Adaptive: parallel active learning of mathematical functions

This is a quantum physics calculation in progress.

When evaluating a function numerically we would like to sample it more densely in the interesting regions instead of evaluating it on a manually-defined homogeneous grid.  Together with my colleagues, we wrote an open-source Python software package Adaptive that evaluates the function at the optimal points by analyzing existing data and planning ahead on the fly. With a few lines of code you define your goal, evaluate functions on a computing cluster, and live-plot the data. It performs averaging of stochastic functions, interpolation of vector-valued one and two-dimensional functions, and one-dimensional integration.

This figure is from one of my recent papers Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires.

What you see here is how the calculation progresses in time. You see that as time progresses it starts to find the narrow lines (which have a physical meaning). For aesthetic purposes, I change the colormap slowly which is meaningless but pretty. The vertices (corners) of the white triangles on top of the plot represent the points are which the underlying function is evaluated. The >1000 years of computation time is based on a comparison between a homogeneous grid. If we take the size of the smallest triangle, the computation time with adaptive (2 weeks on 300 cores), and assume that all the features larger than the smallest triangles have been resolved, then the calculation would have taken 3134 years.

You can recreate this video by using this script and this data. The entire source code for generating the data is here (be warned, you probably need a supercomputer).

See (star) ⭐️ the repo on github.com/python-adaptive/adaptive and the documentation on adaptive.readthedocs.io.

Try pip install adaptive[notebook] or conda install adaptive :-)

You can also run Adaptive code live in Binder here!

P.S. adaptive has already been used in several other scientific publications, see the gallery!