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 accu-
racy, 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.