| Abstract: |
| Rare transition events in meta-stable systems under noisy fluctuations are crucial for many non-equilibrium physical and chemical processes. The primary contributions to reactive flux are predominantly near the transition pathways that connect two meta-stable states. This work examines 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, accelerating the computation. 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. |
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