From Theory to Demonstration: A Case Study in Engineering Demonstration Models

A recently proposed approach aims to improve the accuracy of simulation results. It does this by combining outputs from multiple lower-accuracy runs, where accuracy is controlled by tuneable parameters such as step sizes or tolerances. This method is called Sparse Probabilistic Richardson Extrapolation (SPRE). While conceptually straightforward, implementing and demonstrating SPRE in practice presents a range of non-trivial software engineering challenges. A key practical challenge lies in designing simulation models that exhibit sufficiently stable and predictable behaviour as parameters vary. In this talk, we share the story of developing such models through a series of visually engaging examples, including animated 3D physics simulations and flocking multi-agent systems, highlighting both unsuccessful and successful attempts. These examples illustrate the difficulty of aligning theoretical assumptions with real computational models. We also discuss the Python implementation of SPRE designed with performance, flexibility, and reproducibility in mind. A central requirement of the method is automatic differentiation, which we achieve using JAX to compute exact gradients of complex computational functions. JAX also enables just-in-time compilation, delivering significant performance improvements for the repeated evaluations required by the method. This work demonstrates that implementing advanced methods is only part of the challenge; equally important is constructing meaningful examples that reveal their strengths and limitations. By combining modern tools with careful model design, we show how research software engineering practices, particularly around performance, abstraction, and testing, enable emerging ideas to become usable, reproducible, and compelling software tools.