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.

用于模拟对流扩散方程（ADE）的传统概率方法通常会忽略相关数值方法内离散化的熵贡献，例如粒子数。很多时候，高度离散的数值模型在准确性方面的收益被其相关的计算成本或数据中的噪声所抵消。我们解决了在模拟中需要多少个粒子才能在一维对流-扩散输运中最好地近似和估计参数的问题。为此，我们使用著名的Akaike信息准则（AIC）和最近开发的称为计算信息准则（COMIC）的更正来指导模型选择过程。采用随机游走和传质粒子跟踪方法来求解各个离散水平的模型方程。数值结果表明，与AIC选择的模型相比，COMIC提供了最佳数量的粒子，可以在参数估计和模型预测方面描述更有效的模型，即使数据稀疏或嘈杂，采样量不均匀也是如此整个物理域，或者数据的错误分布是非IID高斯的。