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REVIEW 3 major objections 5 minor 57 references

Pre-training a generic decoder on simulated biokinetic growth curves matches a fully bio-structured ODE decoder trained on real data — under data scarcity, simulation can substitute for architecture engineering.

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2026-08-02 07:29 UTC pith:EMPFMLUR

load-bearing objection Useful empirical comparison of simulation pretraining vs architecture priors for bioprocess models, but the headline substitutability claim compares 11-dataset averages to 7-dataset averages and needs a same-subset reanalysis. the 3 major comments →

arxiv 2607.20539 v1 pith:EMPFMLUR submitted 2026-07-10 cs.LG cs.AI

Leveraging Biokinetic Knowledge Priors for Data-Scarce Bioprocess Modeling

Kyunghoon Hur , Eunjung Jeon , Hyun Woo Kim , Gyubok Lee , Seongjun Yang This is my paper
classification cs.LG cs.AI
keywords bioprocess modelingdata scarcitysimulation pre-trainingbiokinetic ODE priorsmicrobial growth curvesneural decoderarchitecture-level priorsbioreactor state prediction
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tackles a concrete bottleneck: deep learning has transformed early drug discovery, but biomanufacturing lags because bioreactor experiments are costly, slow, and rarely shared, leaving each lab with a handful of curves. Its claim is that decades-old biokinetic growth equations — Monod saturation kinetics, Baranyi lag dynamics, Gompertz sigmoid growth — can supply the missing training signal through two interchangeable channels: simulating synthetic curves to pre-train a generic decoder, or embedding the ODE in the decoder's forward pass. Across 11 datasets and 7 bacterial species both channels beat no-prior baselines, and the central finding is that the cheap channel matches the expensive one: a plain MLP pre-trained on simulated curves reaches R² ≈ 0.515, statistically on par with R² = 0.554 for a fully ODE-structured decoder trained on real data alone. The paper concludes that simulation pre-training is the practical, data-efficient recipe — provided the simulation mixes several biokinetic families with broad parameter sampling; single-family narrow sampling helps less, and smooth but structureless random curves transfer almost nothing.

Core claim

The paper's central discovery is that biokinetic ODE knowledge enters a neural net through two substitutable channels, not one. The architecture channel embeds the Monod–Baranyi growth system — cell density, substrate, product, and a lag-adaptation state, optionally multiplied by a temperature/pH cardinal envelope — inside the decoder's forward pass (the BioStruct-ODE models). The data channel ignores architecture: it samples organism-specific parameters from literature ranges, integrates the same ODE families into synthetic growth curves, pre-trains an ordinary MLP decoder on them, and fine-tunes on real data. The two perform alike: MLP+pre-training reaches R² ≈ 0.515 while BioStruct-ODE+Ca

What carries the argument

The central object is the Monod–Baranyi growth-ODE system — a small set of coupled equations tracking cell density, substrate, product, and a lag-adaptation state, with growth rate following Monod saturation kinetics, a carrying-capacity term K, an explicit death term, and, in the Cardinal variant, envelope functions of temperature and pH. The same system does double duty: as an architecture template (BioStruct-ODE embeds it in the forward pass with a parameter head emitting organism-specific parameters and a small neural correction scaled by ε), and as a simulation generator (parameters sampled from literature ranges ±50%, integrated into synthetic curves for pre-training). The argument tur

Load-bearing premise

The result rests on the assumption that the classical growth equations faithfully generate the shapes of real microbial growth curves in these datasets, so that simulated curves carry genuine biokinetic knowledge rather than merely smooth, plausible trajectories.

What would settle it

Take real growth curves that the biokinetic families fit poorly (for example, the curves the paper's own with-growth filter discards, per-curve Monod–Baranyi fit R² < 0.4) and pre-train the same MLP on those shapes; if transfer stays strong, the prior is smoothness, not biokinetics. Alternatively, pre-train on simulated curves with parameters deliberately drawn outside biological ranges — declining instead of saturating shapes; if R² stays near the random-GP control level, biokinetic specificity is confirmed as the active ingredient.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A generic neural decoder pre-trained on simulated biokinetic curves matches a bespoke ODE-embedded decoder trained only on real data (R² ≈ 0.515 vs 0.554, within seed-level variation), so practitioners with scarce data can choose the cheaper channel.
  • Effective simulation data is specific: mixing several biokinetic ODE families with broad (about ±50%) parameter sampling beats single-family narrow sampling, and both beat a smooth but structureless random-GP control — biokinetic specificity, not smoothness, drives the transfer.
  • Pre-training beats joint mixing of simulated and real data, and its benefit saturates at a simulation-to-real ratio around 10:1, giving a concrete budget rule.
  • Architecture priors, simulation pre-training, and test-time context are additive: the best configuration (bio-structured decoder + pre-training + 30% context) reaches R² = 0.577, with about 10% of the curve the most cost-effective context level.
  • On the paper's case studies, the corrected errors correspond to specific biokinetic terms — lag dynamics and carrying capacity — indicating the prior teaches dynamic structure rather than generic smoothing.

