Papers › Forecasting the power of Higher Order Weak Lensing Statistics with automatically...
Forecasting the power of Higher Order Weak Lensing Statistics with automatically differentiable simulations
Denise Lanzieri, François Lanusse, Chirag Modi, Benjamin Horowitz, Joachim Harnois-Déraps, Jean-Luc Starck, The LSST Dark Energy Science Collaboration
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We present the Differentiable Lensing Lightcone (DLL), a fully differentiable physical model designed for being used as a forward model in Bayesian inference algorithms requiring access to derivatives of lensing observables with respect to cosmological parameters. We extend the public FlowPM N-body code, a particle-mesh N-body solver, simulating lensing lightcones and implementing the Born approximation in the Tensorflow framework. Furthermore, DLL is aimed at achieving high accuracy with low computational costs. As such, it integrates a novel Hybrid Physical-Neural parameterisation able to compensate for the small-scale approximations resulting from particle-mesh schemes for cosmological N-body simulations. We validate our simulations in an LSST setting against high-resolution κTNG simulations by comparing both the lensing angular power spectrum and multiscale peak counts. We demonstrate an ability to recover lensing C_ℓ up to a 10% accuracy at ℓ=1000 for sources at redshift 1, with as few as ∼0.6 particles per Mpc/h. As a first use case, we use this tool to investigate the relative constraining power of the angular power spectrum and peak counts statistic in an LSST setting. Such comparisons are typically very costly as they require a large number of simulations, and do not scale well with the increasing number of cosmological parameters. As opposed to forecasts based on finite differences, these statistics can be analytically differentiated with respect to cosmology, or any systematics included in the simulations at the same computational cost of the forward simulation. We find that the peak counts outperform the power spectrum on the cold dark matter parameter Ω_c, on the amplitude of density fluctuations σ₈, and on the amplitude of the intrinsic alignment signal A_(IA).
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