How do I train an ANN to deal with diverging inputs

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For inputs: Let Y be results axis from data from various samples, influenced by one known variable and other uncontrolled conditions. There will be regions on the X axis (the control variable) where multiple very different Y values will cluster close to the same X value. The ANN model uses the data on the Y axis to predict the values that would be on the X axis.

I am using similar divergent data to train the ANN, but when validating with new data, I still get significant error and spread in regions where the Y inputs vary wildly.