Where Pith is reading between the lines

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

  • A cheap diagnostic follows from the paper's random-GP control: in any data-scarce domain with classical mechanistic models, pre-train on smooth but structure-free curves first; if transfer is near zero while mechanistic-curve transfer is large, the model is genuinely learning mechanism, and spending effort on a mechanistic simulator is justified.
  • The cross-organism transfer evidence (R² ≈ 0.11 off-diagonal vs ≈ 0.57 diagonal) implies the simulation prior is organism-specific; a natural next experiment is multi-organism pre-training followed by species-specific fine-tuning to test whether the transfer gap can be closed.
  • Because the study covers only batch bacterial cultivation, the substitutability claim is untested precisely where industrial data is scarcest — fed-batch, perfusion, and continuous processes; simulation pre-training may be the only viable prior there, but that extension remains open.
  • If substitutability generalizes, the field-level cost calculus shifts: engineering effort should go into curated per-organism simulator libraries (parameter ranges, ODE families) rather than bespoke ODE-embedded network design.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies how to inject biokinetic ODE knowledge into neural trajectory predictors for batch microbial growth. It compares a data-level prior (simulation pre-training of a generic decoder on synthetic ODE curves) with an architecture-level prior (ODE-embedded decoders, including the proposed BioStruct-ODE and BioStruct-ODE+Cardinal), on 11 public datasets spanning 7 bacterial species, under a shared encoder/decoder framework. The central claim is that the two channels are substitutable: an MLP pre-trained on composite-biokinetic, broad-sampled simulation reaches R²≈0.515, matching BioStruct-ODE+Cardinal trained from scratch on real data (R²=0.554), with the gap said to lie within seed-level standard deviations. The paper also reports ablations on simulation-data construction, pre-training vs joint training, context conditioning, and component-level analysis of the biokinetic architecture.

Significance. If the substitutability claim holds, the paper would provide a practically useful recipe: practitioners with scarce real data could prefer generic decoders pre-trained on simulated biokinetic curves over bespoke ODE-embedded architectures. The study is more careful than prior isolated comparisons: it uses a shared encoder across baselines, a random-GP control to isolate biokinetic specificity, component ablations (Table 8), five seeds, and public datasets. These are real strengths. However, the headline comparison is not commensurate as reported, and the evaluation population is subject to outcome-based selection, so the central empirical claim is currently unsupported as stated.

major comments (3)
  1. [§4.2, Tables 1–2] The central substitutability finding compares non-commensurate averages. Table 1 states that BioStruct-ODE+Cardinal is evaluated only on the 7 datasets carrying an explicit temperature axis, while every other baseline, including MLP, is evaluated on all 11. Table 2 says its ctx-0% scratch rows match Table 1 exactly, so the +Cardinal row (0.554±0.212) is a 7-dataset average, whereas MLP+Pretrain (0.515±0.205) is an 11-dataset average. The text in §4.2 that the gap 'lies within the seed-level standard deviations reported in Table 1' compares standard deviations from different populations and does not establish equivalence. A same-subset comparison (e.g., MLP+Pretrain on the same 7 datasets), per-dataset paired differences, and preferably an explicit equivalence test are needed. Without this, the headline substitution claim is unsupported.
  2. [Appendix A.2 (dataset-level exclusion)] The empirical claims are made on a post hoc selected set of datasets. Appendix A.2 states that three datasets on which no baseline reached a best mean R² ≥ 0.42 at size L (Yeast Y1000+, S. aureus Buchanan, S. aureus ComBase) were excluded at the dataset level, while BL21 (UCL), with best R² ≈ 0.346, was retained. Excluding datasets based on achievable R² biases the benchmark toward easier problems and can alter average rankings and the substitution comparison. Please report results on the full suite, or use a pre-specified inclusion rule, and show sensitivity to this threshold.
  3. [Appendix A.2 (with-growth filter)] The curve-level 'with growth' filter retains only curves whose per-curve Monod–Baranyi NLS fit attains R² ≥ 0.4. Because this is the same ODE family used for simulation pre-training and as the BioStruct-ODE architecture template, the evaluation population is conditional on the biokinetic prior being an adequate description of the data. This is not neutral for the comparison: it removes precisely the curves where the prior would be most likely to fail. The paper should report results on unfiltered data or provide a sensitivity analysis over the threshold; otherwise the 'consistently outperform' claim applies only to a selected subpopulation.
minor comments (5)
  1. [Appendix C.1 / Table 7 / §4] The ODE-Fit baseline is described inconsistently: §4 says it uses 'Monod or Gompertz forms', Appendix C.1 says it 'fits a Gompertz ODE per training curve', and Table 7 lists 'NLS Monod–Baranyi'. Please clarify which form is actually used.
  2. [References] The reference 'Borisyak et al., Deep set neural networks for irregular bioprocess time series, arXiv preprint arXiv:2312.00000, 2023' appears to use a placeholder arXiv ID (2312.00000 is not a real paper identifier). Please verify the citation.
  3. [Figure 2] Figure 2 reports 5-seed means without error bars or per-seed points. Given that the substitutability claim rests on differences of ~0.04–0.05 R², adding confidence intervals or per-seed values would materially strengthen the presentation.
  4. [§4.1] The phrase 'per-curve standard deviation of 1.20' for MLP is likely meant as 'standard deviation across datasets' or 'per-dataset standard deviation'; as written it is confusing.
  5. [Table 2 / §4.3] The text says 'all eight trainable baselines' in Table 2, but the table contains more rows and the +Cardinal row is on a 7-dataset subset. Please clarify the count and mark the subset for each row.

