The fast committor machine: Interpretable prediction with kernels

Area of Science:

• Computational chemistry and physics
• Stochastic processes and dynamical systems

Background:

• The committor function is crucial for analyzing transition pathways in complex systems.
• Accurate estimation of the committor is computationally demanding for large systems.

Purpose of the Study:

• Introduce the fast committor machine (FCM), an efficient and interpretable algorithm for approximating the committor function.
• Develop a method that leverages simulated trajectory data for enhanced predictive accuracy.

Main Methods:

• FCM employs a kernel-based model to represent the committor function.
• Kernel construction emphasizes low-dimensional subspaces relevant to transition pathways.
• Randomized linear algebra is utilized for efficient coefficient determination, achieving linear scaling with data size.

Main Results:

• FCM demonstrates higher accuracy compared to neural networks with similar parameter counts.
• The algorithm exhibits faster training times in numerical experiments.
• FCM provides greater interpretability than comparable neural network models.

Conclusions:

• The fast committor machine offers a significant advancement in the efficient and accurate approximation of committor functions.
• FCM's interpretability aids in understanding the underlying dynamics of stochastic systems.
• This method shows promise for applications in molecular dynamics and other complex system analyses.