PCR-GP: Prior-Coupled Residual Gaussian Processes for Few-Shot Lipid Nanoparticle Formulation

We study few-shot surface transfer in formulation science: given a dense response surface at pH 4.5 over inputs (DDAB, TFR) to Z-average (DLS), infer the full pH 6 surface while measuring as few pH 6 points as possible. We propose a pH-anchored Prior–Coupled Residual Gaussian Process (PCR–GP) that treats the target surface as a global affine transform of a source GP plus a learnable discrepancy: f6(x) = ρg(x) + β + r(x). The source GP g is trained once on the dense pH 4.5 data and provides a strong spatial prior. The coupling (ρ, β) is estimated from the few pH 6 labels using a stability-aware freeze→ridge→clip procedure, after which a residual GP r is fit on the target labels to capture cross-pH differences. Active selection evaluates target uncertainty on a feasible candidate set and snaps the next experiment to the highest-uncertainty unused location. The framework reports fixed-scale uncertainty maps and log-scaled error curves for comparability across rounds. On real formulation data, PCR–GP reconstructs the pH 6 surface with very few additional assays while maintaining high accuracy, outperforming naive direct learning and prior-informed baselines. The approach is simple, sample-efficient, and broadly applicable whenever one condition is cheap/dense and another is expensive/sparse.