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Multi-fidelity batch Bayesian optimization for bioprocess development across scales

Adrian Martens, Mathias Neufang, Alessandro Butté, Moritz von Stosch, Antonio del Rio Chanona, Laura Marie Helleckes

arXiv:2508.10970v2q-bio.QMstat.ML

TL;DR

Bioprocess development requires many costly experiments across scales. The paper evaluates a multi-fidelity batch Bayesian optimization workflow using a simulated CHO process. The authors report stronger performance than standard industrial strategies and simultaneous cost reduction and optimization-performance gains in the studied scenarios.

  • Problem

    Bioprocess development remains complex and costly, requiring many experiments across multiple stages and scales.

    Source: §1 · p. 1

  • Method

    The paper evaluates a multi-fidelity batch Bayesian optimization workflow using a simulated CHO bioprocess and a model of cell growth and substrate kinetics.

    Source: §2.1.1 · p. 3, §2.2.4 · p. 8

  • Results

    The proposed BO framework outperformed standard industrial strategies across scenarios with different or more aligned clone performance over scales, with simultaneous cost reduction and optimization-performance gains.

    Source: §4 · p. 21

  • Takeaways & Limitations

    The authors describe automated, data-efficient bioprocess development as promising while noting scaling and real-world applicability remain open.

    Source: §4 · p. 21

    The sufficiency of the fidelity-level model for capturing differences across scales remains an open question; richer multi-task modeling may add hyperparameters and make learning more challenging.

    Source: §3.4 · p. 20

Abstract

from arXiv · show

Bioprocesses are central to modern biotechnology, enabling sustainable production of pharmaceuticals, specialty chemicals, cosmetics, and food. However, developing high-performing processes remains costly and complex, requiring iterative, multi-scale experimentation from microtiter plates to pilot reactors. Conventional Design of Experiments (DoE) approaches often struggle to address process scale-up and the joint optimization of reaction conditions and biocatalyst selection. We present a multi-fidelity batch Bayesian optimization framework to accelerate bioprocess development and reduce experimental costs. The method integrates Gaussian processes tailored for multi-fidelity modeling and mixed-variable optimization. At each iteration, the algorithm proposes not only the next experimental conditions but also the appropriate scale and choice of biocatalyst (i.e., cell clones). To benchmark performance, we developed a custom simulation of a Chinese hamster ovary bioprocess that captures the non-linear, coupled dynamics of scale-up across different clones. Multiple case studies demonstrate that the proposed workflow achieves a reduction in experimental costs while improving yield compared to industrial DoE baselines. This work provides a data-efficient strategy for bioprocess optimization and highlights opportunities for incorporating transfer learning and uncertainty-aware design for sustainable biotechnology.

1 Introduction

Bioprocess development requires costly experiments across scales, while nonlinear process behavior and limited information transfer challenge traditional screening and DoE. This study introduces a simulation-based multi-fidelity batch BO workflow that jointly optimizes process conditions and biocatalyst selection.

1.1 Stages of bioprocess development

  • Development proceeds from early clone screening to secondary screening and optimization, then pilot-scale integration; early screening trades process information for lower-cost experimentation.MTPs are used in early screening, while MBRs support secondary screening and optimization before pilot-scale work.Source: §1.1 · p. 2, Figure 1 · p. 2

1.2 Challenges of traditional process development workflow

  • Scale-up combines nonlinear, system-specific variables with noisy, sparse data, complicating the transfer of information between scales.Small-scale experiments are more homogeneous than larger-scale processes, which can contain additional heterogeneities.Source: §1.2 · p. 2
  • Many DoE methods assume limited parameter interaction, whereas bioprocesses have nonlinear relationships and interdependencies.The paper argues that these characteristics require advanced models and experimental designs for characterization and cross-scale knowledge transfer.Source: §1.2 · p. 2

1.3 Aim of this study

  • The study evaluates multi-fidelity batch BO for optimizing biocatalysts and process conditions across scales against traditional industrial DoE approaches.The benchmark uses a simulation-based Chinese hamster ovary cell process.Source: §1.3 · p. 3

2 Methods

The methods construct a simulated CHO bioprocess and a batch Bayesian optimization workflow for selecting conditions, clones, and scales. The model represents scale-dependent behavior and cost, while Gaussian-process methods handle fidelity, batches, and categorical clone choices.

