Observational Insights on DBI K‐Essence Models Using Machine Learning and Bayesian Analysis

ABSTRACT We perform a late‐time cosmological study, we compare the performance of two Dirac–Born–Infeld (DBI) type k‐essence scalar field extensions of the model to the standard framework and a scenario using the Chevallier–Polarski–Linder (CPL) equation of state parametrization. We solve background dynamics numerically as functions of redshift and incorporate them into a Bayesian inference pipeline accelerated by machine learning. We use a Flax‐based surrogate emulator to replace repeated direct integrations of the ODE system, reducing computational cost. A hybrid scheme that combines stochastic variational inference (SVI) with No‐U‐Turn Hamiltonian Monte Carlo constrains cosmological parameters using the Pantheon+SH0ES Type Ia supernova sample, DESI BAO (DR2) data, and cosmic chronometer measurements without CMB‐based priors. In both DBI k‐essence formulations, present‐day dark energy equations of state are consistent with cosmic acceleration, indicating a ‐like regime with a modest redshift dependence. The model is marginally favored by conventional model selection measures such as , AIC, BIC, and DIC, which are based on goodness of fit and penalized. However, Bayesian predictive measures like WAIC and PSIS–LOO show no significant differences between , , and DBI k‐essence scenarios. All have similar model weights and out‐of‐sample predictive performance for the datasets. Thus, DBI k‐essence models mimic the success of the classic paradigm while allowing controlled, redshift‐dependent deviations from a strict cosmological constant that are consistent with present late‐time observations.