A major challenge in extracting information from current and upcoming surveys of cosmological large-scale structure (LSS) is the limited availability of computationally expensive high-fidelity simulations. We introduce calibrated neural quantile estimation, a new simulation-based inference (SBI) method that leverages a large number of approximate simulations for training and a small number of high-fidelity simulations for calibration. This approach guarantees an unbiased posterior regardless of approximate simulation accuracy, while achieving near-optimal constraining power when the approximate simulations are reasonably accurate. As a proof of concept, we demonstrate that cosmological parameters can be inferred at field level from projected 2-dimensional dark matter density maps up to $k_{\max }\sim 1.5h/\mathrm{Mpc}$ at $z=0$ by training on $\sim {10}^4$ particle-mesh simulations with transfer function correction and calibrating with $\sim {10}^2$ particle-particle (PP) simulations. The calibrated posteriors closely match those obtained by directly training on $\sim {10}^4$ expensive PP simulations, but at a fraction of the computational cost. Our method offers a practical and scalable framework for SBI of cosmological LSS, enabling precise inference across vast volumes and down to small scales.

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• Cosmology
• Large scale structure of the Universe
• Astrophysical & cosmological simulations
• Data analysis
• Machine learning
• Statistical methods