Why tensile prediction exceeds porosity or swelling
Pulling a sample to failure gives tensile strength as force per cross-sectional area. Predicting that value from composition data is much harder for protein-based bio-materials than it first appears. This post covers our current method, its data requirements, and where confidence declines.
Some bio-material properties follow composition changes fairly consistently. Porosity in a hydrogel scaffold, for example, often tracks polymer concentration and crosslinker ratio across a broad range. With carefully selected data, 30-40 points can support a useful model.
Tensile strength differs for two reasons. First, it is a failure property rather than an equilibrium property. The result depends on defect distribution, fibril alignment, crosslink density gradients, and sample preparation and conditioning, not composition alone. Identical compositions can differ by 15-25% when casting and drying protocols vary.
Second, collagen composite composition and tensile strength have a strongly non-linear relationship with important interactions. More collagen can improve strength up to a threshold, then reduce it through fiber entanglement and uneven crosslinking. The direction can also change with the plasticizer or co-polymer used.
Composition variables currently tracked
For cultured collagen composites, our most informative inputs are collagen concentration (% w/v), crosslinker type and ratio, carbodiimide versus genipin and its molar ratio to available amine groups, co-polymer fraction when present, including hyaluronic acid, gelatin, or synthetic polymer, pH during gelation, and conditioning time before testing.
Process conditions can matter as much as composition, but labs often record them less carefully. External datasets may provide detailed composition records while omitting process history. That imbalance limits what we can learn because unobserved process variation widens prediction uncertainty.
In Celleste's internal dataset, labs record gelation temperature, casting geometry, drying rate when applicable, and hydration state at testing. This is manageable in systematic development work, but a meaningful change for exploratory formulation where conditions are set manually and vary between batches.
The model architecture and its outputs
We use Gaussian process regression with a composite kernel. A squared-exponential term represents smooth composition-property relationships, while a linear term handles cases dominated by monotonic effects. The output is a posterior distribution over tensile strength, so each result is a range at a stated confidence level rather than a point estimate.
A point estimate without uncertainty can mislead. If the output is "predicted tensile strength: 0.42 MPa" and the formulation specification requires 0.35 MPa, the decision to run depends on confidence. A narrow interval may support proceeding. A wide interval may support a smaller confirmation batch first. The uncertainty must be visible for the prediction to guide that decision.
We also produce a sensitivity map showing which composition variables contribute most to uncertainty for that prediction. If collagen concentration dominates, improving its measurement may help. If unlogged process variables dominate, the limiting issue is process recording rather than composition precision.
Where the model loses confidence
Three cases widen confidence intervals enough to limit formulation decisions.
First, the query can fall outside the convex hull of the training data. This is the usual extrapolation warning. We flag formulations far from observed examples, while still displaying a prediction and an explicit out-of-distribution warning.
Second, a lab may have little historical data and poor coverage of its formulation space. With fewer than 20 validated batches, the estimate relies largely on the broader dataset and prior knowledge. That is more structured than intuition, but the intervals reflect limited lab-specific calibration.
Third, structural components may interact in ways our current features do not represent. We treat composition as feature vectors rather than simulating molecular structure. Some co-polymer and crosslinker combinations therefore produce tensile behavior we cannot distinguish. Consistently higher error for a co-polymer family exposes these gaps, which we report to labs.
Case study: genipin-crosslinked collagen-gelatin blends
A lab developing a wound scaffold tested collagen-gelatin blends from 60:40 to 90:10, with varying genipin concentrations. We predicted tensile strength for each candidate before the full batch protocol was run.
For 80:20 to 90:10 blends, intervals were narrow, roughly plus or minus 12% of the predicted value, and point estimates fell within that range of the measurements. Uncertainty doubled for 60:40. Retrospectively, higher gelatin fractions changed crosslinking kinetics in a way linked to gelatin molecular weight, which was not recorded for that supplier lot. The lab investigated and found molecular weight variation.
We are not claiming the prediction was wrong in a way that harmed the lab's decision. Its wide interval correctly indicated that the 60:40 formulation required experimental verification before entering the specification. For this use, calibrated uncertainty was more useful than unsupported certainty.
What we are not saying
Computational prediction cannot replace tensile testing for bio-material qualification. It helps prioritize formulations and their test order, but the measurement remains necessary, especially when failure load affects clinical performance.
We also do not claim equal fidelity across protein-based systems. Silk fibroin composites, bacterial cellulose scaffolds, and collagen systems have different structure-property relationships. Our calibration is densest for collagen and collagen-gelatin systems. Silk and bacterial cellulose predictions carry greater uncertainty and should be treated accordingly.
The value is not simply a low benchmark error. It is the ability to down-select a large composition space before committing to batch runs. If a prediction can remove 60% of candidate formulations from the experimental queue without testing them, it has served its purpose, even when absolute error exceeds that of a pure ML benchmark.
