Estimating Parameters of Gravitationally Lensed Quasars with Simulation-Based Inference and SplineCNNs

The Hubble Tension is considered a crisis for the LCDM model in modern cosmology. Addressing this prob-lem presents opportunities for identifying issues in data acquisition and processing pipelines or discovering new physics related to dark matter and dark energy. Time delays in the time-varying flux of gravitationally lensed quasars can be used to precisely measure the Hubble constant ( H 0 ) and potentially address the aforementioned crisis. Gaussian Processes (GPs) are typically used to model and infer quasar light curves; unfortunately, the optimization of GPs incurs a bias in the time-evolution parameters. In this work, we intro-duce a machine learning approach for fast, unbiased inference of quasar light curve parameters. Our method is amortized, which makes it applicable to very large datasets from next-generation surveys, like LSST. Addi-tionally, since it is unbiased, it will enable improved constraints on H 0 . Our model uses Spline Convolutional VAE (SplineCVAE) to extract descriptive statistics from quasar light curves and a Sequential Neural Posterior Estimator (SNPE) to predict posteriors of Gaussian process parameters from these statistics. Our SplineCVAE reaches reconstruction loss RMSE=0.04 for data normalized in the range [0 , 1] . SNPE predicts the order of magnitude of time-evolution parameters with an absolute error of less than 0.2.