Spherical Fourier Neural Operators for Cosmic Microwave Background Delensing

Alessio Spurio Mancini

Keywords: cosmology, differentiable inference, spherical harmonic transforms

TL;DR: For the first time, we delens CMB maps using Spherical Fourier Neural Operators, using a completely differentiable framework written in JAX.

Abstract: Gravitational lensing by large-scale structure distorts the cosmic microwave background (CMB), mixing primordial E-mode polarization into lensing-induced B-modes that obscure the faint primordial gravitational wave signature. Delensing---recovering the unlensed CMB signal---is critical for next-generation experiments targeting tensor-to-scalar ratios $r < 0.001$. We present the first application of Spherical Fourier Neural Operators (SFNO) to CMB delensing, demonstrating that neural operators can learn this non-local transformation on the sphere. Our implementation leverages recent advances in differentiable spherical harmonic transforms on HEALPix pixelizations to enable gradient-based training in JAX. Training on realistic Planck-based simulations, our SFNO architecture successfully recovers unlensed B-mode polarization maps, demonstrating effective learning of the delensing transformation and showing that neural operators combined with differentiable spherical transforms can address fundamental challenges in cosmological data analysis.

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Submission Number: 58