A current challenge is to compute the native structures of proteins from their amino acid sequences. A main approach of bioinformatics is threading, in which a protein to be predicted is computationally threaded onto protein fragments of similar sequence having an already known structure. However, ∼15% of proteins cannot be folded in this way; this has been called the glass ceiling, and the proteins are called nonthreadables. For these, physical molecular dynamics (MD) modeling is promising because it does not require templates. We find that MD, when used with an accelerator called MELD, can fold many nonthreadables. For 41 nonthreadable proteins with fewer than 125 residues, MELD-accelerated MD (MELD × MD) folds 20 of them to better than 4 Å error. In 10 cases, MELD × MD succeeds even when the force field does not properly encode the native state. In 11 cases, MELD × MD foretells its own success; seeing large Boltzmann populations in the simulations predicts it has converged to the correct native state. MELD × MD acceleration can be applied to a broad physical protein modeling range.