Ensuring Physical Realism in Monte Carlo Simulations: A Cholesky Decomposition Approach

Monte Carlo simulations are widely employed for modeling random processes in physical materials, often utilizing exponential covariance functions to generate correlated vectors of random variables. However, an inherent challenge arises when these simulations produce negative values for variables such as elastic modulus or thermal conductivity, which are physically implausible. This study addresses this issue by investigating the impact of the covariance function’s parameter, sigma, on the feasibility of the simulated vectors. Through Cholesky decomposition, it is observed that a critical value of σ ensures that the generated vectors remain strictly non-negative. This finding highlights a crucial threshold for maintaining physical realism in simulations and provides a valuable insight for practitioners in the field. The study not only contributes to the refinement of Monte Carlo simulations but also prompts further exploration into the nuanced interplay between covariance functions and the feasibility of simulated results.