StringNET: Neural Network based Variational Method for Transition Pathways
This addresses the computational bottleneck of calculating transition pathways in non-equilibrium physical and chemical processes, representing an incremental improvement over traditional chain-of-state methods.
The authors tackled the problem of efficiently computing transition pathways between meta-stable states in noisy systems, which is crucial for computational chemistry, by proposing StringNET, a neural network-based variational method that unifies gradient descent and re-parametrization into a single framework with a pre-training strategy. They demonstrated superior performance on analytical, chemical, and Ginzburg-Landau functional energy examples, though no concrete numerical results were provided in the abstract.
Rare transition events in meta-stable systems under noisy fluctuations are crucial for many non-equilibrium physical and chemical processes. In these processes, the primary contributions to reactive flux are predominantly near the transition pathways that connect two meta-stable states. Efficient computation of these paths is essential in computational chemistry. In this work, we examine the temperature-dependent maximum flux path, the minimum energy path, and the minimum action path at zero temperature. We propose the StringNET method for training these paths using variational formulations and deep learning techniques. Unlike traditional chain-of-state methods, StringNET directly parametrizes the paths through neural network functions, utilizing the arc-length parameter as the main input. The tasks of gradient descent and re-parametrization in the string method are unified into a single framework using loss functions to train deep neural networks. More importantly, the loss function for the maximum flux path is interpreted as a softmax approximation to the numerically challenging minimax problem of the minimum energy path. To compute the minimum energy path efficiently and robustly, we developed a pre-training strategy that includes the maximum flux path loss in the early training stage, significantly accelerating the computation of minimum energy and action paths. We demonstrate the superior performance of this method through various analytical and chemical examples, as well as the two- and four-dimensional Ginzburg-Landau functional energy.