Amoss: Improving Simulation Speed and Numerical Stability of Large-Scale Mixed Continuous/Conditional Stochastic Differential Simulations

Abstract

Amoss is an equation-orientated stochastic simulation platform, developed on open-source software. It is designed to facilitate the development and simulation of Sasol value chain models using the Moss methodology. The main difficulties with the original Moss methodology was that plant recycles were difficult to incorporate and that plant or model changes meant rebuilding the entire Moss model. The first version of automatic-Moss was developed by Edgar Whyte in an effort to address these problems. It was successful as a proof of concept, but generated simulations were numerically unstable and very slow. A second version of the tool was to be developed to address numerical stability and simulation speed. The stochastic simulations stemming from Amoss models are large-scale and contain mixed continuous/conditional algebraic equation sets, with first order stochastic differential equations. Additionally, optimal flow allocation as a disjunctive optimisation is often encountered. The complexity of these factors makes finite difference approximation the main solution. The equation ordering, simulation approach and code generation features of the Amoss tool were investigated and re-implemented. A custom equation ordering method, which uses interval arithmetic and weighted maximal matching for numerically stable matching, followed by Dulmage-Mendelsohn decomposition and Cellier’s tearing, was implemented. For implicitly ordered systems, a fixed-point iterative Newton method, where conditional variables are separated from continuous variables for solving stability, was implemented. The optimal allocation problem with heuristic allocation was generalised to plants with recycles. Fast simulation code utilising parallel processing, efficient solving and function evaluation, efficient intermediate data storage and fast file writing, was implemented. Amoss simulations are now substantially faster than the industry equivalent and can reliably model Moss methodology problems.