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

TL;DR

This paper introduces the Computational Information Criterion (COMIC) as a tool to determine the optimal number of particles in particle-tracking simulations for advection-diffusion equations, especially under sparse or noisy data conditions.

Contribution

It demonstrates that COMIC outperforms AIC in selecting efficient models for particle-tracking with noisy or sparse data, improving parameter estimation and prediction accuracy.

Findings

COMIC identifies the optimal particle number more effectively than AIC.

COMIC improves model efficiency in noisy or sparse data scenarios.

The method handles non-IID Gaussian error distributions.

Abstract

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