ML docker containers local setup done. Now how to deploy in a shared cloud platform using Kubernetes?

docker kubernetes marklogic

Docker Desktop with Kubernetes enabled is enough for developing your setup (in this setup Docker already runs in a VM).
Usually you'll start writing some Kubernetes YAML manifests and applying them to your cluster. In your case with the database requiring a consistent naming of nodes, etc. a StatefulSet might be the right option. There is an article by Marklogic describing this.

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