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arxiv: 2602.17679 · v2 · pith:57CA4ZQZnew · submitted 2026-02-04 · 💻 cs.LG · math.OC

Joint Parameter and State-Space Bayesian Optimization: Using Process Expertise to Accelerate Manufacturing Optimization

Saksham Kiroriwal , Julius Pfrommer , J\"urgen Beyerer This is my paper

Pith reviewed 2026-05-21 13:48 UTC · model grok-4.3

classification 💻 cs.LG math.OC
keywords Bayesian optimizationmanufacturing optimizationGaussian process networksstate-space modelingprocess expertisebioethanol productionhigh-dimensional systemsmulti-stage processes
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The pith

Incorporating expert-derived features from intermediate data into a graph-based Bayesian optimization model lets complex manufacturing processes reach targets twice as fast.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a framework that improves Bayesian optimization for high-dimensional, multi-stage manufacturing systems by using process expert knowledge to pull useful signals from intermediate observations. Instead of treating the whole process as an opaque black box, it models the system as a directed acyclic graph that respects the underlying process structure and incorporates extracted low-dimensional features from high-dimensional state-space time series. On a detailed simulation of a multi-stage bioethanol production process, the resulting method reaches the target performance level twice as fast and more consistently than standard approaches. This speed-up directly reduces the experimental time and material costs required to mature new manufacturing processes. The work shows how domain knowledge can be systematically combined with probabilistic models to make optimization more practical for real industrial settings.

Core claim

The POGPN-JPSS framework extends Partially Observable Gaussian Process Networks by adding joint parameter and state-space modeling. This lets the optimizer use low-dimensional latent features that process experts extract from high-dimensional intermediate state-space data. When tested on a challenging simulation of a multi-stage bioethanol production process, the method reaches the desired performance threshold twice as fast and with greater reliability than current state-of-the-art Bayesian optimization techniques.

What carries the argument

The POGPN-JPSS framework, which models the manufacturing process as a directed acyclic graph and injects expert-extracted low-dimensional latent features from high-dimensional state-space observations into the joint parameter and state-space optimization.

If this is right

  • Achieves the desired performance threshold twice as fast as state-of-the-art methods.
  • Demonstrates greater reliability when converging to target performance levels.
  • Translates directly into substantial savings in experimental time and resources during process maturation.
  • Shows that structured probabilistic models gain practical value when combined with domain-expert feature extraction.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same expert-feature approach could shorten optimization cycles in other multi-stage chemical or pharmaceutical manufacturing settings.
  • Replacing manual expert feature extraction with learned representations might further reduce the human effort required to apply the method.
  • Real-world deployment on physical equipment rather than simulation would test whether the reported speed-up survives noise and unmodeled dynamics.
  • The graph-based structure may lend itself to transfer learning across related processes that share similar intermediate stages.

Load-bearing premise

Process expert knowledge can be used to extract low-dimensional latent features from high-dimensional state-space time series data in a manner that meaningfully improves optimization performance.

What would settle it

Running the same bioethanol production simulation and finding that POGPN-JPSS does not reach the target performance threshold at least twice as fast as standard Bayesian optimization baselines would disprove the central performance claim.

Figures

Figures reproduced from arXiv: 2602.17679 by Julius Pfrommer, J\"urgen Beyerer, Saksham Kiroriwal.

Figure 1
Figure 1. Figure 1: A multi-stage bioethanol production process [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Observed state-space dynamics from a single simulation run of the multi-stage bioethanol production [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Histograms of key process observations from 50 random simulation runs. The observations shown [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The Directed Acyclic Graph (DAG) for the bioethanol process is shown alongside the Bayesian [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

