Visualizing Neural Network Developing Perturbation Theory
This provides a benchmark for machine-assisted physics research, though it is incremental as it applies existing neural network methods to a specific quantum mechanics problem.
The researchers tackled the problem of whether neural networks can discover physical laws by training one to predict s-wave scattering length directly from scattering potentials in a quantum two-body system, showing that the network develops perturbation theory order-by-order as potential strength increases.
In this letter, motivated by the question that whether the empirical fitting of data by neural network can yield the same structure of physical laws, we apply the neural network to a simple quantum mechanical two-body scattering problem with short-range potentials, which by itself also plays an important role in many branches of physics. We train a neural network to accurately predict $ s $-wave scattering length, which governs the low-energy scattering physics, directly from the scattering potential without solving Schrödinger equation or obtaining the wavefunction. After analyzing the neural network, it is shown that the neural network develops perturbation theory order by order when the potential increases. This provides an important benchmark to the machine-assisted physics research or even automated machine learning physics laws.