Using PostgreSQL as dummy model storage:

Train a model in Python.
Establish PostgreSQL connection, dump your model in Pickle data format to the "models" table. Obviously, the data type of the main column should be BLOB.
Anytime you want to use the model for some application, unpickle it from the "models" table.

The "models" table may have extra columns for storing the model in alternative data formats such as PMML. Assuming you've used correct Python-to-PMML conversion tools, you can assume that the Pickle representation and the PMML representation of the same model will be functionally identical (ie. making the same prediction when given the same input). Using PMML in Java/JVM applications is easy.
I'm restricted to a PostgreSQL as 'model storage' for the models itself or respective components (coefficients, ..). Obviously, PostgreSQL is far from being a fully-fledged model storage, so I can't rule out that I have to implement the whole model training process in Java [...].
I couldn't find a solution that involves a PostgreSQL database as intermediate storage for the models. Writing files directly to the disk/other storages isn't really an option for me. I considered calling Python code from within the Java application but I don't know whether this would be an efficient solution for subsequent inference tasks and beyond [...]. Are there ways to serialize PMML or other formats that can be loaded via Java implementations of the algorithms? Or ways to use the model definitions/parameters directly for reproducing the model [...]?
How to save XGBoost/LightGBM model to PostgreSQL database in Python for subsequent inference in Java?