Bayesian optimization (BO) is a powerful method for optimizing black-box manufacturing processes, but its performance is often limited when dealing with high-dimensional multi-stage systems, where we can observe intermediate outputs. Standard BO models the process as a black box and ignores the intermediate observations and the underlying process structure. Partially Observable Gaussian Process Networks (POGPN) model the process as a Directed Acyclic Graph (DAG). However, using intermediate observations is challenging when the observations are high-dimensional state-space time series. Process-expert knowledge can be used to extract low-dimensional latent features from the high-dimensional state-space data. We propose POGPN-JPSS, a framework that combines POGPN with Joint Parameter and State-Space (JPSS) modeling to use intermediate extracted information. We demonstrate the effectiveness of POGPN-JPSS on a challenging, high-dimensional simulation of a multi-stage bioethanol production process. Our results show that POGPN-JPSS significantly outperforms state-of-the-art methods by achieving the desired performance threshold twice as fast and with greater reliability. The fast optimization directly translates to substantial savings in time and resources. This highlights the importance of combining expert knowledge with structured probabilistic models for rapid process maturation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes POGPN-JPSS, a Bayesian optimization framework that augments Partially Observable Gaussian Process Networks (POGPN) with Joint Parameter and State-Space (JPSS) modeling. Process-expert knowledge is used to extract low-dimensional latent features from high-dimensional state-space time series of intermediate outputs in multi-stage systems. The method is evaluated on a high-dimensional simulation of a multi-stage bioethanol production process, where it is claimed to reach a desired performance threshold twice as fast and with greater reliability than state-of-the-art approaches.

Significance. If the empirical results hold after appropriate controls, the work could meaningfully advance sample-efficient optimization for structured, high-dimensional manufacturing processes by showing how domain-derived features can be integrated into DAG-structured probabilistic models. The practical payoff in reduced time and resource use for process maturation is clear if the gains are attributable to the proposed joint modeling rather than dimensionality reduction alone.

major comments (2)
  1. Abstract and experimental results section: the headline claim of a factor-of-two speedup and greater reliability is load-bearing for the paper's contribution, yet no ablation is described that isolates the effect of the JPSS joint inference from the expert feature extraction step itself. A comparison of POGPN using the same hand-crafted low-dimensional features but without JPSS versus the full POGPN-JPSS is required to establish that the DAG-structured joint modeling, rather than the dimensionality reduction, drives the reported gains.
  2. Method section on JPSS integration: the description of how the joint parameter and state-space inference operates on the extracted latent features within the POGPN DAG lacks sufficient technical detail on the inference algorithm, the form of the state-space model, and any assumptions about conditional independence, making it difficult to assess whether the framework is a substantive extension or primarily a wrapper around existing components.
minor comments (2)
  1. The abstract and results presentation would benefit from explicit reporting of the number of independent runs, error bars or confidence intervals, and any statistical tests used to support the 'twice as fast' and 'greater reliability' claims.
  2. Notation for the latent features and their mapping from high-dimensional observations should be introduced more clearly with an equation or diagram to avoid ambiguity when describing the input to the POGPN.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive report. The comments identify key areas where additional evidence and technical detail would strengthen the manuscript. We address each major comment below and will revise the paper accordingly.

read point-by-point responses

  1. Referee: Abstract and experimental results section: the headline claim of a factor-of-two speedup and greater reliability is load-bearing for the paper's contribution, yet no ablation is described that isolates the effect of the JPSS joint inference from the expert feature extraction step itself. A comparison of POGPN using the same hand-crafted low-dimensional features but without JPSS versus the full POGPN-JPSS is required to establish that the DAG-structured joint modeling, rather than the dimensionality reduction, drives the reported gains.

    Authors: We agree that the current experimental section does not contain an explicit ablation isolating the JPSS joint inference from the expert-derived feature extraction. While the manuscript compares POGPN-JPSS against several state-of-the-art baselines, it does not report results for POGPN equipped with the same low-dimensional features but without the joint parameter and state-space modeling. In the revised manuscript we will add this ablation to the experimental results section, using the same bioethanol simulation setup, to demonstrate whether the reported gains are attributable to the joint modeling rather than dimensionality reduction alone. revision: yes

  2. Referee: Method section on JPSS integration: the description of how the joint parameter and state-space inference operates on the extracted latent features within the POGPN DAG lacks sufficient technical detail on the inference algorithm, the form of the state-space model, and any assumptions about conditional independence, making it difficult to assess whether the framework is a substantive extension or primarily a wrapper around existing components.

