Learning Equations from Data: Exhaustive Symbolic Regression
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Salle 9111
Symbolic Regression (SR) algorithms learn analytic expressions which fit data accurately and in a highly interpretable manner. As such, these methods can be used to help uncover "physical laws" from data or provide simple and interpretable effective descriptions of complex, non-linear phenomena. Conventional SR suffers from two fundamental issues which I address here. First, typical SR methods search the space stochastically and hence do not necessarily find the best function. Second, the criteria used to select the equation optimally balancing accuracy with simplicity have been variable and poorly motivated. I will introduce a new method for SR – Exhaustive Symbolic Regression (ESR) - which addresses both of these issues. To illustrate the power of ESR, I will apply it to a catalogue of cosmic chronometers and the Pantheon+ sample of supernovae to learn the Hubble rate as a function of redshift, finding ~40 functions (out of 5.2 million considered) that fit the data more economically than the Friedmann equation. I will then employ ESR to learn the form of the radial acceleration relation (RAR) of galaxy dynamics and therefore assess the claim that its asymptotic limits provide evidence for a new law of nature, namely Modified Newtonian Dynamics.
