates when data are expensive, high-dimensional, noisy, or indirect.

• Compressed sensing and active learning - I develop methods for sample-efficient recovery using ideas from sparse approximation, Christoffel functions, generalized sampling, and information design.

• Approximation theory for computational science - My work investigates how classical and modern approximation tools can support reliable algorithms for PDEs, inverse problems, and uncertainty quantification.

• Operator learning and high-dimensional models - I am interested in learning maps between function spaces, including parameter-to-solution maps for PDEs and other scientific operators.

• Generative models and inverse problems - Recent projects explore how conditional generative models can be used with principled measurement design for compressed sensing and imaging-type inverse problems.

Students and mentoring

I work with undergraduate and graduate students on projects in scientific machine learning, compressed sensing, active learning, uncertainty quantification, computational imaging, and PDE-based modeling. Student projects often combine mathematical analysis, algorithm design, numerical experiments, and reproducible software.

Prospective students interested in scientific computing, approximation theory, compressed sensing, numerical analysis, or reliable machine learning are welcome to contact me.