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Harnessing Deep Neural Networks to Solve Inverse Problems in Quantum Dynamics: Machine-Learned Predictions of Time-Dependent Optimal Control Fields

preprint
submitted on 02.09.2020 and posted on 02.09.2020 by Xian Wang, Anshuman Kumar, Christian Shelton, Bryan Wong
Inverse problems continue to garner immense interest in the physical sciences, particularly in the context of controlling desired phenomena in non-equilibrium systems. In this work, we utilize a series of deep neural networks for predicting time-dependent optimal control fields, E(t), that enable desired electronic transitions in reduced-dimensional quantum dynamical systems. To solve this inverse problem, we investigated two independent machine learning approaches: (1) a feedforward neural network for predicting the frequency and amplitude content of the power spectrum in the frequency domain (i.e., the Fourier transform of E(t)), and (2) a cross-correlation neural network approach for directly predicting E(t) in the time domain. Both of these machine learning methods give complementary approaches for probing the underlying quantum dynamics and also exhibit impressive performance in accurately predicting both the frequency and strength of the optimal control field. We provide detailed architectures and hyperparameters for these deep neural networks as well as performance metrics for each of our machine-learned models. From these results, we show that machine learning approaches, particularly deep neural networks, can be employed as a cost-effective statistical approach for designing electromagnetic fields to enable desired transitions in these quantum dynamical systems.

Funding

National Science Foundation Grant No. CBET-1833218

National Science Foundation Grant No. CHE-1808242

History

Email Address of Submitting Author

usagi@alum.mit.edu

Institution

University of California, Riverside

Country

United States

ORCID For Submitting Author

0000-0002-3477-8043

Declaration of Conflict of Interest

no conflict of interest

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