Full-component reconstruction of three-dimensional fluid stress tensors
Forces govern how fluids deform biological tissues, regulate cardiovascular function, and determine the performance and failure of soft materials. Recent advances in flow birefringence, including the use of suspended anisotropic nanomaterials to optically encode stress in fluids, have made direct stress measurement experimentally accessible in projection. However, direct experimental access to all six components of the three-dimensional (3D) fluid stress tensor has remained unattainable because optical measurements provide only path-integrated observables. Recovering local 3D stresses from such data constitutes an intrinsically underdetermined tensor tomography problem, where two optical observables must determine six independent stress components. Here we introduce U-FlowPET, an unsupervised physics-informed framework that integrates photoelastic tomography with the governing equations of fluid mechanics to reconstruct the full 3D stress tensor without relying on constitutive assumptions, geometric symmetry, or labeled training data. Rather than learning from labeled reference stress fields, the method identifies physically admissible stress fields that satisfy momentum balance and continuity while remaining consistent with measured optical projections. We validate the approach using analytical, numerical, and experimental datasets. In axisymmetric pipe flow with an analytical solution, all six stress components are reconstructed with normalized mean absolute errors below 4%. Robust reconstruction is further demonstrated in curved-pipe flow without symmetry assumptions and in experimental pipe-flow data despite measurement noise. By enabling direct 3D stress-field reconstruction from optical data alone, U-FlowPET extends fluid analysis from observing motion to quantifying force and establishes a new framework for stress-based diagnostics in biological flows and functional materials.