Physics-informed machine learning for micro-perforated panels: Reproducible prediction, uncertainty, and design optimization

Porosity, hole radius, panel thickness, and thickness-to-diameter ratio govern sound absorption in micro-perforated panels (MPPs) through viscous–thermal losses in submillimeter apertures. A physics-informed machine-learning workflow is presented for predicting the frequency-averaged absorption coefficient α¯, combining acoustically motivated feature design with probabilistic prediction and calibrated uncertainty. A quality-controlled dataset of 1000 MPP geometries spanning hole radius, porosity, thickness, perforation-shape class, and frequency-averaged absorption coefficient was used to benchmark 28 regression pipelines under leakage-safe fivefold cross-validation. A smooth Maa-inspired prior, monotone in porosity and saturating in thickness ratio, was combined with residual learning. Gaussian-process (GP) variants were the strongest single learners, with the Matérn-kernel GP and physics-informed (PI) residual GP both achieving root mean square error = 0.138 and R2 = 0.763. Physics-informed Gaussian-process (PI-GP) posteriors provided near-nominal 95% coverage (0.945; mean width = 0.485), whereas split-conformal intervals were more conservative (coverage = 0.970; mean width = 0.573). Measured impedance-tube spectra for six additively manufactured circular MPPs using the Cavity 1 configuration were added as independent validation data. All measured Cavity 1 absorption values fell within the GP and conformal 95% intervals, supporting uncertainty consistency while revealing point-prediction discrepancies associated with unmodeled cavity, fabrication, mounting, and layout effects.