2.1.1 Base Model

  • The CHO model uses ODEs for cell growth and substrate kinetics, with product-formation terms added to represent process performance.Product formation depends on viable biomass and glucose and includes growth-associated and non-growth-associated yields.Source: §2.1.1 · p. 3, §2.1.2 · p. 3

2.1.3 Temperature and pH Influence Modeling

  • Temperature and pH modify maximum growth through bell-shaped influence factors, with parameters controlling each curve’s shape and optimum.The model uses a smoother temperature response than pH to reflect tighter cellular pH constraints.Source: §2.1.3 · pp. 3–4

2.1.4 Clone Modeling

  • Clone diversity is simulated by sampling parameters around base values, while feed modeling distinguishes MTP’s single variable pulse from the three-pulse capability of MBR and pilot reactors.The clone variations represent differences in productivity, robustness, and growth; total feed is constrained by a maximum amount.Source: §2.1.4 · pp. 4–5, §2.1.5 · p. 5

2.1.6 Scale Modeling

  • Scale factors represent growth and death effects, with scale-dependent measurement noise and approximate per-experiment costs distinguishing MTP, MBR, and pilot experiments.The simulation assumes MBR resembles a scaled-down pilot reactor; MTP is modeled as most unreliable, followed by pilot and then MBR.Source: §2.1.6 · pp. 5–6, Table 2 · p. 6, §2.1.7 · p. 6

2.2.1 Bayesian Optimization

  • Bayesian optimization uses probabilistic surrogate predictions and acquisition functions to trade off exploration and exploitation under costly evaluations.Gaussian processes provide predictions and uncertainty estimates, with kernels encoding similarity between inputs.Source: §2.2.1 · p. 6, §2.2.2 · pp. 6–7

2.2.3 Multi-Fidelity

  • The GP models fidelity as an input dimension, using discrete levels whose relative spacing represents similarity in behavior across data sources.The fidelity axis is learnable over a practical range, and MBR is placed near pilot because it is assumed to be a relatively accurate scale-down model.Source: §2.2.3 · p. 7

2.2.4 Batch Evaluation

  • Batch selection uses fantasizing to condition sequentially on temporary observations, and Monte Carlo sampling to approximate batch acquisition values.Fantasizing is repeated over multiple fantasy samples; its approximation error can accumulate as batch size increases.Source: §2.2.4 · p. 8

2.2.5 Categorical Variables

  • Clone choices are modeled as related categorical tasks using either an intrinsic coregionalization kernel or a learned embedding combined with the continuous-input kernel.The ICM learns clone correlations, while the embedding maps one-hot clone labels to learnable positions.Source: §2.2.5 · pp. 8–9

2.3 Acquisition functions

The framework adapts batch expected improvement, upper confidence bound, and GIBBON for multi-fidelity optimization, then selects among fidelity-specific batches using adjusted acquisition scores. Low-fidelity batch selection uses a custom grid-search strategy, while the comparison scenario models a funnel-like industrial DoE workflow.

2.3.1 Extended Multi-Point Log Expected Improvement (extended qLogEI)

  • Batch qLogEI extends expected improvement to jointly score batches using Monte Carlo samples from the GP posterior, and a log transformation improves acquisition maximization.The batch size q can exceed one.Source: §2.3.1 · p. 10
  • The multi-fidelity qLogEI correction balances information gain against evaluation cost and discounts lower-fidelity batches according to their correlation with target-fidelity evaluations.The fidelity factor is a customized choice whose impact on optimization requires careful evaluation.Source: §2.3.1 · p. 10

2.3.2 Extended Multi-Point Upper Confidence Bound (Extended qUCB)

  • Extended qUCB uses Monte Carlo sampling for batches and applies cost- and fidelity-awareness; its β hyperparameter controls the amount of exploration.UCB favors locations with high predictive means or substantial uncertainty.Source: §2.3.2 · p. 10