    Authors: We acknowledge that the current description of the JPSS integration is high-level and does not fully specify the inference procedure, the precise state-space model, or the conditional independence assumptions. In the revised manuscript we will expand the relevant subsection to include: (i) the exact form of the state-space transition and emission distributions used on the latent features, (ii) the inference algorithm (including any variational or sampling-based approach), and (iii) the conditional independence structure imposed by the POGPN DAG when the JPSS component is incorporated. These additions will clarify the technical contribution and facilitate reproducibility. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation combines existing components with independent empirical validation.

full rationale

The paper introduces POGPN-JPSS as a combination of POGPN (modeling processes as DAGs) with joint parameter and state-space modeling, using expert-derived low-dimensional features from high-dimensional time series. No equations, predictions, or results are shown to reduce by construction to quantities fitted on the demonstration data. The central performance claims rest on simulation experiments rather than self-definitional steps or load-bearing self-citations. Per the rules, this is self-contained against external benchmarks with no exhibited reduction (e.g., no fitted parameter renamed as prediction or ansatz smuggled via citation), warranting score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that expert knowledge yields useful low-dimensional features; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Process-expert knowledge can reliably extract low-dimensional latent features from high-dimensional state-space time series that improve downstream optimization.
    Invoked to justify the use of intermediate observations within the POGPN-JPSS framework.

pith-pipeline@v0.9.0 · 5754 in / 1294 out tokens · 37287 ms · 2026-05-21T13:48:10.673832+00:00 · methodology

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Works this paper leans on

32 extracted references · 32 canonical work pages · 3 internal anchors

  1. [1]

    Causal bayesian optimization

    Virginia Aglietti, Xiaoyu Lu, Andrei Paleyes, and Javier González. Causal bayesian optimization. In International Conference on Artificial Intelligence and Statistics, pages 3155–3164. PMLR, 2020

    work page 2020

  2. [2]

    Unexpected improvements to expected improvement for bayesian optimization.Advances in Neural Information Processing Systems, 36:20577–20612, 2023

    Sebastian Ament, Samuel Daulton, David Eriksson, Maximilian Balandat, and Eytan Bakshy. Unexpected improvements to expected improvement for bayesian optimization.Advances in Neural Information Processing Systems, 36:20577–20612, 2023

    work page 2023

  3. [3]

    J. F. Andrews. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates.Biotechnology and Bioengineering, 10(6):707–723, 1968. doi:10.1002/bit.260100602

    work page doi:10.1002/bit.260100602 1968

  4. [4]

    Bayesian optimization of function networks.Advances in neural information processing systems, 34:14463–14475, 2021

    Raul Astudillo and Peter Frazier. Bayesian optimization of function networks.Advances in neural information processing systems, 34:14463–14475, 2021

    work page 2021

  5. [5]

    Botorch: A framework for efficient monte-carlo bayesian optimization.Advances in neural information processing systems, 33:21524–21538, 2020

    Maximilian Balandat, Brian Karrer, Daniel Jiang, Samuel Daulton, Ben Letham, Andrew G Wilson, and Eytan Bakshy. Botorch: A framework for efficient monte-carlo bayesian optimization.Advances in neural information processing systems, 33:21524–21538, 2020

    work page 2020

  6. [6]

    Brasington, J

    A. Brasington, J. Halbritter, R. Wehbe, and R. Harik. Bayesian optimization for process planning selections in automated fiber placement.Journal of Composite Materials, 56:4275 – 4296, 2022. doi:10.1177/00219983221129010

    work page doi:10.1177/00219983221129010 2022

  7. [7]

    Convergence of sparse variational inference in gaussian processes regression.Journal of Machine Learning Research, 21(131):1–63, 2020

