Scientific Context
Measurements of the Cosmic Microwave Background (CMB) polarization are among the most promising avenues for detecting primordial gravitational waves through the tensor-to-scalar ratio r. However, classical analysis pipelines (time-ordered data → maps → spectra → likelihood) rely on numerous approximations and treat instrumental noise, foregrounds, and cosmological signals in separate stages.
Simulation-Based Inference (SBI) provides an alternative approach: instead of assuming an explicit likelihood, one trains neural estimators on simulations and infers posteriors directly from data. This strategy is central to the ERC SciPol project, which aims to build next-generation end-to-end CMB analysis tools.
Internship Objectives
The goal of this internship is to design and study a minimal, fully self-contained toy pipeline for CMB B-mode analysis, and to apply Simulation-Based Inference to infer key parameters such as:
- the tensor-to-scalar ratio r,
- the dust foreground amplitude Adust,
- and/or the noise amplitude σₙ.
The student will explore whether SBI can provide improved posterior estimation compared to standard Gaussian likelihood approaches, in a controlled and computationally light setting.
Work Plan
0. Implementation of the framework (Weeks 1-2)
- explore existing and open-access tools; assess their capabilities
- design/conception of the needed framework, in connection with FURAX
- simple validation cases, profiling, etc.
1. Forward simulation of polarized skies (Weeks 3 - 4)
- Generate low-resolution polarized CMB maps with varying r (e.g., nside = 16–32).
- Add a simple polarized dust component (PySM3 or analytic template).
- Include white and/or correlated noise.
- Extract summary statistics (pixel maps, or EE/BB pseudo-spectra).
2. Application of Simulation-Based Inference (Weeks 4 - 6)
- Implement SBI using libraries such as sbi, swyft, or JAX-based flows.
- Train neural posterior estimators for {r}, {r, A_dust}
- Assess convergence, degeneracies, and the ability of SBI to capture non-Gaussian structures.
3. Benchmark against classical methods (Weeks 6 - 8)
- Implement a standard Gaussian likelihood on maps or spectra.
- Compare posteriors from likelihood vs SBI: bias, variance, robustness to foreground uncertainty.
4. Optional Extensions (Weeks 8 - 10)
Depending on progress:
- explore compressed summaries for SBI,
- infer a simple noise or systematic parameter (e.g. a 1/f knee),
- prototype a small JAX-based differentiable simulator.
Expected Outcomes
- A complete and transparent toy pipeline for B-mode analysis.
- Neural posterior estimators trained on simulated CMB data.
- A quantitative comparison between SBI and classical inference.
- A short scientific report, the oral presentation in front of the M2 jury, and reusable notebooks, contributing to ERC SciPol methodological developments.