# Wetting Property Inference

In hierarchical Bayesian inversion, putting the forward model inside the likelihood means every posterior evaluation costs one forward solve per cell. A triangular transport-map likelihood trained once per design now serves every cell, and is used to infer contact angle and capillary length from photographs of a hole in a thin liquid film. At a synthetic validation design the map's posteriors agree with direct sampling in the wetting properties and pass simulation-based calibration; a single posterior needs several hundred times fewer forward-model evaluations than a gradient-free ensemble sampler, and further posteriors at the same design add no forward solve.

In hierarchical Bayesian inversion, putting the forward model inside the likelihood means every posterior evaluation costs one forward solve per cell. A triangular transport-map likelihood trained once per design now serves every cell, and is used to infer contact angle and capillary length from photographs of a hole in a thin liquid film. At a synthetic validation design the map's posteriors agree with direct sampling in the wetting properties and pass simulation-based calibration; a single posterior needs several hundred times fewer forward-model evaluations than a gradient-free ensemble sampler, and further posteriors at the same design add no forward solve.