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Gravitational lensing by massive galaxy clusters distorts the observed cosmicmicrowave background (CMB) on arcminute scales, and these distortions carryinformation about cluster masses. Standard approaches to extracting clustermass constraints from the CMB cluster lensing signal are either sub-optimal,ignore important physical or observational effects, are computationallyintractable, or require additional work to turn the lensing measurements intoconstraints on cluster masses. We apply simulation based inference (SBI) usingneural likelihood models to the problem. We show that in circumstances wherethe exact likelihood can be computed, the SBI constraints on cluster masses arein agreement with the exact likelihood, demonstrating that the SBI constraintsare close to optimal. In scenarios where the exact likelihood cannot befeasibly computed, SBI still recovers unbiased estimates of individual clustermasses and combined constraints from multiple clusters. SBI will be a powerfultool for constraining the masses of galaxy clusters detected by future cosmicsurveys. Code to run the analyses presented here will be made publiclyavailable.

Inferring galaxy cluster masses from cosmic microwave background lensing with neural simulation based inference