WordPress provides a specific way to load AJAX requests. These requests will always use https://yoursite.com/wp-admin/admin-ajax.php?action=[action-name-here] URL format. They can be either POST or GET requests.
With Swift Performance you can cache resource-intensive AJAX requests (eg AJAX search).
You should specify the action names, Swift Performance will automatically cache these requests, but not other AJAX requests.
You can also set cache expiry time for AJAX requests in seconds. For example you can use it to cache custom ajax search or cache WP datatables AJAX responses.