2.3.3 General-purpose Information-Based Bayesian Optimization (GIBBON)

  • GIBBON supports arbitrary batch sizes and multiple fidelities without extra extensions, using correlation-based penalization to lower-bound estimated information gain.Its information-gain term measures each batch point against sampled potential maxima of the target-fidelity objective.Source: §2.3.3 · p. 11

2.4 The Multi-Fidelity Batch Bayesian Optimization Framework

  • The workflow fits a multi-task GP, optimizes a batch separately at each fidelity, adjusts scores by fidelity correlation, evaluates the selected batch, and updates the model.The implementation supports varying batch sizes, heterogeneous clones, and multiple experimental levels.Source: §2.4 · p. 11, Algorithm 1 Multi-Fidelity Bayesian… · p. 12

2.4.1 Individual Treatment of Batches from Different Fidelity Levels

  • Fidelity-specific batches compete by acquisition score under assumed fixed batch sizes; smaller, less-constrained microbioreactor and pilot batches use BoTorch optimization with fantasy models.Separate optimization by fidelity reduces overall complexity, while large batch selection remains computationally burdensome.Source: §2.4.1 · p. 12, §2.4.3 · p. 12, Algorithm 2 Grid Search for… · p. 13

2.4.2 Microtiter Plates: Dealing with Larger Batch Size and Additional Constraints

  • For microtiter plates, a temperature-pH grid search handles mixed-integer constraints, while Latin hypercube sampling selects clones after direct clone optimization yields poor diversity and often zero acquisition values.Algorithm 2 evaluates candidate batches across temperature-pH combinations and returns the best-scoring batch.Source: §2.4.2 · p. 12, Algorithm 2 Grid Search for… · p. 13

2.5 The Comparison Scenario

  • The industrial DoE benchmark uses 20 iterations across four microtiter, eleven microbioreactor, and five pilot-scale iterations, following a funnel from clone screening to local pilot-scale exploitation.The funnel is scaled down from reality because the study uses 30 clones rather than 100 or more.Source: §2.5 · p. 13

3 Results & Discussion

The study evaluates a multi-fidelity batch Bayesian optimization workflow for simulated CHO bioprocess development, including clone selection and process conditions across reactor scales. Across two clone-performance distributions, BO outperformed industrial benchmarks, with results varying by acquisition function, clone representation, and screening information.

3.1 The Optimization Problem

  • The workflow combines multi-fidelity batch BO with a simulated CHO process that retains nonlinear dynamics and scale-dependent behavior while remaining computationally tractable.The optimization uses accumulated product titer at the end of a fixed experiment duration; MTP experiments omit feeding and have restricted temperature, pH, and clone choices.Source: §3.1 · pp. 13–15

3.2 Results of the Clone Representation Case Study

  • GIBBON with a three-dimensional entity embedding performed best overall among the tested BO approaches, while the best clone representation varied by acquisition function.For qUCB, the two-dimensional embedding achieved 61 mg L−1; for qLogEI, ICM was about 14% better than the two-dimensional embedding.Source: §3.2 · pp. 15–16, Table 4 · p. 15

3.3 Results of the Cell Distribution Case Study

  • In Distribution A, GIBBON reached 66 mg L−1 at C35,260, up to 78% above the best industrial method, LHS at 37 mg L−1.GIBBON and qLogEI exceeded the best industrial baseline by iterations 4 and 12, respectively.Source: §3.3 · p. 16, Figure 6 · p. 17
  • In Distribution B, qUCB reached 57 mg L−1 versus factorial design’s 29 mg L−1; by iteration 20, qLogEI gained 78% at 3% lower cost and qUCB 100% at 40% lower cost.GIBBON reached 55 mg L−1 over 17 iterations, and qLogEI reached 51 mg L−1 over 24 iterations.Source: §3.3 · pp. 18–19, Figure 8 · p. 19
  • Industrial staged screening can lock in suboptimal clones early, whereas BO dynamically mixes scales and incorporates previous experiments to explore clones and conditions together.The industrial methods did not identify high-performing clones in either distribution; their later MBR and pilot stages exploited the early selections.Source: §3.3 · p. 19
  • Flexible MTP feeding provides clone-response information but can introduce misleading signals when scale-down models are poorly calibrated; GIBBON may also over-prioritize costly high-fidelity experiments.The authors advise care with GIBBON’s fidelity-selection mechanisms in this non-standard screening setting.Source: §3.3 · p. 20

