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Tsunamis in the last two decades have resulted in the loss of life of over 200,000 people and have caused billions of dollars in damage. There is therefore great motivation for the development and improvement of current tsunami warning systems. The work presented here represents advancements made towards the creation of a neural network-based tsunami warning system which can produce fast inundation forecasts with high accuracy. This was done by first improving the waveform resolution and accuracy of Tsunami Squares, an efficient cellular automata approach to wave simulation. It was then used to create a database of precomputed tsunamis in the event of a magnitude 9+ rupture of the Cascadia Subduction Zone, located only ∼100 km off the coast of Oregon, US. Our approach utilized a convolutional neural network which took wave height data from buoys as input and proved successful as maps of maximum inundation could be predicted for the town of Seaside, OR with a median error of ∼0.5 m.