I'm not sure why you're unable to apply the _exp... model - I would guess that there's Splunk permissions issue. Are you trying to apply it from another user or app? Experiment models are scoped to the user/app that created them.
The _exp... prefix tells you that this model is controlled by the Experiment - any alerts created from the Experiment will use this model, scheduled training will overwrite this model, etc.
If you'd like to use this model outside an Experiment, the recommended approach is using the "Publish" function, which will clone the Experiment's models to a location of your choice (and allows you to specify a different name). Note that this is a one-time action - it'll export the current state of your model, but if your model changes you would need to Publish again.
Experiments don't support partial fit at this time - you would need to use the "fit" command on the search page to do that.
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