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Protein language models trained on evolutionary data have emerged as powerful tools for predictive problems involving protein sequence, structure and function. However, these models overlook decades of research into biophysical factors governing protein function. We propose mutational effect transfer learning (METL), a protein language model framework that unites advanced machine learning and biophysical modeling. Using the METL framework, we pretrain transformer-based neural networks on biophysical simulation data to capture fundamental relationships between protein sequence, structure and energetics. We fine-tune METL on experimental sequence–function data to harness these biophysical signals and apply them when predicting protein properties like thermostability, catalytic activity and fluorescence. METL excels in challenging protein engineering tasks like generalizing from small training sets and position extrapolation, although existing methods that train on evolutionary signals remain powerful for many types of experimental assays. We demonstrate METL’s ability to design functional green fluorescent protein variants when trained on only 64 examples, showcasing the potential of biophysics-based protein language models for protein engineering.