Architecturally Constrained Solutions to Ill-Conditioned Problems in QUBIC

Abstract

This article introduces a new physics-guided Machine Learning framework, with which we solve the generally non-invertible, ill-conditioned problems through an analytical approach and constrain the solution to the approximate inverse with the architecture of Neural Networks. By informing the networks of the underlying physical processes, the method optimizes data usage and enables interpretability of the model while simultaneously allowing estimation of detector properties and the propagation of their corresponding uncertainties. The method is applied in reconstructing Cosmic Microwave Background (CMB) maps observed with the novel interferometric QUBIC experiment aimed at measuring the tensor-to-scalar ratio r.