Single-axis high-energy X-ray diffraction tomography for elastic residual strain: uniqueness and stability of solutions in the presence of equilibrium constraints

What the math gives to ML

The paper gives a constructive example of using a mechanical PDE constraint to remove non-uniqueness from an underdetermined tensor inverse problem. Its transferable asset is the Fourier-domain elimination of constrained degrees of freedom, together with an explicit determinant identifying characteristic frequencies where inversion becomes unstable. A neural implementation can use this as a differentiable spectral projection layer that maps arbitrary symmetric-tensor predictions toward mechanically equilibrated fields, while damping frequencies near characteristic planes. This is most promising for neural operators, implicit fields, and physics-informed models predicting stress or strain tensors.