A Machine Learning Approach to Finslerian Cosmological Dark Energy Model

arXiv:2610.26882v2 Announce Type: new Abstract: Modified extensions of the standard cosmological models often introduce complex parameter degeneracies that severely impact sampling convergence of the parameter space while analyzing the model observationally. In this work, we present an accelerated Bayesian inference technique using a Heteroscedastic Deep Ensemble with Monte Carlo Dropout incorporating distance-gated local residual corrections to emulate complex likelihood surfaces and avoid extrapolation beyond the trained region. We demonstrate this methodology on a unified dark energy cosmological model equipped with Finsler geometry. The model is studied using the recent observational datasets, including Cosmic Chronometers (CC), Pantheon$+$SH$0$ES, and DESI DR$2$ BAO measurements. While the conventional sampling procedure struggles with slow mixing of parameter chains ($\tau_{max}=1578.3$), the neural network, specially trained densely in high likelihood regions, yields converged and highly resolved posterior distributions of the model parameters without significantly compromising the minimum chi-square value. We further discuss the results for physical inferences and also compare the present dark energy model with $\Lambda\text{CDM}$ statistically using AIC and BIC.