Deep learning of committor and explainable artificial intelligence analysis for identifying reaction coordinates

Abstract

In complex molecular systems, the reaction coordinate (RC) that characterizes transition pathways is essential to understand underlying molecular mechanisms. This review surveys a framework for identifying the RC by applying deep learning to the committor, which provides the most reliable measure of the progress along a transition path. The inputs to the neural network are collective variables (CVs) expressed as functions of atomic coordinates of the system, and the corresponding RC is predicted as the output by training the network on the committor as the learning target. Because deep learning models typically operate in a black-box manner, it is difficult to determine which input variables govern the predictions. The incorporation of eXplainable Artificial Intelligence (XAI) techniques enables quantitative assessment of the contributions of individual input variables to the predictions. This approach allows the identification of CVs that play dominant roles and demonstrates that the committor distribution on the surface using important CVs is separated by well-defined boundaries. The framework provides an explainable deep learning strategy for assigning a molecular mechanism from the RC and is applicable to a wide range of complex molecular systems.

Figures (12)

• Figure 1: Schematic illustration of the explainable deep learning framework for identifying RCs based on committor $p_\mathrm{B}^*$ sampling. First, MD trajectories are generated to sample the committor $p_\mathrm{B}^*$ for the target transition process. The candidate CVs, $x_i$, are utilized as input features and mapped to the output $q$ by a neural network model of $N_\mathrm{layer}$ consisting of $\mathbf{N}_\mathrm{node}$. The neural network is trained such that the committor $p_\mathrm{B}^*$ follows a sigmoidal function $p_\mathrm{B}(q) = [1 + \tanh(q)]/2$, where $q$ serves as the RC. Finally, XAI analysis identifies the dominant CVs contributing to the RC $q$, enabling evaluation of the committor $p_\mathrm{B}^*$ distribution on the corresponding free-energy landscape. Reproduced from Y. Mori, K.-i. Okazaki, T. Mori, K. Kim, and N. Matubayasi, J. Chem. Phys. 153, 054115 (2020), mori2020Learning with the permission of AIP Publishing, K. Kawashima, T. Sato, K.-i. Okazaki, K. Kim, N. Matubayasi, and T. Mori, APL Mach. Learn 3, 016113 (2025)kawashima2025Investigating; licensed under a Creative Commons Attribution (CC BY) license, and T. Kikutsuji, Y. Mori, K.-i. Okazaki, T. Mori, K. Kim, and N. Matubayasi, J. Chem. Phys. 156, 154108 (2022) kikutsuji2022Explaining; licensed under a Creative Commons Attribution (CC BY) license.
• Figure 2: (a) Atomic indices assigned to alanine dipeptide. The three major dihedral angles, $\varphi$, $\psi$, and $\theta$, are indicated. (b) Probability distribution in the $(\varphi, \psi)$ plane. The dashed lines define state A $[(-150^\circ, 0^\circ )\le (\varphi, \psi) \le (30^\circ, 180^\circ)]$, state B $[(30^\circ, -180^\circ )\le (\varphi, \psi) \le (130^\circ, 0^\circ )]$, and the intermediate region TS $[(-30^\circ, -80^\circ ) \le (\varphi, \psi)\le (20^\circ,-30^\circ)]$. (c) Probability distribution in the $(\varphi, \theta)$ plane. In (b) and (c), points are colored according to the committer value $p_\mathrm{B}^*$. as indicated by the color bar. Reproduced from T. Kikutsuji, Y. Mori, K.-i. Okazaki, T. Mori, K. Kim, and N. Matubayasi, J. Chem. Phys. 156, 154108 (2022) kikutsuji2022Explaining; licensed under a Creative Commons Attribution (CC BY) license.
• Figure 3: (a) Relationship between the committer value $p_\mathrm{B}^*$ and the RC $q$ predicted by LR (red) and DNN (green) for the test dataset (800 points). The black solid line denotes the sigmoidal function $p_\mathrm{B}(q) = [1+ \tanh(q)]/2$. (b) Probability distribution of the committer $p_\mathrm{B}^*$ obtained from LR (red) and DNN (green) within the range $-0.2 < q < 0.2$ shown in (a). Reproduced from T. Kikutsuji, Y. Mori, K.-i. Okazaki, T. Mori, K. Kim, and N. Matubayasi, J. Chem. Phys. 156, 154108 (2022) kikutsuji2022Explaining; licensed under a Creative Commons Attribution (CC BY) license.
• Figure 4: Feature contribution of each CV in absolute value obtained using LIME (red) and SHAP (blue). From left to right: $0 \le p_\mathrm{B}^* < 0.1$ (near state A), $0.49 < p_\mathrm{B}^* < 0.51$ (near TS), and $0.9 < p_\mathrm{B}^* \le 1$ (near state B). The rightmost panel shows the absolute values of the coefficients $(w_1, w_2, \cdots, w_{90})$ obtained from the LR model. Reproduced from T. Kikutsuji, Y. Mori, K.-i. Okazaki, T. Mori, K. Kim, and N. Matubayasi, J. Chem. Phys. 156, 154108 (2022) kikutsuji2022Explaining; licensed under a Creative Commons Attribution (CC BY) license.
• Figure 5: Scatter plot for RMSEs between the predicted and reference $p_\mathrm{B}$ for the training and test data sets. Filled and open circles indicate the RMSEs using full points and those at about the TS ($-0.2 < q_i < 0.2$), respectively. Blue and red colors are the results in vacuum and water. $q_2$ in water shows a sign of slight overfitting, yet the RMSE against the test data is only marginally larger than the other RCs. Reproduced from K. Kawashima, T. Sato, K.-i. Okazaki, K. Kim, N. Matubayasi, and T. Mori, APL Mach. Learn 3, 016113 (2025)kawashima2025Investigating; licensed under a Creative Commons Attribution (CC BY) license.