Visualizing Neural Network Developing Perturbation Theory

Collaborative Innovation Center of Quantum Matter, Beijing, 100084, China (Dated: March 12, 2018) Motivated by the question that whether the empirical fitting of data by neural networks can yield the same structure of physical laws, we apply neural networks to a quantum mechanical two-body scattering problem with short-range potentials--a problem by itself plays an important role in many branches of physics. After training, the neural network can accurately predict s - wave scattering length, which governs the low-energy scattering physics. By visualizing the neural network, we show that it develops perturbation theory order by order when the potential depth increases, without solving the Schr odinger equation or obtaining the wavefunction explicitly. The result provides an important benchmark to the machine-assisted physics research or even automated machine learning physics laws. Human physicists have made great achievements in discovering laws of physics during the last several centuries.