Learned Committors as Reaction Coordinates for Nucleation Rates

Abstract

A central challenge in the analysis of first-order phase transitions is the identification of optimal reaction coordinates. In principle, the committor is the ideal choice; however, its computational cost has historically made it intractable. Here, we train a convolutional neural network ($p_B$-NN) as a proxy for the committor on brute-force committor labels and use it directly as the coordinate of a Markov state model. Applied to magnetisation reversal in the two-dimensional Ising model, $p_B$-NN reproduces brute-force nucleation rates across a range of thermodynamic conditions. The largest geometric cluster size also recovers accurate rates despite providing a poor pointwise predictor of the committor. These results demonstrate that an effective reaction coordinate for nucleation rate calculation must reliably separate the metastable and stable basins, but need not preserve the committor pointwise for every microstate. We stress that this distinction has direct implications for the choice of collective variable in rare-event simulations of nucleation more broadly.