Entropic criteria for computational models of advection-diffusion equations

Abstract

Traditional probabilistic methods for the estimation of parameters within advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, i.e.number of particles, within associated numerical methods. Many times, the gain in accuracyof a highly discretized numerical model is outweighed by its associated computational costs.The research project herein seeks to answer the question of how many particles one should usein a numerical simulation to best approximate and estimate parameters in one-dimensionaladvective-diffusive transport with constant coefficients. To answer this question, we use thewell-known Akaike Information Criteria (AIC) and a recently-developed correction calledthe Computational Information Criteria (COMIC) to guide the model selection process.Two Lagrangian numerical methods - the random-walk particle tracking (RWPT) and mass-transfer particle tracking (MTPT) methods - are employed to solve the ADE at variouslevels of discretization. The numerical results demonstrate that the newly developed COMICprovides an optimal number of particles that can describe a more efficient model in termsof parameter estimation and model prediction compared to the model selected by the AIC.These results demonstrate the need for future modelers and scientific researchers to utilizecomputationally-driven selection criteria in order to best select numerical models.