Hello, are you using JMP Pro by any chance? In that platform you can publish the prediction formula to the Formula Depot for later use on any data table which is very useful.
If you aren't using JMP Pro then there are probably a few different workarounds. Joining could work but what if you concatenated in new data to your existing file? Assuming the new data has the same column names this could work. Also consider getting the data table structure from the red triangle shown below by copying the script of the data table with no data. Then once you populate new data into that file the model columns should automatically update.
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