The observation of strongly lensed Type Ia supernovae enables both the luminosity and angular diameter distance to a source to be measured simultaneously using a single observation. This feature can be used to measure the distance duality parameter $\eta \left(z\right)$ without relying on multiple datasets and cosmological assumptions to reconstruct the relation between angular and luminosity distances. In this paper, we show how this can be achieved by future observations of strongly lensed Type Ia systems. Using simulated datasets, we reconstruct the function $\eta \left(z\right)$ using both parametric and non-parametric approaches, focusing on Genetic Algorithms and Gaussian processes for the latter. In the parametric approach, we find that in the realistic scenario of $N_{\mathrm{lens}}=20$ observed systems, the parameter ${ϵ}_0$ used to describe the trend of $\eta \left(z\right)$ can be constrained with the precision achieved by current SNIa and BAO surveys, while in the futuristic case ($N_{\mathrm{lens}}=1000$) these observations could be competitive with the forecast precision of upcoming LSS and SN surveys. Using the machine learning approaches of Genetic Algorithms and Gaussian processes, we find that both reconstruction methods are generally well able to correctly recover the underlying fiducial model in the mock data, even in the realistic case of $N_{\mathrm{lens}}=20$. Both approaches learn effectively from the features of the mock data points, yielding $1\sigma$ constraints that are in excellent agreement with the parameterised results.

观测具有强透镜的Ia型超新星使得可以通过一次观测同时测量到光源的光度和角直径距离。此功能可用于测量距离对偶参数 $\eta （ž）$无需依赖多个数据集和宇宙学假设来重建角度距离和光度距离之间的关系。在本文中，我们展示了如何通过对强透镜Ia型系统的未来观察来实现这一目标。使用模拟数据集，我们重建函数 $\eta （ž）$同时使用参数方法和非参数方法，重点是遗传算法和后者的高斯过程。在参数方法中，我们发现在实际情况下 ${ñ}_{\mathrm{镜片}}=20$ 观察系统，参数 ${ϵ}_0$ 用来描述趋势 $\eta （ž）$ 可能会受到当前SNIa和BAO调查所达到的精度的限制，而在未来的情况下（${ñ}_{\mathrm{镜片}}=1000$）这些观察结果可能与即将进行的LSS和SN调查的预测精度具有竞争力。使用遗传算法和高斯过程的机器学习方法，我们发现，即使在实际情况下，这两种重构方法通常也能够正确地恢复模拟数据中的基准模型。 ${ñ}_{\mathrm{镜片}}=20$。两种方法都可以从模拟数据点的特征中有效学习，从而产生 $\mathrm{1个}\sigma$ 与参数化结果非常吻合的约束。