In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a robust framework for extracting theoretical insights from observational data. However, its computational demands can be substantial, primarily due to the need for numerous likelihood function evaluations. Our proposed method utilizes the power of deep learning, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process. Unlike traditional approaches, our method trains neural networks on-the-fly using the current set of live points as training data, without the need for pre-training. This flexibility enables adaptation to various theoretical models and datasets. We perform simple hyperparameter optimization using genetic algorithms to suggest initial neural network architectures for learning each likelihood function. Once sufficient accuracy is achieved, the neural network replaces the original likelihood function. The implementation integrates with nested sampling algorithms and has been thoroughly evaluated using both simple cosmological dark energy models and diverse observational datasets. Additionally, we explore the potential of genetic algorithms for generating initial live points within nested sampling inference, opening up new avenues for enhancing the efficiency and effectiveness of Bayesian inference methods.

翻译：本文提出了一种新颖方法以加速贝叶斯推断过程，特别聚焦于嵌套采样算法。贝叶斯推断在宇宙学参数估计中发挥着关键作用，为从观测数据中提取理论见解提供了稳健框架。然而，其计算需求通常非常庞大，主要源于大量似然函数评估的必要性。我们提出的方法利用深度学习的力量，采用前馈神经网络在贝叶斯推断过程中动态近似似然函数。与传统方法不同，我们的方法无需预训练，而是实时使用当前活跃点集作为训练数据训练神经网络。这种灵活性使其能够适应各种理论模型和数据集。我们通过遗传算法进行简单的超参数优化，为学习每个似然函数建议初始神经网络架构。一旦达到足够精度，神经网络便替代原始似然函数。该实现与嵌套采样算法集成，并已使用简单宇宙学暗能量模型及多样化的观测数据集进行了全面评估。此外，我们探索了遗传算法在嵌套采样推断中生成初始活跃点的潜力，这为提升贝叶斯推断方法的效率与效能开辟了新途径。