3.4 Overarching Recommendations and Future Directions

  • Method choice can reflect priorities: GIBBON with a three-dimensional embedding favors yield, qLogEI offers a more balanced profile, and qUCB favors cost reduction; earlier high-fidelity evaluations can inform cross-scale relationships.These recommendations arise from the tested scenarios and acquisition-function behavior.Source: §3.3 · p. 18, §3.4 · p. 20
  • The simulation may make MTP less informative than in real systems, while fidelity modeling, large-batch optimization, and scaling clone counts remain areas for improvement.Larger clone sets would require sparse GP techniques to manage computational load.Source: §3.4 · pp. 20–21

4 Conclusion & Outlook

The study evaluates a multi-fidelity batch Bayesian optimization workflow in a custom bioprocess simulator. It reports better performance than standard industrial strategies under different cross-scale clone-performance scenarios, while identifying real-world validation and cross-process transfer as future opportunities.

4 Conclusion & Outlook

  • The study investigates simulation-based multi-fidelity batch BO to streamline bioprocess development and minimize experimental costs for sustainable production.The motivation highlights pharmaceuticals and specialty chemicals.Source: §4 · p. 21
  • The framework combines batch selection and fidelity modeling and is evaluated with a custom simulator capturing nonlinear dynamics, scale-dependent variability, and heterogeneous clone performance.The simulator was designed to support systematic comparisons of optimization strategies.Source: §4 · p. 21
  • The BO framework outperformed standard industrial strategies across scenarios with differing or aligned clone performance across scales when the clone representation model was carefully chosen.GIBBON and qLogEI performed strongly, and the study reports that cost reduction and optimization-performance increase could be achieved simultaneously.Source: §4 · p. 21
  • The outlook identifies automated, data-efficient development as promising while noting remaining challenges in scaling and real-world applicability.The paper connects these methods to development of high-performing and sustainable bioprocesses.Source: §4 · p. 21
  • The framework targets single-process optimization; transferring surrogate models or optimization trajectories across bioprocesses and testing the full pipeline on real-world data remain future directions.The paper describes real-world bioprocess development data as a crucial next step for further validation.Source: §4 · p. 21

Abbreviations

The section lists abbreviations used in the paper, including BO for Bayesian optimization, GP for Gaussian process, and DoE for Design of Experiments.

Abbreviations

  • The glossary expands BO as Bayesian optimization, GP as Gaussian process, DoE as Design of Experiments, and MBR as microbioreactor.It also lists terms including CHO, DDO, EI, GIBBON, ICM, LHS, ODE, qLogEI, qUCB, RBF, and UCB.Source: Abbreviations · p. 21

Conflicts of interest

The authors declare no conflicts of interest.

Conflicts of interest

A.1 Clone Parameter Range

Table 5 gives lower and upper bounds used to generate process parameters in the simulation study.

A.1 Clone Parameter Range

  • Table 5 presents lower and upper bounds for process-parameter generation in the simulation study.Its subscripts X, G, L, A, and Q denote viable cells, glucose, lactate, ammonia, and glutamine, respectively.Source: Table 5 · p. 23

A.2 Cost Estimation

The cost estimate is calculated per experiment from personnel and material costs, with energy consumption treated as negligible. Preparation time is allocated across experiments according to batch size.

A.2 Cost Estimation

  • The estimate is per single experiment and separates personnel and material costs, while assuming energy use is negligible.For MTP, one experiment means one well.Source: §A.2 · p. 23
  • A three-hour preparation time per industrial batch is divided by batch size: 96 MTP experiments, 12 MBR experiments, or one pilot experiment.This allocation yields the assumed time per individual experiment at each scale.Source: §A.2 · p. 23
  • The per-experiment cost calculation uses medium cost and reactor volume, hourly labor cost and experiment time, plus single-use reactor cost when applicable.The formula is introduced after the cost assumptions; the listed symbols specify its inputs.Source: §A.2 · p. 23

A.3 Higher Embedding Dimensions

Higher-dimensional clone embeddings offered little improvement over the three-dimensional representation, and increasing dimensionality beyond a point appeared to reduce framework performance.

