PDE Reaction–Diffusion Spheroid Modeling for Probabilistic Chemotherapy Drug Search

Bayesian optimization (BO) over finite combinatorial pools is scored, almost universally, by a single scalar measured in a well-mixed monolayer assay. Savitar, a curve-aware interaction-structured kernel, attains the lowest mean regret on such pools by converting per-constituent response curves into activity-gated embeddings coupled through a shared low-rank tensor factorization. Part I summarizes that method and its cross-domain evidence. Part II asks a question the original evaluation cannot: whether the combinations a curve-aware optimizer selects remain the best ones once space is modeled. We simulate the selections of sixteen BO methods on the NCI-ALMANAC panel (Holbeck et al., 2017) in a spatially resolved spheroid reaction–diffusion model with oxygen-limited proliferation, hypoxic resistance, and finite drug transport. The well-mixed ODE bridge used previously is exactly rank-preserving (Spearman ρ = −1.0000); the spheroid is not (ρ = −0.56, with 36.5% of within-cell-line pairs re-ordered). In vitro potency explains 23% of the variance in spheroid outcome; one spatial quantity raises this to 86%. Savitar keeps a large advantage over every structural baseline but places fifth of sixteen on spheroid log-kill AUC, and the deficit is mechanistic: outcome tracks residual hypoxic fraction (ρ = −0.969) more tightly than potency (ρ = −0.767), and Savitar selects combinations 7.5 percentage points more potent in vitro that leave 62% more hypoxic tissue. Combination BO should be scored on spatially resolved, outcome-anchored readouts.