A problem that has remained without an analytical solution for three centuries: researchers train a network on N-body simulations and then extract legible formulae that beat existing estimates.
Predicting when a system of several planets will destabilize, with collisions or ejections, has resisted astronomers since Newton's time. Machine learning already knows how to make good predictions, but in the form of a black box, without teaching physicists anything. Dan Tamayo's team proposes to get around this pitfall.
From black box to formula
The method proceeds in two stages: first, a neural network is trained on a large set of many-body simulations by learning a small number of interpretable variables, and then a symbolic regression looks for closed algebraic expressions that reproduce what it has learned. The resulting equations predict instability better than known analytical estimates, and remain valid over a wide range of mass ratios, spacings, and orbital eccentricities.
Because they use only a few variables, these formulas lend themselves to dynamic interpretation, which makes it possible to link predictions to existing theories. The authors see them as an example of how neural networks and symbolic learning can combine to produce scientific knowledge, not just predictions.
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