MolBasis
A.IMPROVE2-termESOL (Delaney 2004) · n=954

ESOL · logS

Aqueous solubility logS · log mol/L

closed-form kernel
ŷ = β₀ + β₁ · z(cavity^1.00) + β₂ · z(hb_acceptor^1.75)
0.844
nested-CV r
in-sample, winner's-curse-safe
0.646
scaffold-blind r
25% held-out OOD
+21.6%
blind MAE-vs-NULL lift
gate = +30%
0.94
MAE (log mol/L)
grouped-LOO

In-sample → out-of-distribution

How the correlation holds when moving to unseen scaffolds.

nested-CV r (in-sample)0.844
scaffold-blind r (OOD)0.646
Blind MAE-vs-NULL lift21.6%

Vertical marker = the +30% production gate.

Blind calibration slope

Slope of measured vs predicted on the blind set. 1.0 = no magnitude compression.

0.96
slope (ideal 1.0)
Below +30% blind gate

What it is

Aqueous solubility from cavity (desolvation cost) plus acceptor (hydration reward). Unique-pair winner under nested CV — but the 2-term form overfits on 25% scaffold-blind held-out.

The physics

Dissolving costs cavity formation and pays back H-bond hydration; the two compete. The physics is sound; the sample is just small for a 2-term fit.

upper / lower bound

Published nested-CV r=0.844 is a full-data UPPER bound. Blind lift is only +21.6% (below the +30% gate). Report the 1-term fallback as the commercial floor. Engineering note logged for v0.92.1.

caveat

Diagnostic v2 (2026-06-06): the system is well-conditioned (cond#=1.3) — this is GENUINE statistical overfitting, not numerical instability. 0 of the top-50 LOO-ranked pairs survive r_cv≥0.5. The 1-term cavity fallback is the honest lower bound (blind r≈0.66).

How the methods compare

Watch the hidden cost. The General Solubility Equation is a one-line formula — but it needs the experimental melting point, a lab measurement. The most accurate method (D-MPNN) needs a large labelled corpus. This kernel needs neither: no measured melting point, no training set, just one σ-profile.

Reported error

Each method's own reported error in log units — lower is better. Different datasets and splits, so this is an orientation, not a controlled benchmark.

D-MPNN (Chemprop)0.58 log units · RMSE
COSMO-RS0.60 log units · typical
General Solubility Equation (GSE)0.90 log units · typical
ESOL · logS · this kernel0.94 log units · MAE
ESOL (MLR)1.01 log units · RMSE

Lower error isn’t the whole story — read it against input cost and requirements below.

Input cost

Per-molecule compute/data burden to predict a new molecule — shorter is cheaper.

General Solubility Equation (GSE)2D structure (pencil / inference)
ESOL (MLR)2D structure (pencil / inference)
D-MPNN (Chemprop)2D structure (pencil / inference)
ESOL · logS · this kernelone QM calculation (SCF)
COSMO-RSone QM calculation (SCF)

What each method needs

External dependencies each method carries. An amber dot means the method requires it — fewer dots means fewer things to procure or that can go wrong.

Method3D geometryMD / samplingtraining corpusa measured valueproprietary paramsdeps
ESOL · logS · this kernel1
General Solubility Equation (GSE)1
ESOL (MLR)1
D-MPNN (Chemprop)1
COSMO-RS3

This kernel needs only a 3D geometry for its one SCF — no MD, no training corpus, no measured value, no proprietary software.

Competing methods

How this property is predicted elsewhere — with the input each method needs (a key differentiator) and the literature reference. Numbers are each method’s own reported figure on its own benchmark, so they are indicative, not a head-to-head on an identical split.

MethodClassReported performanceInput neededReference
ESOL · logSthis kernelclosed-formPearson r 0.844 (nested-CV) · 0.646 scaffold-blind · MAE 0.94 log mol/Lone DFT SCF σ-profile · no training set · no MDMF-FQSL (this lab)
General Solubility Equation (GSE)empirical≈0.9 log units — but requires the measured melting pointexperimental melting point + logPJain & Yalkowsky, J. Pharm. Sci. 2001
ESOL (MLR)group-contributionRMSE 1.01, avg abs err 0.75 log (n=2874); blind AAE 0.834 2-D descriptors (clogP, MW, aromatic fraction, rotatable bonds)Delaney, J. Chem. Inf. Comput. Sci. 2004
D-MPNN (Chemprop)ML / GNNRMSE ≈ 0.58 log on ESOL (graph NN)2D molecular graph + a labelled training setYang et al., J. Chem. Inf. Model. 2019
COSMO-RSphysics≈0.5–0.7 log units (needs a fusion term for solids)DFT σ-profile + a melting/fusion term for crystalsKlamt; COSMO-RS solubility

Metrics are as published by each method on its own dataset (different splits, different cohorts) — treat them as an orientation of the landscape, not a controlled benchmark. The differentiator for this kernel is the input column: a single closed-form solve from one σ-profile, with no training corpus, no MD, and no measured melting point.

Descriptors used

cavitycavity_area_aa2 — solvent-accessible surface area of the COSMO cavity (Ų)
acceptorhb_acceptor_mass — hydrogen-bond acceptor surface area (σ-degree classified)

Version history

  1. 2026-05-29v0.91.1 ship

    ⭐ Unique-pair winner under nested CV, r=0.844.

  2. 2026-06-06Overfit diagnostic v2

    Well-conditioned; genuine 2-term overfitting on 75% subsample. r_cv collapses to ~0.02. 1-term fallback is the honest floor.