A.3 Higher Embedding Dimensions

  • Five-, six-, and ten-dimensional embeddings showed only little performance improvement over the three-dimensional embedding.The comparison is reported for final cumulative maximum endpoint concentrations across acquisition functions in Distribution A.Source: §A.3 · p. 23, Table 7 · p. 24
  • Further increasing embedding dimensionality past a certain point seems to reduce framework performance.Similar results were previously obtained by Hutter et al. [50].Source: §A.3 · pp. 23–24
  • Table 7 compares clone representations for three acquisition functions across 10 runs, reporting mean and standard deviation of final cumulative maximum endpoint concentrations.The highest-performing representation for each acquisition function is highlighted.Source: Table 7 · p. 24

A.4 Fidelity Level Evaluation Distribution Plots

The fidelity schedules differed by acquisition function: GIBBON favored pilot-scale evaluations, while qUCB increased use of higher fidelities later in optimization.

A.4 Fidelity Level Evaluation Distribution Plots

  • GIBBON showed a pronounced tendency toward pilot-scale evaluations, with the pilot share rising and falling over cycles of three to four iterations.The periodic pattern is described for pilot-scale experiments.Source: §A.4 · p. 24
  • For qUCB, higher-fidelity evaluations increased between iterations 20 and 30, alongside shorter runtime attributed to more frequent expensive experiments.The passage hypothesizes that the pattern may reflect MTP experiments lacking feeding information.Source: §A.4 · p. 24
  • The reported qUCB fidelity pattern was similar to qLogEI, while GIBBON's pilot-scale tendency was more pronounced.The comparison with qLogEI is stated without further detail here.Source: §A.4 · p. 24

A.5 Effect of a Flexible Feeding Pulse in MTP Experiments

With flexible feeding, Bayesian optimization outperformed industrial methods in both clone distributions, although the industrial approaches were more competitive early in Distribution B. The reported comparisons also associate early clone lock-in in Distribution A with industrial methods stalling at a lower peak.

A.5 Effect of a Flexible Feeding Pulse in MTP Experiments

  • With flexible feeding in Distribution A, industrial methods improved only during the first five iterations and stalled at 36 mg L−1; qUCB reached 61 mg L−1, 70% above the best industrial baseline, while reducing costs by 13%.The plateau could reflect early fixation on MTP-scale clones 14, 15, and 29, potentially preventing discovery of superior clone-condition combinations.Source: §A.5 · p. 24
  • GIBBON's evaluations were dominated by a mix of MBR and mainly pilot-scale experiments, whereas qUCB primarily used MTP evaluations and shifted gradually to higher fidelities.The qUCB shift toward higher fidelities was more pronounced in Distribution A than B, but less so than for qLogEI.Source: Figure 9 · p. 25, Figure 10 · p. 26
  • The authors conclude that mixed-fidelity BO is the more robust choice across the two data landscapes, with better global exploration and avoidance of the Distribution A scale-up lock-in pattern.They recommend it for maximizing result generation regardless of data landscape.Source: §A.5 · p. 25
  • 61 mg L−1 was qUCB's peak in Distribution A, 70 % above the best industrial baseline while reducing total costs by 13 %.Industrial methods stalled at 36 mg L−1; Figure 11 compares optimization behavior over iterations and cumulative evaluation cost.Source: §A.5 · p. 24, Figure 11 · p. 26
  • 63 mg L−1 was GIBBON's peak in Distribution B, 41 % above Factorial, with BO methods incurring approximately 3 % higher total cost than industrial baselines.Factorial reached 45 mg L−1; Figure 12 compares optimization behavior over iterations and cumulative evaluation cost.Source: §A.5 · p. 24, Figure 12 · p. 27

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