Circularity Check

0 steps flagged

No significant circularity: the two injection channels are both built from external literature ODEs, and the comparison is empirical rather than definitional.

full rationale

The paper's central claim is an empirical substitution finding: a generic MLP pre-trained on simulation curves (R2≈0.515) is compared with a bio-structured ODE decoder trained on real data (R2≈0.554). The ODE families (Monod, Baranyi, Gompertz, Rosso) are external literature models, and the simulation parameters are sampled from literature warm-start means rather than fitted to the evaluation targets. The same warm-start means are also used to initialize the BioStruct-ODE ParamHead; this is a controlled way of giving both channels the same prior, not a fitted input being renamed as a prediction. Evaluation uses public datasets not generated by the authors, so the comparison is not against the paper's own simulated data. The with-growth filter (keeping curves with per-curve Monod-Baranyi NLS fit R2 >= 0.4) selects an evaluation population that is consistent with the prior, and should be considered when interpreting transfer claims, but it is disclosed preprocessing and does not by itself make the prediction equal to the prior. The noted mismatch between MLP+pretrain on 11 datasets and BioStruct-ODE+Cardinal on 7 temperature-axis datasets is a serious internal-validity and evaluation-comparability concern, not a circularity: the two numbers may not be commensurable, but neither number is derived from the other by construction. There are no load-bearing self-citations, no imported uniqueness theorems, and no ansatz smuggled in via self-referential citation. The paper's limitation statements (e.g., illustrative RQ4 evidence, 5-seed variance limits) further support treating the main result as an empirical claim requiring more careful evaluation rather than a circular derivation.

Axiom & Free-Parameter Ledger

6 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities; the ODE families and the Baranyi lag state q are taken from the literature. Its own free parameters are the hand-chosen simulation ranges, the warm-start inheritance from literature fits, fixed loss weights, and the data-inclusion threshold. The R²≥0.4 Monod-Baranyi filter is an ad-hoc representativeness assumption that partially enforces the ODE-adequacy domain assumption. None of these is definitionally circular, but together they control both channels being compared.

