Satellite measurements observe the ocean in narrow swaths and leave large gaps between measured regions. We test whether a computer model guided by measurements can fill in the gaps in a map of ocean motion. Using a simplified simulation of ocean motion, we find that increasing the observed information improves reconstruction accuracy. The results also identify saturation points, which differ across settings, beyond which further observations produce little additional change in reconstruction error. At similar observed area, smaller and more widely distributed observations generally produced more accurate reconstructions than fewer, larger observations. We train a model on real ocean data to generate complete field estimates. The model produces blurry results that do not closely match the original ocean motion. Therefore, improving this model and conducting systematic error analysis across multiple ocean fields are important directions for future work.