From biased molecular simulations to unbiased free energy landscapes

Understanding the free energy landscape is a fundamental step for understanding the thermodynamics and kinetics of complex molecular processes such as phase transitions, conformational changes, and chemical reactions. Traditional molecular dynamics simulations, however, are often limited by the difficulty of sampling rare-event due to high free-energy barriers. To address these challenges, accelerated simulation techniques employing biasing forces have been developed, though they can pollute the estimation of the underlying unbiased free energy profiles. In this work, we introduce a novel inference framework that reconstructs unbiased free energy landscapes directly from biased simulation data. Our approach employs an overdamped Langevin model and exploits a Bayesian maximum likelihood estimation strategy to accurately determine the drift and diffusion parameters governing the system's effective dynamics. The methodology is systematically validated using a series of benchmark toy models, including both one and two dimensional double-well potentials under unbiased and biased conditions. Results show that when an optimal collective variable is chosen, the framework successfully recovers the true free energy landscape; conversely, suboptimal projections lead to noticeable inaccuracies, underscoring the critical role of variable selection. This work not only enhances the efficiency of free energy estimation from biased simulations but also provides a robust tool for extracting detailed thermodynamic and kinetic insights, with potential applications across biophysics, chemistry, and materials science.