We have found that limiting non-physical outputs relies on a careful curation of training data, an appropriate loss function, and a physics-informed neural network architecture. Each of these aspects is necessary but insufficient on its own to produce a reliable, stable seasonal forecast system. The design process that led to the most success was informed by physical and scientific reasoning through all stages and relied only on advanced ML techniques when more basic methods were insufficient. For this reason, we have found that tightly coupling scientific and ML engineering expertise is necessary for successfully developing fully data-driven forecast systems.
This forecast system is being used operationally in private markets and has undergone extensive testing and validation, both internal to our company and by external parties. The scientific methodology has also been reviewed and approved by the National Science Foundation on two separate occasions.