    David R Burt, Carl Edward Rasmussen, and Mark Van Der Wilk. Convergence of sparse variational inference in gaussian processes regression.Journal of Machine Learning Research, 21(131):1–63, 2020

    work page 2020

  8. [8]

    Okwudire

    Seokhyun Chung, Cheng-Hao Chou, Xiaozhu Fang, Raed Al Kontar, and C. Okwudire. A multi-stage approachforknowledge-guidedpredictionswithapplicationtoadditivemanufacturing.IEEE Transactions on Automation Science and Engineering, 19:1675–1687, 2022. doi:10.1109/tase.2022.3160420

    work page doi:10.1109/tase.2022.3160420 2022

  9. [9]

    Fermentation technology: Scale-up and seed train operations, 2023

    Bioprocess Pilot Facility. Fermentation technology: Scale-up and seed train operations, 2023. URL https://bpf.eu/fermentation/. Industrial guideline and case example

    work page 2023

  10. [10]

    A Tutorial on Bayesian Optimization

    Peter I Frazier. A tutorial on bayesian optimization.arXiv preprint arXiv:1807.02811, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  11. [11]

    Rapid ethanol fermentation of cellulose hydrolysate

    TK Ghose and RD Tyagi. Rapid ethanol fermentation of cellulose hydrolysate. ii. product and substrate inhibition and optimization of fermentor design.Biotechnology and Bioengineering, 21(8):1401–1420, 1979

    work page 1979

  12. [12]

    HighBridge, 2006

    Eliyahu M Goldratt, Jeff Cox, and David Whitford.The goal. HighBridge, 2006

    work page 2006

  13. [13]

    Gaussian Processes for Big Data

    James Hensman, Nicolo Fusi, and Neil D Lawrence. Gaussian processes for big data.arXiv preprint arXiv:1309.6835, 2013. 8

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  14. [14]

    Seed train optimization for suspension cell culture

    Tanja Hernández Rodríguez, Ralf Pörtner, and Björn Frahm. Seed train optimization for suspension cell culture. InBMC Proceedings, volume 7, page P9. Springer, 2013

    work page 2013

  15. [15]

    Vanilla bayesian optimization performs great in high dimensions.arXiv preprint arXiv:2402.02229, 2024

    Carl Hvarfner, Erik Orm Hellsten, and Luigi Nardi. Vanilla bayesian optimization performs great in high dimensions.arXiv preprint arXiv:2402.02229, 2024

    work page arXiv 2024

  16. [16]

    Therealcostofmanufacturingdowntime(2020–2025): Sectorinsights&forecast

    IDS-INDATA. Therealcostofmanufacturingdowntime(2020–2025): Sectorinsights&forecast. Technical report, 2025. URL https://idsindata.co.uk/manufacturing-downtime-costs-and-forecasting/. Accessed: 2025-08-26

    work page 2020

  17. [17]

    Scaling up animal cell culture: Technical challenges and opportunities for biomanufacturing, 2020

    Good Food Institute. Scaling up animal cell culture: Technical challenges and opportunities for biomanufacturing, 2020. URL https://gfi.org/resource/scaling-up-animal-cell-culture/ . Technical white paper

    work page 2020

  18. [18]

    Parametric gaussian process regressors

    Martin Jankowiak, Geoff Pleiss, and Jacob Gardner. Parametric gaussian process regressors. In International conference on machine learning, pages 4702–4712. PMLR, 2020

    work page 2020

  19. [19]

    Adam: A Method for Stochastic Optimization

    Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980, 2014

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  20. [20]

    Schmitt, and Jurgen Beyerer

    Saksham Kiroriwal, Julius Pfrommer, Hendrik Mende, Robert H. Schmitt, and Jurgen Beyerer. Joint parameter and state-space modelling of manufacturing processes using gaussian processes. In2024 IEEE 22nd International Conference on Industrial Informatics (INDIN), pages 1–6, 2024

    work page 2024

  21. [21]

