The hybridizations of machine learning and quantum physics have caused essential impacts to the methodology in both fields. Inspired by quantum potential neural network, we here propose to solve the potential in the Schrodinger equation provided the eigenstate, by combining Metropolis sampling with deep neural network, which we dub as Metropolis potential neural network (MPNN). A loss function is proposed to explicitly involve the energy in the optimization for its accurate evaluation. Benchmarking on the harmonic oscillator and hydrogen atom, MPNN shows excellent accuracy and stability on predicting not just the potential to satisfy the Schrodinger equation, but also the eigen-energy. Our proposal could be potentially applied to the ab-initio simulations, and to inversely solving other partial differential equations in physics and beyond.

中文翻译：

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通过深度神经网络和都市采样预测量子势

机器学习和量子物理学的混合对这两个领域的方法论产生了重要影响。受量子势神经网络的启发，我们在此提出通过将 Metropolis 采样与深度神经网络相结合来求解提供本征态的薛定谔方程中的势，我们将其称为 Metropolis 势神经网络 (MPNN)。提出了一个损失函数来明确地将能量参与到优化中，以对其进行准确评估。以谐振子和氢原子为基准，MPNN 在预测满足薛定谔方程的潜力以及本征能量方面表现出出色的准确性和稳定性。我们的提议可能适用于 ab-initio 模拟，以及物理及其他领域的其他偏微分方程的逆求解。