Arby $-$ Fast data-driven surrogates

TL;DR

Arby is a Python package that provides fast, data-driven surrogate models for complex simulations, enabling quick evaluations without solving PDEs, demonstrated on a pendulum and CMB spectra.

Contribution

We introduce Arby, a fully data-driven Python toolkit for building reduced-order models using the Reduced Basis and Empirical Interpolation methods, simplifying surrogate modeling.

Findings

Efficiently approximated 80,000 CMB spectra with only 84 basis solutions.

Demonstrated ease of use with a simple pendulum example.

Achieved accurate surrogate models at minimal computational cost.

Abstract

The availability of fast to evaluate and reliable predictive models is highly relevant in multi-query scenarios where evaluating some quantities in real, or near-real-time becomes crucial. As a result, reduced-order modelling techniques have gained traction in many areas in recent years. We introduce Arby, an entirely data-driven Python package for building reduced order or surrogate models. In contrast to standard approaches, which involve solving partial differential equations, Arby is entirely data-driven. The package encompasses several tools for building and interacting with surrogate models in a user-friendly manner. Furthermore, fast model evaluations are possible at a minimum computational cost using the surrogate model. The package implements the Reduced Basis approach and the Empirical Interpolation Method along a classic regression stage for surrogate modelling. We illustrate the simplicity in using Arby to build surrogates through a simple toy model: a damped pendulum. Then, for a real case scenario, we use Arby to describe CMB temperature anisotropies power spectra. On this multi-dimensional setting, we find that out from an initial set of $80,000$ power spectra solutions with $3,000$ multipole indices each, could be well described at a given tolerance error, using just a subset of $84$ solutions.