    Partially observable gaussian process network and doubly stochastic variational inference.arXiv preprint arXiv:2502.13905, 2025

    Saksham Kiroriwal, Julius Pfrommer, and Jürgen Beyerer. Partially observable gaussian process network and doubly stochastic variational inference.arXiv preprint arXiv:2502.13905, 2025

    work page arXiv 2025

  22. [22]

    Scalable bayesian optimization accelerates process optimization of penicillin production

    Qiaohao Liang and Lipeng Lai. Scalable bayesian optimization accelerates process optimization of penicillin production. InNeurIPS 2021 AI for Science Workshop, 2021

    work page 2021

  23. [23]

    A kinetic study of the lactic acid fermentation

    Robert Luedeking and Edgar L Piret. A kinetic study of the lactic acid fermentation. batch process at controlled ph.Journal of Biochemical and Microbiological Technology and Engineering, 1(4):393–412, 1959

    work page 1959

  24. [24]

    Inducing point allocation for sparse gaussian processes in high-throughput bayesian optimisation

    Henry B Moss, Sebastian W Ober, and Victor Picheny. Inducing point allocation for sparse gaussian processes in high-throughput bayesian optimisation. InInternational Conference on Artificial Intelligence and Statistics, pages 5213–5230. PMLR, 2023

    work page 2023

  25. [25]

    The maintenance energy of bacteria in growing cultures.Proceedings of the Royal Society of London

    SJ Pirt. The maintenance energy of bacteria in growing cultures.Proceedings of the Royal Society of London. Series B. Biological Sciences, 163(991):224–231, 1965

    work page 1965

  26. [26]

    Gaussian processes in machine learning

    Carl Edward Rasmussen. Gaussian processes in machine learning. InSummer school on machine learning, pages 63–71. Springer, 2003

    work page 2003

  27. [27]

    Effect of ph and temperature on bioethanol production: Evidences from the fermentation of sugarcane molasses using saccharomyces cerevisiae

    UY Salihu, UG Usman, AY Abubakar, and G Mansir. Effect of ph and temperature on bioethanol production: Evidences from the fermentation of sugarcane molasses using saccharomyces cerevisiae. Dutse Journal of Pure and Applied Sciences, 8(4b):9–16, 2022

    work page 2022

  28. [28]

    Doubly stochastic variational inference for deep gaussian processes

    Hugh Salimbeni and Marc Deisenroth. Doubly stochastic variational inference for deep gaussian processes. Advances in neural information processing systems, 30, 2017

    work page 2017

  29. [29]

    Application of bayesian optimization for pharmaceutical product development.Journal of Pharmaceutical Innovation, 15(3):333–343, 2020

    Syusuke Sano, Tadashi Kadowaki, Koji Tsuda, and Susumu Kimura. Application of bayesian optimization for pharmaceutical product development.Journal of Pharmaceutical Innovation, 15(3):333–343, 2020

    work page 2020

  30. [30]

    Shields, Jason M

    Benjamin J. Shields, Jason M. Stevens, Jun Li, Marvin Parasram, Farhan N. Damani, Jesus I Martinez Alvarado, J. Janey, Ryan P. Adams, and A. Doyle. Bayesian reaction optimization as a tool for chemical synthesis.Nature, 590:89 – 96, 2021. doi:10.1038/s41586-021-03213-y

    work page doi:10.1038/s41586-021-03213-y 2021

  31. [31]

    Model-based causal bayesian optimization

    Scott Sussex, Anastasiia Makarova, and Andreas Krause. Model-based causal bayesian optimization. arXiv preprint arXiv:2211.10257, 2022

    work page arXiv 2022

  32. [32]

    O. J. Sánchez and C. A. Cardona. Trends in biotechnological production of fuel ethanol from different feedstocks.Bioresource Technology, 99(13):5270–5295, 2008. doi:10.1016/j.biortech.2007.11.013. 9

    work page doi:10.1016/j.biortech.2007.11.013 2008