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

02 September 2020, Version 1
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

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.

Keywords

neural networks
deep neural networks
machine learning
inverse problems
electron dynamics
time dependent Schrödinger equation
Optimal Control Theory
Optimal Control
electronic excited states
theoretical chemistry
supervised machine learning

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