feat(trainer): add TPU utility to compute numNodes for multi-slice TPU

[richabanker]

What this PR does / why we need it:
Introduce the get_tpu_num_nodes utility function in the Trainer backend to calculate VM host/node requirements for multi-slice TPU TrainJobs based on the user-specified slice count and physical TPU topology.

Which issue(s) this PR fixes (optional, in Fixes #<issue number>, #<issue number>, ... format, will close the issue(s) when PR gets merged):

Issue #kubeflow/trainer#3407

Checklist:

• Docs included if any changes are user facing

[google-oss-prow]

[APPROVALNOTIFIER] This PR is NOT APPROVED

This pull-request has been approved by:
Once this PR has been reviewed and has the lgtm label, please assign electronic-waste for approval. For more information see the Kubernetes Code Review Process.

The full list of commands accepted by this bot can be found here.

Details

Needs approval from an approver in each of these files:

• OWNERS

Approvers can indicate their approval by writing /approve in a comment
Approvers can cancel approval by writing /approve cancel in a comment

[github-actions]

🎉 Welcome to the Kubeflow SDK! 🎉

Thanks for opening your first PR! We're happy to have you as part of our community 🚀

Here's what happens next:

• If you haven't already, please check out our Contributing Guide for repo-specific guidelines and the Kubeflow Contributor Guide for general community standards
• Our team will review your PR soon! cc @kubeflow/kubeflow-sdk-team

Join the community:

• Slack: Join our #kubeflow-ml-experience and #kubeflow-trainer Slack channels
• Meetings: Attend the Kubeflow SDK and ML Experience bi-weekly meetings

Feel free to ask questions in the comments if you need any help or clarification!
Thanks again for contributing to Kubeflow! 🙏

[Copilot]

Pull request overview

Note

Copilot was unable to run its full agentic suite in this review.

Adds a TPU helper utility to compute required host/node counts from slice count and topology, along with parametrized tests to validate expected behavior and error handling.

Changes:

• Introduced get_tpu_num_nodes() to compute total TPU host nodes from num_slices, topology, and chips_per_host.
• Added a parametrized pytest suite covering common 2D/3D topologies, multi-slice scaling, and invalid topology inputs.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 6 comments.

File	Description
kubeflow/trainer/backends/kubernetes/utils.py	Adds get_tpu_num_nodes() utility and related validation/error handling.
kubeflow/trainer/backends/kubernetes/utils_test.py	Adds parametrized unit tests for get_tpu_num_nodes() success and failure cases.

[richabanker]

cc @siyuanfoundation @fedebongio

[andreyvelich]

/ok-to-test
/retest

[richabanker]

/ok-to-test

[richabanker]

/retest

[siyuanfoundation]

/lgtm Thank you!