Fifteen validated batches can look like not enough data for a computational formulation tool. Sometimes a lab has 15 validated batches across two composition variables. Sometimes it has 200 batches with incomplete records. The objection is reasonable, but these are different problems and need different responses.
The first case is genuinely small data: fewer than 20-30 systematic batches in a reasonably defined composition space. The second is a larger but poorly structured dataset, with many batches and inconsistent records. Both create real challenges. Still, "you need more data" applies only to part of the first case.
What Bayesian approaches do differently
Classical machine learning for property prediction is mostly frequentist. It estimates model parameters from data and then applies them. Reliable estimation requires enough data, with the amount depending on problem dimensionality. For bio-material formulations with five to ten composition variables and several target properties, many batches may be needed to cover the parameter space.
Bayesian methods begin with a prior distribution over model parameters, describing what is believed before data is observed. As data arrives, that prior is updated. The resulting posterior represents the revised beliefs. When data is sparse, prior knowledge provides regularization that data volume alone cannot provide.
This matters in bio-material formulation because substantial prior knowledge exists. Protein biochemistry indicates that collagen fiber formation is favored in a pH range around 7-8 and a temperature range around 25-37 degrees C. Polymer science indicates that crosslink density increases mechanical stiffness. These relationships are not specific to one formulation or lab, but they encode physical knowledge that can inform predictions when a local dataset is small.
Practically, a Bayesian model with reasonable priors can produce useful predictions from data that would be too sparse for frequentist regression. Here, useful means confidence intervals that identify which formulations merit testing, even when absolute prediction accuracy is modest.
Gaussian process regression for small datasets
Gaussian process regression, the core model used by Celleste, is Bayesian and well suited to small datasets in structured composition spaces. Its kernel encodes prior beliefs about how smoothly properties vary with composition and at what scale. With sparse data, the kernel regularizes the estimate. With dense data, it matters less and the model follows observations more closely.
A practical property of Gaussian processes is that prediction uncertainty rises smoothly as a prediction moves away from observed points. A GP indicates when it is extrapolating, and by how much, through the width of its confidence intervals. This does not guarantee accuracy, but it provides a calibrated signal for where to trust the model and where to remain skeptical.
GPs have a computational limitation. Once a dataset grows beyond a few hundred points, naive inference becomes expensive. We use sparse GP approximations to keep inference tractable while retaining most calibration properties of the exact GP. The approximation is established in the literature, and we test its calibration during validation.
Small datasets as a genuine constraint
Small datasets are not always harmless. They are a binding constraint when:
The composition space is genuinely novel relative to available prior knowledge. If a material combination has no analog in published literature and no mechanistic theory from which to form a prior, enough data is needed to estimate the composition-property relationship from scratch. This is uncommon in bio-materials, where most systems have some mechanistic basis, but it does occur.
The target property has high intrinsic variability. Failure properties such as tensile strength at break or fracture toughness can vary substantially between batches at constant composition. Separating a systematic composition effect from that noise requires more data than estimating a smoother property. Priors cannot remove this limitation because the noise is real.
The goal is to identify a global optimum rather than screen candidates. Finding the single best formulation in a large composition space, especially with multiple local optima, requires enough data to map the landscape. Bayesian methods can make exploration more efficient through active learning, but they cannot reduce the minimum data requirement below a threshold for this task.
Poor data structure is a separate problem
Labs often have more data than they can readily use. Formulation records may be spread across notebooks, spreadsheets, and personal memories. Batch records may list composition but omit process conditions. Measurements may also use different protocols at different project stages, making the values difficult to compare.
This is a data engineering problem, not a data volume problem. More batches do not make a poorly structured record more useful. Standardizing the record format and completing missing fields does.
When labs join Celleste, one early step is uploading historical data. Typically 40-60% of records are usable as-is for model calibration, with another 20-30% usable after the lab fills missing fields from notes or memory. The remaining records have gaps that cannot be filled. Reaching 60% usable historical data usually more than doubles the effective dataset size for calibration.
Active learning for efficient dataset growth
For labs starting from scratch, random batch execution is not the most efficient route to a useful predictive model. Active learning uses current model uncertainty to choose which compositions to test next.
Active learning can select the next experiment to reduce overall uncertainty across the composition space, identify the best formulation found so far, or balance those objectives. The approach is established in experimental design literature, but it remains underused in bio-material development because someone must update the model and choose the next experiment. Most labs lack the computational infrastructure for that step.
In the Celleste workflow, active learning suggestions appear automatically once a lab has logged a minimum number of validated batches. The suggested formulations are those where the model is most uncertain in a composition-space region relevant to the lab's target properties. A lab following these suggestions will typically reach useful model calibration in roughly half the number of batches compared with random exploration of the same space. This is not a theoretical bound. It is what we observe in practice, while material costs and equipment availability mean labs do not always follow the optimal suggestions.
