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Autoregressive solver #730

@Davide-Miotti

Description

@Davide-Miotti

This issue addresses the need for a framework that handles autoregressive problems, i.e. problems where the current state of a system is consumed by the model to forecast the state at the next time step.
The main feature missing in PINA is an AutoregressiveSolver.

My idea is to implement some early version the following components:

  • AutoregressiveCondition: this is NOT compulsory, InputTargetCondition should be adequate if the user does enough pre-processing, however I believe that as the library grows a differentiation could be desirable.
    For a first implementation an autoregressive condition than only handles torch tensors with a specific shape could be enough.
  • AutoregressiveSolver: this is inevitable since it must recursively call the model on its own output
  • some strategy to weight differently the loss as the recursive cycle progress within the AutoregressiveSolver

Describe alternatives you've considered
Main alternatives are to implement a standalone AutoregressiveSolver or also implement an AutoregressiveCondition

Additional context
In the future a framework for autoregressive problems might come handy in many different applications.

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