- I wanted to see how far I could push this idea.Electrostatic charge configuration for N=625 in equilibrium.
- Probably not.The Thomson problem is a classical physics question, “What configuration of N positive charges on the unit sphere minimizes the energy?”
- N=11 puts the charges in a configuration that completely breaks the symmetry — while the charges are in equilibrium, they are distributed in such a way that there are more on one side than the other; it has a net dipole moment!Solving this in TF is surprisingly easy.
- For any value of N, we can converge to a stable solution energy minima in a matter of seconds, and we can refine that to the full floating point precision in a matter of minutes by tapering down the learning rate.
- That’s an impressive 10x speedup!Minimal energy for N=100 charges, prettified.Visualizing the configurations illustrates the regularity and the apparent symmetry, even if we are content knowing that it might not be the global minimum.
Is Google’s machine intelligence library TensorFlow (TF) good for something beyond deep learning? How well can it tackle a classic physics problem?
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