ActiveAdmin association autocomplete without complicated plugins.

active_admin.css.scss

@import 'active_admin/mixins';
@import 'active_admin/base';
@import 'jquery.ui.autocomplete';

active_admin.js.coffee

#= require active_admin/base
#= require jquery.ui.autocomplete

$ ->
  $('.autocomplete').each (index, input) ->
    $input = $(input)
    $hiddenInput = $($(input).data('hidden-input'))

    $input
      .autocomplete
        minLength: 3
        delay: 600
        source: (request, response) ->
          $.ajax
            url: $input.data('url')
            dataType: 'json'
            data: 
              term: request.term
            success: (data) -> response(data)
        select: (event, ui) ->
          $input.val(ui.item.label)
          $hiddenInput.val(ui.item.id)
          false
      .data('ui-autocomplete')._renderItem = (ul, item) ->
        $('<li></li>')
         .data('item.autocomplete', item)
         .append('<a>' + item.label + '</a>')
         .appendTo(ul)

autocomplete_input.rb

# app/admin/inputs/autocomplete_input.rb
class AutocompleteInput
  include Formtastic::Inputs::Base
  include Formtastic::Inputs::Base::Stringish
  include ActionDispatch::Routing::UrlFor
  include Rails.application.routes.url_helpers

  def to_html
    input_wrapping do
      label_html <<
        builder.text_field(method, input_html_options) <<
        builder.hidden_field(id_method, id: hidden_input_id, required: nil, autofocus: nil)
    end
  end

  def input_html_options
    {
      class: 'js-autocomplete',
      value: object.send(method)&.display_name,
      data: {
        url: search_url,
        hidden_input: "##{hidden_input_id}",
        original_value: object.send(method)&.display_name
      }
    }.merge(super)
  end

  def name_method
    "#{method}_name".to_sym
  end

  def id_method
    "#{method}_id".to_sym
  end

  def hidden_input_id
    "#{object.class.name.downcase}_#{id_method}"
  end

  def search_url
    options[:url] || url_for(action: 'search', controller: "nucleus/#{method.to_s.pluralize}")
  end
end

autocomplete_serializer.rb

class AutocompleteSerializer < ActiveModel::Serializer
  attribute :id
  attribute :label

private

  def label
    object.name
  end
end

Gemfile

gem 'active_model_serializers'
gem 'activeadmin'
gem 'jquery-ui-rails'

posts.rb

ActiveAdmin.register Post do
  form do |f|
    f.inputs 'Details' do
      # standard usage
      f.input :user, as: :autocomplete
      
      # or for associations that don't resolve directly to the model name or
      # an ActiveAdmin resource that is aliased like ActiveAdmin.register Widget, as: 'Gadget' do
      f.input :author, as: :autocomplete, url: search_admin_users_path
    end
  end
end

users.rb

ActiveAdmin.register User do
  collection_action :search, method: :get do
    users = User.where('LOWER(name) ILIKE ?', "#{params[:term]}%")
    render json: users, each_serializer: AutocompleteSerializer, root: false
  end
end

Thanks for this. Very helpful.
FYI, I made following changes to get this working:
I changed the controller from nucleus to admin
I had to change the selector in the JS method to return $('.autocomplete input')
and my scss import looks like:
@import 'jquery-ui/core';
@import 'jquery-ui/autocomplete';
@import 'jquery-ui/theme';
when using the jquery-ui-rails gem

@SeriouslyAwesome That's really nice. I just recommend you to avoid using include Rails.application.routes.url_helpers. Instead create a private method and use it to access the named routes or other routes methods:

def url_helpers
  Rails.application.routes.url_helpers
end

Then you can do this: url_helpers.url_for(...)

@SeriouslyAwesome how might we alter this for use with filters rather than inputs?

Nice! But looks messy. How about packing as a gem?