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This PR aims at adding the Fused Unbalanced Gromov Wasserstein (FUGW) loss and solver to ot.batch, in order to solve N FUGW problems in parallel.

Motivation and context / Related issue

PR#775 added the ot.batch module for computing N optimal transport problems in parallel. Both the linear and quadratic problems are available but not the FUGW problem, which is useful in some applications.

How has this been tested (if it applies)

My modifications still need to be tested

PR checklist

  • [ x] I have read the CONTRIBUTING document.
  • The documentation is up-to-date with the changes I made (check build artifacts).
  • All tests passed, and additional code has been covered with new tests.
  • I have added the PR and Issue fix to the RELEASES.md file.

@github-actions github-actions bot added the Tests label Oct 24, 2025
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