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Computer manufacturers spend a huge amount of time, resources, and money in designing new systems and newer configurations, and their ability to reduce costs, charge competitive prices, and gain market share depends on how good these systems perform. In this work, we concentrate on both the system design and the architectural design processes for parallel computers and develop methods to expedite them. Our methodology relies on extracting the performance levels of a small fraction of the machines in the design space and using this information to develop linear regression and neural network models to predict the performance of any machine in the whole design space. In terms of architectural design, we show that by using only 1% of the design space (i.e., cycle-accurate simulations), we can predict the performance of the whole design space within 3.4% error rate. In the system design area, we utilize the previously published Standard Performance Evaluation Corporation (SPEC) benchmark numbers to predict the performance of future systems. We concentrate on multiprocessor systems and show that our models can predict the performance of future systems within 2.2% error rate on average. We believe that these tools can accelerate the design space exploration significantly and aid in reducing the corresponding research/development cost and time-to-market.