Comparison of Physics-Based Modeling and Polynomial Regression Methods: A Monte Carlo Simulation for Kinetic Energy Estimation

Predictive modeling can be approached using physics-based relationships or flexible statistical regression models. While physical laws provide theoretical accuracy when correctly specified, their predictive robustness under parameter misspecification, measurement noise, and structural errors remains a critical question. This study conducted a Monte Carlo simulation (1000 replications) comparing a fixed physics-based model, linear regression, and quadratic polynomial regression for kinetic energy estimation. Four distinct scenarios were evaluated across response noise levels (𝜎∈{1,5,10}): a correctly specified baseline (𝐸=𝑣2), mass misspecification (𝐸=1.1𝑣2), velocity measurement error (𝑢∼𝑁(0,0.252)), and a nonquadratic relationship (𝐸=𝑣2+0.01𝑣3). Performance was assessed against both noisy test observations and the noise-free true function using Root Mean Squared Error (RMSE), mean paired differences (𝐷), and model dominance proportions.The results demonstrate that model superiority is strictly governed by the data-generating mechanism. When correctly specified (Baseline), the physics-based model achieved absolute dominance (100% win rate across replications). It also retained a strong probabilistic edge under predictor measurement error, winning up to 98.6% of replications against the noise-free function. Conversely, under parameter misspecification and structural nonquadratic deviation, quadratic regression achieved lower RMSE in 100% of replications (𝐷=−3.7689 and 𝐷=−3.0496 at 𝜎=1, respectively). These findings highlight that physical knowledge maximizes predictive performance under accurate assumptions, but empirical regression models provide a necessary adaptation mechanism when domain knowledge is parameterically or structurally flawed