Data efficient learning of molecular slow modes from nonequilibrium metadynamics

Enhanced sampling simulations help overcome free energy barriers and explore molecular conformational space by applying external bias potential along suitable collective variables (CVs). However, identifying optimal CVs that align with the slow modes of complex molecular systems with many coupled degrees of freedom can be a significant challenge. Deep time-lagged independent component analysis (Deep-TICA) addresses this issue by employing an artificial neural network that generates non-linear combinations of molecular descriptors to learn the slowest degrees of freedom. Training Deep-TICA CVs, however, typically requires long equilibrium simulations that can sample multiple recrossing events across various metastable conformations of the molecule. This requirement can often be prohibitively expensive, thereby limiting its widespread application. In this study, we present an algorithm that enables the training of Deep-TICA CVs using a limited amount of trajectory data obtained from short, non-equilibrium metadynamics simulations that only sample one forward transition from the initial to the final state. We achieve this by utilizing the variational Koopman algorithm, which reweights short off-equilibrium trajectories to reflect the equilibrium probability densities. We demonstrate that enhanced sampling simulations conducted along the Koopman reweighted Deep-TICA CV can accurately and efficiently converge the free energy surface for systems such as the Müller-Brown potential, alanine dipeptide, and the chignolin mini-protein. Our approach, therefore, addresses the key challenge of inferring slow modes from limited trajectory data, making it more feasible to use deep learning CVs to study molecular processes of practical relevance.