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A zeal for low-level and aggressively optimized numerical routines. Familiarity with C, and ideally the floating point standard, would be great but is not required. For testing and distribution, a good understanding of Github pipelines and automated workflows would be ideal. The project leader does not entirely reject the use of LLMs for development, but they frequently do not produce fast low-level code, and can needlessly rewrite many lines of code that place a review burden on project leaders. An ideal fit would be somebody who uses them like search engines, as they can be useful for discovering numerical tricks and rapidly familiarizing with the methods of numerical analysis, but then writes code themselves.

The project mentor develops a library for rapid evaluation of a challenging function that has broad applications in Gaussian processes. Fitting the Matern covariance model to data involves evaluating and differentiating the second-kind modified Bessel function, which does not have a simple closed form solution and must be evaluated numerically with a variety of different strategies. Differentiation, particularly with respect to the order parameter, requires particularly careful implementation and is done using automatic differentiation.

This library is prototyped in the Julia programming language, but will ultimately be released as a production-ready library in the C language and will be offered as a package in languages such as python and R.

Immediate development goals for the library include: (1) offering by far the fastest Matern covariance evaluation routines, (2) derivatives with respect to all parameters that are accurate to double precision and fast, and (3) extensions involving smarter parameterizations of geometric anisotropy and other enhancements that can serve as a backbone for casual users of front-end languages like R and Python.

An intern could contribute to this project by:

0) packaging code up neatly in R and python packages (many languages)
1) developing and enhancing an automated testing suite for all three major OSes (C)
2) developing a robust build process (C, LLVM)
3) micro-optimizing current code (Julia, C)
4) potentially implementing new routines and numerical strategies (Julia)

Interns are expected to be able to sit for extended periods. Specific physical demands will be discussed with mentors during the interview process.

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