This work pertains to the laser powder bed fusion (LPBF) additive manufacturing process. The goal of this work is to mitigate the expense and time required for qualification of laser powder bed fusion processed parts. In pursuit of this goal, the objective of this work is to develop and apply a physics-based model predictive control strategy to modulate the thermal history before the part is built. The key idea is to determine a desired thermal history for a given part a priori to printing using a physics-based model. Subsequently, a model predictive control strategy is developed to attain the desired thermal history by changing the laser power layer-by-layer. This is an important area of research because the spatiotemporal distribution of temperature within the part (also known as the thermal history) influences flaw formation, microstructure evolution, and surface/geometric integrity, all of which ultimately determine the mechanical properties of the part. Currently, laser powder bed fusion parts are qualified using a build-and-test approach wherein parameters are optimized by printing simple test coupons, followed by examining their properties via materials characterization and testing - a cumbersome and expensive process that often takes years. These parameters, once optimized, are maintained constant throughout the process for a part. However, thermal history is a function of over 50 processing parameters including material properties and part design, consequently, the current approach of parameter optimization based on empirical testing of simple test coupons seldom transfers successfully to complex, practical parts. Rather than instinctive process parameter optimization, the model predictive control strategy presents a radically different approach to LPBF part qualification that is based on understanding and modulating the causal thermal physics of the process. The approach has three steps: (Step 1) Predict - given a part geometry, use a rapid, mesh-less physics-based simulation model to predict its thermal history, analyze the predicted thermal history trend, isolate potential red flag problems such as heat buildup, and set a desired thermal history that corrects deleterious trends. (Step 2) Parse - iteratively simulate the thermal history as a function of various laser power levels layer-by-layer over a fixed time horizon. (Step 3) Select - the laser power that provides the closest match to the desired thermal history. Repeat Steps 2 and 3 until the part is completely built. We demonstrate through experiments with various geometries two advantages of this model predictive control strategy when applied to laser powder bed fusion: (i) prevent part failures due to overheating and distortion, while mitigating the need for anchoring supports; and (ii) improve surface integrity of hard to access internal surfaces.