How to reduce uncertainty in object pose estimation under complex contacts is crucial to autonomous robotic manipulation and assembly. In this paper, we introduce an approach through forecasting contact force from simulated complex contacts with calibration based on real force sensing. A constraint-based haptic simulation algorithm is used with sphere-tree representation of contacting objects to compute contact poses and forces, and through matching the computed forces to measured real force data via a regression model, the least-uncertain estimate of the relative contact pose is obtained. Our approach can handle multi-region complex contacts and does not make any assumption about contact types or contact locations. It also does not have restriction on object shapes. We have applied the force forecast approach to reducing uncertainty in estimating object poses in challenging peg-in-hole robotic assembly tasks and demonstrate the effectiveness of the approach by successful completion of contact-rich two-pin and three-pin real peg-in-hole assembly tasks with complex shapes of pins and holes.