Physics-informed machine learning for reconstructing three-dimensional velocity fields from two-dimensional concentration fields

We present a multi-domain physics-informed neural network (MDPINN) framework for reconstructing three-dimensional (3D) velocity fields from sparse two-dimensional concentration measurements in complex microfluidic flows. The approach is demonstrated in intersecting channels at a Reynolds number of 320, where strong 3D mixing occurs. Using planar concentration data obtained via confocal laser scanning microscopy (CLSM), the MDPINN infers the full 3D concentration and velocity fields by enforcing governing flow and transport equations. Using synchronized concentration–velocity data obtained from computational fluid dynamics (CFD) simulations, we first show that only nine optimally placed data planes (approximately 10% of total data) are sufficient to accurately reconstruct the full fields, achieving maximum absolute errors below 8% in concentration and 7% in velocity. A systematic analysis of data placement provides an optimized sampling strategy that includes near-wall measurements at z+ ≈ 1 and a normalized inter-plane spacing below 0.165. We then apply the validated MDPINN framework to experimental CLSM data, from which the inferred velocity fields differ from idealized CFD predictions, demonstrating the value of experimental data-based reconstruction in capturing realistic flow behavior. This study provides a practical tool that reconstructs difficult-to-measure velocity fields from easily accessible scalar data, which is applicable to a variety of fluidic systems.