Flexible uncertainty calibration for machine-learned interatomic potentials

Reliable uncertainty quantification (UQ) is essential for developing machine-learned interatomic potentials (MLIPs) in predictive atomistic simulations. Conformal prediction (CP) is a statistical framework that constructs prediction intervals with guaranteed coverage under minimal assumptions, making it an attractive tool for UQ. However, existing CP techniques, while offering formal coverage guarantees, often lack accuracy, scalability, and adaptability to the complexity of atomic environments. In this work, we present a flexible uncertainty calibration framework for MLIPs, inspired by CP but reformulated as a parameterized optimization problem. This formulation enables the direct learning of environment-dependent quantile functions, producing sharper and more adaptive predictive intervals at negligible computational cost. Using the foundation model MACE-MP-0 as a representative case, we demonstrate the framework across diverse benchmarks, including ionic crystals, catalytic surfaces, and molecular systems. Our results achieve substantial improvements in uncertainty-error correlation, improve the detection of high-error configurations for active learning, and transfer reliably across distinct exchange-correlation functionals. Importantly, it is general, data efficient, and compatible with diverse MLIP architectures and baseline UQ schemes, offering a practical route toward robust and transferable atomistic simulations.