Lithographic apparatus, device manufacturing method and associated data processing apparatus and computer program product

A lithographic process includes clamping (CL) a substrate (W) onto a substrate support (WT), measuring (AS) positions of marks across the clamped substrate, and applying a pattern to the clamped using the positions measured. A correction (WCOR) is applied to the positioning of the applied pattern in localized regions of the substrate, based on recognition of a warp-induced characteristic (402, 404, 406) in the positions measured across the substrate. In one embodiment the correction is generated by firstly inferring one or more shape characteristics of the warped substrate (FFW) using the measured positions and other information (CDAT). Then, based on the inferred shape characteristics, a clamping model is applied (WCM) to simulate deformation of the warped substrate in response to clamping. Thirdly said correction (LCOR) is calculated based on the simulated deformation. Some or all of these steps may be integrated and/or implemented by a look-up table.