Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Architecturally Constrained Solutions to Ill-Conditioned Problems in QUBIC

Leonora Kardum

TL;DR

Ill-posed inverse problems in CMB map reconstruction from QUBIC TOD arise from non-invertible instrumental operators. The authors introduce a physics-guided, modular neural architecture that embeds analytical inverses of known operators while learning only the ill-conditioned or unknown pieces, stabilizing the inversion. On simulated data, this approach reduces the effective conditioning of the forward model and achieves lower reconstruction error than PCG, with interpretable, physically meaningful parameters and orders-of-magnitude fewer trainable parameters. This framework offers a scalable, interpretable path for applying AI to complex, ill-posed instrumentation problems beyond CMB mapping.

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.

Architecturally Constrained Solutions to Ill-Conditioned Problems in QUBIC

TL;DR

Ill-posed inverse problems in CMB map reconstruction from QUBIC TOD arise from non-invertible instrumental operators. The authors introduce a physics-guided, modular neural architecture that embeds analytical inverses of known operators while learning only the ill-conditioned or unknown pieces, stabilizing the inversion. On simulated data, this approach reduces the effective conditioning of the forward model and achieves lower reconstruction error than PCG, with interpretable, physically meaningful parameters and orders-of-magnitude fewer trainable parameters. This framework offers a scalable, interpretable path for applying AI to complex, ill-posed instrumentation problems beyond CMB mapping.

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.

Paper Structure

This paper contains 8 sections, 10 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Operator-based Modelling of the QUBIC Instrument
  3. Modular Neural Architecture with Embedded Physics
  4. Examples of operator inversion
  5. Bolometer time response as a dynamic module.
  6. Projection operator as a learnable module.
  7. Application to CMB Map Reconstruction
  8. Conclusion

Figures (2)

  • Figure 1: (a) Schematic of the QUBIC instrument. (b) Synthesized beam, the interferometric pattern, at 150 GHz with 9 peaks. Taken from qubicIII.
  • Figure 2: Simulated sky in Q Stokes, the corresponding reconstructed sky, and the reconstruction error. (a) Example reconstruction with the PCG method. (b) Example reconstruction with the proposed method.