A Physics-Informed Dual-Stem Neural Network With Data Generation Engine for Label-Scarce and Sparse-Data Inverse Problems
TL;DR
Results demonstrate effective label-scarce estimation in this case, while extension to other inverse problems requires an affordable differentiable forward model, sufficiently accurate coarse localization, and structured mismatch that can be learned from scarce measurements.
Abstract
Inverse problems in computational physics often face dual scarcity: few real measurements and no ground-truth labels during deployment. When an imperfect forward model exhibits structured simulation-to-measurement mismatch and the target parameter is coupled with nuisance factors, neither model-based fitting nor supervised learning alone is sufficient. This paper presents a modular framework: (i) Measurement-Guided Data Augmentation (MDGA) converts each measurement into a dense local simulation bank via coarse fitting and Latin Hypercube Sampling; (ii) a Physics-Informed Dual-Stem Network (PI-DSN) processes real and simulated inputs through separate feature extractors and predicts a residual correction using label-free physics-consistency losses; and (iii) a label-free checkpoint selection protocol ranks candidates using forward-model consistency metrics while isolating ground-truth labels for final evaluation only. Evaluation is conducted in a Fraunhofer diffraction filament-metrology case where off-axis acquisition limits each setup to 5–10 patterns, the target diameter couples to nuisance parameters, and the forward model introduces structured mismatch. Results demonstrate effective label-scarce estimation in this case, while extension to other inverse problems requires an affordable differentiable forward model, sufficiently accurate coarse localization, and structured mismatch that can be learned from scarce measurements.