Interpretable symbolic regression for cosmological parameter recovery from CMB power spectra

Interpretable machine-learning methods provide a complementary approach to cosmological parameter inference by yielding explicit analytic relations between observables and model parameters. We investigate symbolic regression as an interpretable framework for recovering cosmological parameters from cosmic microwave background (CMB) power spectra in a controlled synthetic setting. Synthetic TT, TE, and EE angular power spectra are generated using CAMB across a five-parameter ΛCDM-inspired parameter space, and symbolic regression models are trained to recover n_s, ln(10¹⁰A_s), ω_b, ω_cdm, and τ. Predictive performance is evaluated using held-out test data together with robustness and uncertainty analyses, and comparisons are made against Random Forest and multilayer perceptron (MLP) baselines. Symbolic regression recovers n_s, ln(10¹⁰A_s), ω_cdm, and τ with high accuracy (R² ≳ 0.99), yielding compact analytic expressions that capture physically plausible spectral sensitivities. Perturbation and feature-ablation analyses recover qualitatively expected parameter sensitivities, including the importance of low-ℓ polarization information for τ and higher-ℓ structure for n_s. Robustness tests show stable performance under controlled perturbations and resampling variations. In contrast, ω_b is substantially more difficult to infer directly from raw spectra, but feature engineering based on acoustic peak morphology significantly improves recovery and produces compact interpretable relations. These results indicate a parameter-dependent pattern in the symbolic recoverability of cosmological information from CMB spectra and suggest that symbolic regression, particularly when combined with physics-informed feature design, provides a complementary interpretable surrogate-modeling framework for constructing compact mappings between CMB observables and cosmological parameters in controlled synthetic settings. This is a preprint version of a manuscript under revision at Astronomy and Computing following peer review. Associated datasets, trained models, and reproducibility materials:https://doi.org/10.5281/zenodo.20224914 Code repository:https://github.com/rudhresh1997/cmb-symbolic-regression