question about bi-harmonic energy

[waveleaf27]

In the tetrahedral sphere representation, bi-harmonic energy across the deformation gradient field effectively addresses mesh issues like irregular triangles, non-manifoldness, and floating artifacts.
If I switch to a triangle mesh representation, is there an equivalent or adapted form of 'bi-harmonic energy' that can similarly resolve these mesh issues?
Thanks @gmh14 @bohanwang