Bayesian Optimization of a Bioprocess across Reactor Scales

A simulated bioreactor runs at three scales: microplate (10 EUR), benchtop (500 EUR) and pilot (2000 EUR). A recipe has five variables: temperature (20 to 60 °C), pH (3 to 9.5) and three feed rates (0 to 2 g/L/h). One-dimensional sweeps show that the rich-media feed is the dominant, almost linear factor, glucose is a threshold factor (yield drops if F1 is near 0 and saturates above 0.3 g/L/h), temperature has an optimum up to about 33 °C, and pH and glutamine are nearly flat. Repeats of one fixed recipe quantify noise and bias per scale:

Noise is the coefficient of variation, $\mathrm{CV}=\sigma/|\mu|$, since the plain standard deviation ranked the scales wrongly; bias is scale mean minus pilot mean.

One Gaussian Process models the yield over $\mathbf{z}=[\mathbf{x},s]$, the recipe $\mathbf{x}$ and the scale index $s$. The covariance is a Matern kernel with smoothness 5/2, with $r=\lVert\mathbf{z}-\mathbf{z}'\rVert$ and a separate length-scale per input dimension:

The GP gives a predictive mean and standard deviation, from which the Expected Improvement over the best observed yield is computed, with $\Phi$ and $\varphi$ the standard normal CDF and PDF:

Dividing by the scale cost, the next experiment maximizes

1. Warm-up: 5 cheap micro-scale runs.
2. Fit the GP: inputs are recipe and scale, with the Matern 5/2 kernel.
3. Pick the next run: 10,000 random candidates, maximize EI / cost.
4. Run and update: run the simulator at the chosen scale and add the result to the GP data. Repeat until the budget is used.
5. Pilot check: 2000 EUR is reserved to test the best recipe on the pilot scale.

• Over ten seeded trials with a 3000 EUR budget, the mean pilot-scale concentration was 18.96 g/L and the best trial reached 23.57 g/L. The reference value was 14 g/L at 15000 EUR.
• The best recipes clustered around 36 °C and pH close to 8; BO also beat a non-adaptive Sobol baseline.