Extreme Ultraviolet (EUV) photolithography is seen as the key enabler for increasing transistor density in the next decade. In EUV lithography, 13.5 nm EUV light is illuminated through a reticle, holding a pattern to be printed, onto a silicon wafer. This process is performed about 100 times per wafer, at a rate of over a hundred wafers an hour. During this process, a certain percentage of the light energy is converted into heat in the wafer. In turn, this heat causes the wafer to deform which increases the overlay error, and as a result, reduces the manufacturing yield. To alleviate this, we propose a firm real-time control system that uses a wafer heat feed-forward model to compensate for the wafer deformation. The model calculates the expected wafer deformation, and then, compensates for that by adjusting the light projection and/or the wafer movement. However, the model computational demands are very high. As a result, it needs to be executed on dedicated HW that can perform computations quickly. To this end, we deploy Graphics Processing Units (GPUs) to accelerate the calculations. In order to fit the computations within the required time budgets, we combine in a novel manner multiple techniques, such as compression and mixed-precision arithmetic, with recent advancements in GPUs to build a GPU-based real-time control system. A proof-of-concept implementation using NVIDIA P100 GPUs is able to deliver decompression throughput of 33 GB/s and a sustained 198 GFLOP/s per GPU for mixed-precision dense matrix-vector multiplication.