A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Abstract Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook entropic contribution discretization, e.g., number particles, within associated numerical methods. Many times, gain in accuracy a highly discretized model is outweighed by its computational costs or noise data. We address question how many particles are needed to best approximate and estimate parameters one-dimensional advective-diffusive transport. To do so, we use well-known Akaike Information Criterion (AIC) recently-developed correction called Computational (COMIC) guide selection process. Random-walk mass-transfer particle tracking employed solve at various levels discretization. Numerical results demonstrate that COMIC provides an optimal can describe more efficient terms parameter estimation prediction compared selected AIC even when data sparse noisy, sampling volume not uniform throughout physical domain, error distribution non-IID Gaussian.