Implement dynamically weighted MSE loss function #2485

Describe the task. It can be a feature, documentation, etc.

In Samudra 2 an improved MSE loss was introduced, using EMA to calculate channel weights dynamically during training. In their case it showed significant improvement in case of channels with low temporal variability.

This loss function is easy to implement and worth having as an option

Hedgedoc URL, if you are keeping notes, plots, logs in hedgedoc.

https://arxiv.org/abs/2606.02610

Area

• datasets, data readers, data preparation and transfer
• model
• science
• infrastructure and engineering
• evaluation, export and visualization
• documentation
• performance