Skip to content

Relate solver-in-the-loop results to Jacobian conditioning on the Kolmogorov setup #277

Open

Description

@dionhaefner

The solver-in-the-loop benchmark (#274) reports, per solver and unroll K, the error gap each training arm closes and the value of the solver gradient (the stopped-gradient arm's error over the full arm's). It is an open question whether those numbers follow from properties the gradient suite already measures, such as the singular-value spectrum of the solver's Jacobian or how FD agreement degrades with horizon.

Answering it needs gradient-suite runs on the Kolmogorov configuration (64², dt = 0.01, forcing and drag, horizons of 1, 4 and 16 correction intervals) next to the campaign results. Each SIL run already records:

  • the training-loss FD error at zero and nonzero readout;
  • the gradient norm at the identity model for the stopped and full arms, per K.

Those are a starting point.

With four eligible solvers, any correlation is suggestive at best. The aim would be to see whether a solver's gradient-suite profile anticipates its SIL behaviour, not to fit a model.

Activity

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Metadata

Metadata

Assignees

No one assigned

    Labels

    No labels
    No labels

    Type

    No type

    Projects

    No projects

      Milestone

      No milestone

      Relationships

      None yet

      Development

      No branches or pull requests

      Issue actions