BPS2026 – Physics-informed neural networks for robust membrane segmentation from noisy tomograms

Segmentation of cellular membranes in cryo-electron tomography (cryo-ET) is essential for uncovering how membranes are organized and remodeled within cells. Recent advances in machine learning have enabled semi-automated segmentation, reducing the need for manual annotation. Yet even state-of-the-art approaches often fail under low signal-to-noise conditions, producing fragmented or jagged membranes that are physically unrealistic. Physics-informed machine learning offers a promising route to overcome these challenges, given its success in other imaging domains, but to our knowledge it has not been applied to electron microscopy data sets. We developed a physics-informed neural network (PINN) that integrates membrane mechanics directly into the segmentation process. The network represents a phase field encoding the membrane shape and is optimized to recover geometries consistent with the input tomogram while minimizing the Helfrich bending energy, which quantifies the curvature-dependent cost of deforming lipid membranes. Incorporating this mechanical constraint improved segmentation accuracy across diverse geometries, including vesicles, budding profiles, and closely opposed membranes. The advantage was most pronounced under high noise, where mechanics-guided PINNs successfully recovered surfaces that the unconstrained framework failed to identify. We further validated the method on cryo-ET data sets of internal organelles in retinal pigment epithelium (RPE1) cells, achieving robust segmentation in low-contrast experimental data. We propose that the PINN’s success arises because mechanical constraints reshape the solution landscape. Under noisy conditions, many local minima arise, corresponding to incorrect membrane segmentations. By enforcing mechanics, the network converges toward a strong global minimum aligned with physically valid solutions, thereby suppressing artifacts. Our findings demonstrate that integrating physical knowledge provides a powerful strategy for robust and realistic membrane segmentation in cryo-ET, paving the way for quantitative biophysical analyses.