Here a script to  create the “MySite” collection, in SAML based authentication

$claim = New-SPClaimsPrincipalClaimValue “<name.surname@domain.com>” ClaimType http://schemas.xmlsoap.org/ws/2005/05/identity/claims/upnTrustedIdentityTokenIssuer “Trusted_Identity_Provider_Name”

$user = $claim.ToEncodedString()

$site=Get-SPSite “<url_collection_site>” 

$serviceContext = Get-SPServiceContext -Site $site

$userProfileConfigManager = New-Object Microsoft.Office.Server.UserProfiles.UserProfileManager($serviceContext)

$mysiteuser = $userProfileConfigManager.GetUserProfile($user)

$mysiteuser.PersonalSiteInstantiationState

$mysiteuser.CreatePersonalSite()

Write-host “Successfully created MySite for user $user” -f green;