A lithographic process includes clamping a substrate onto a substrate support, measuring positions across the clamped substrate, and applying a pattern to the clamped substrate using the positions measured. A correction is applied to the positioning of the applied pattern in localized regions of the substrate, based on recognition of a warp-induced characteristic in the positions measured across the substrate. The correction may be generated by inferring one or more shape characteristics of the warped substrate using the measured positions and other information. Based on the one or more inferred shape characteristics, a clamping model is applied to simulate deformation of the warped substrate in response to clamping. A correction is calculated based on the simulated deformation.