575 research outputs found
Visualizing Neural Network Developing Perturbation Theory
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 -wave scattering length, which governs the low-energy scattering
physics, directly from the scattering potential without solving Schr\"odinger
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.Comment: 5 pages, 4 figure
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