A semi-analytical surrogate model for giant planet evolution: bypassing ordinary differential equation solvers with localised thermodynamics, softplus asymptotes, and B-spline photometry
Context. Evolutionary models translate the observable luminosity, temperature, and colours of giant planets and brown dwarfs into mass and age. Generating their cooling tracks normally requires integrating the internal energy over time with an ordinary differential equation (ODE) solver coupled to pre-computed atmospheric grids, which becomes numerically stiff at sharp transitions such as cloud condensation and the onset of electron degeneracy, and is fragile inside Bayesian retrievals. Aims. We aim to generate continuous cooling tracks and photometric light curves directly from discrete atmospheric grids, without an ODE solver. Methods. We mapped the grids into a logarithmic thermodynamic space and extracted localised surrogate models with Gaussian-weighted regressions at fixed planetary parameters. We fitted the entropy and cooling rate against the internal temperature using bounded piecewise softplus functions to capture structural and cooling-rate transitions; the radius was fitted on the same temperature axis; and band photometry was represented with fixed-knot cubic B-splines. The age followed from numerical integration of these analytic functions, and uncertainties were propagated from the residual scatter of each fit. Results. The surrogate, CoolTrack, reproduces the transition into electron degeneracy and the L-to-T spectral-type transition in the colour-magnitude diagram, converges on Solar System benchmarks, and evaluates a full evolutionary track in milliseconds on a standard desktop CPU. Conclusions. By removing the forward-modelling bottleneck, CoolTrack is suitable for direct use in Bayesian retrieval pipelines, where the age, mass, and formation entropy of a planet can be inferred jointly with its atmospheric properties.