Physics-Informed Neural Networks, Digital Volume Correlation, mechanical regularization, linear elasticity, micro-CT; sparse data

Digital Volume Correlation (DVC) recovers displacement fields from micro-CT images but breaks down in low-texture regions, leaving gaps in the measured field. Finite-element mechanical regularization can bridge these gaps by enforcing equilibrium, at the cost of mesh generation. We propose a meshless alternative based on Physics-Informed Neural Networks, which jointly minimize a data-fidelity term and the residual of the Navier-Cauchy equation of linear elasticity; where observations are absent, the equilibrium residual alone constrains the prediction to remain mechanically consistent.The method is validated on a sandstone micro-CT slice (200×200 px, 14 μm resolution) subjected to a synthetic non-uniform polynomial deformation satisfying the governing equation. Observations are subsampled every 20th pixel, corrupted with Gaussian noise (σ = 0.02), and removed over a gap covering 16% of the domain. Across three gap positions (center, edge, corner; five runs each), the PINN attains the lowest error by orders of magnitude, whereas a data-only network fails for boundary-adjacent gaps (MSE up to 6×10⁻¹) and cubic interpolation degrades more moderately. These results show that the equilibrium constraint provides robust regularization precisely where interpolation and unconstrained networks break down.

Digital Volume Correlation (DVC) recovers displacement fields from micro-CT images but breaks down in low-texture regions, leaving gaps in the measured field. Finite-element mechanical regularization can bridge these gaps by enforcing equilibrium, at the cost of mesh generation. We propose a meshless alternative based on Physics-Informed Neural Networks, which jointly minimize a data-fidelity term and the residual of the Navier-Cauchy equation of linear elasticity; where observations are absent, the equilibrium residual alone constrains the prediction to remain mechanically consistent.The method is validated on a sandstone micro-CT slice (200×200 px, 14 μm resolution) subjected to a synthetic non-uniform polynomial deformation satisfying the governing equation. Observations are subsampled every 20th pixel, corrupted with Gaussian noise (σ = 0.02), and removed over a gap covering 16% of the domain. Across three gap positions (center, edge, corner; five runs each), the PINN attains the lowest error by orders of magnitude, whereas a data-only network fails for boundary-adjacent gaps (MSE up to 6×10⁻¹) and cubic interpolation degrades more moderately. These results show that the equilibrium constraint provides robust regularization precisely where interpolation and unconstrained networks break down.