free parameters (6)
  • Simulation sampling ranges (broad vs narrow) = µmax 0.05-1.50 vs 0.40-0.95 h^-1; K 0.10-1.50 vs 0.50-1.00; lag 0-8 vs 0-4 h; N0 0.01-0.05; noise σ=0.05
    Hand-chosen ranges in Appendix B / Table 6 that define the simulated pre-training distribution; the central substitutability result depends on these choices.
  • Per-organism literature warm-start means (Monod fits) = Per-organism µmax, Ks, K, kd from literature Monod fits (Appendix C)
    ParamHead biases are warm-started from these fits and the same values center the simulation sampling; these numbers were fitted to data in prior literature and inherited without re-fitting.
  • Neural correction scale ε = ε ∈ {0.01, 0.1}
    Equation (3): chosen by hand; controls the balance between biokinetic template and neural residual in all hybrid models.
  • PINN physics-loss weight λ = λ = 0.1 (no per-dataset tuning)
    Equation (5) and Appendix D.1; fixed for all datasets, and the paper states it is not tuned.
  • Sim ratio / mix-weight sweep grids = |sim|/|real| ∈ {1,3,5,10,30}; w_sim ∈ {0.5,1,2,5}
    Hand-chosen sweep values in Section 3.3; the recommended 'moderate sim ratio' recipe is read off this grid.
  • With-growth filter inclusion threshold = Keep curves with per-curve Monod-Baranyi NLS R² ≥ 0.4
    Appendix A.2: a hand-chosen inclusion threshold on fit quality to the prior ODE family; it shapes the benchmark population toward the models being compared.
axioms (4)
  • domain assumption Monod-Baranyi / Gompertz / Rosso biokinetic ODE families adequately describe the real growth dynamics in all 11 datasets
    Section 3.2 Eqs (6)-(8) and Appendix A.2: if real curves deviated from this family, both simulation pre-training and ODE-embedded decoders would lose value and the comparison would be vacuous. The with-growth filter partially enforces this assumption.
  • domain assumption Simulated curves with log-normal noise and literature±50% parameter sampling transfer to real bioreactor curves
    Section 3.3 and Appendix B: transferability of pre-training is assumed; the RQ2 random-GP control is the only direct test of what transfers.
  • domain assumption Literature-derived parameter ranges and warm-starts are valid for the specific strains and conditions in these datasets
    Appendix B/C: simulation centers and ParamHead biases use per-organism literature means; errors in these propagate to both channels.
  • ad hoc to paper Curves retained by the R² ≥ 0.4 Monod-Baranyi filter are a representative benchmark population
    Appendix A.2: this inclusion rule is introduced by the paper, and its effect on the cross-model ranking is not analyzed.

pith-pipeline@v1.3.0-alltime-deepseek · 17162 in / 20871 out tokens · 213204 ms · 2026-08-02T07:29:01.795141+00:00 · methodology

0 comments
read the original abstract

While deep learning has accelerated drug discovery, its impact on biomanufacturing has been considerably more limited. The reason is data scarcity. Bioreactor experiments are high-cost, take days to weeks, and are rarely shared in public form, leaving each research work with only a handful of experiments. The domain itself, however, is rich in prior knowledge. Biokinetic ordinary differential equation (ODE) models have described microbial growth for decades, yet how to inject this knowledge into a neural network has not been studied systematically. We present the first systematic study of how to inject this ODE knowledge into a neural network, comparing a data-level prior that pre-trains a generic decoder on simulated ODE curves against an architecture-level prior that embeds the ODE inside the decoder. Both consistently outperform no-prior baselines across 11 datasets and 7 microbial species. Our central finding is that the two are substitutable. A generic decoder pre-trained on simulation matches a fully bio-structured decoder trained on real data. Simulation pre-training therefore offers a simple, data-efficient recipe for deep learning under bioprocess data scarcity.

Figures

Figures reproduced from arXiv: 2607.20539 by Eunjung Jeon, Gyubok Lee, Hyun Woo Kim, Kyunghoon Hur, Seongjun Yang.

Figure 1
Figure 1. Figure 1: Task overview and the two biokinetic prior-injection channels compared in this paper. (a) Task: given environmental conditions e (e.g., temperature, pH, substrate, medium) and an optional set of early observations C, predict the bioreactor state trajectory yˆ(t) (cell density or an equivalent measurement). (b) Two injection channels: simulation pre-training generates synthetic curves from parameterized bio… view at source ↗
Figure 2
Figure 2. Figure 2: Effect of simulation methodology and injection mode on test R 2 , across three architectures spanning the prior-intensity spectrum (MLP, Hybrid-NeuralODE, BioStruct-ODE+Cardinal). The top row sweeps pre-training sim ratio |sim|/|real| ∈ {1, 3, 5, 10, 30}, and the bottom row sweeps joint-training sim mix weight ∈ {0.5, 1, 2, 5}. Each line depicts a sim variant (composite-biokinetic broad, single-ODE narrow,… view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the test-time context-conditioning proto￾col used in RQ3 (schematic, not measured). A fixed window of timepoints (orange band) is held out as the evaluation set across all context densities, while context observations (filled circles) are drawn only from the complementary context pool (blue band, depicted only when context is supplied). ctx-0% improves R2 by about +0.347 over MLP scratch) a… view at source ↗
Figure 4
Figure 4. Figure 4: Failure-mode comparison of the scratch and +Pretrain predictions of BioStruct-ODE+Cardinal on two hand-selected real test curves. (a) Lag phase, drawn from Listeria Buchanan 1989 at 5 ◦C: the scratch model predicts immediate growth, while +Pretrain captures the lag. (b) Stationary phase, drawn from Com￾Base Yersinia at 0 ◦C: the scratch model overshoots the plateau, while +Pretrain converges near the corre… view at source ↗

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Reference graph

Works this paper leans on

57 extracted references · 1 linked inside Pith

  1. [1]

    Annual Review of Microbiology , volume=

    The growth of bacterial cultures , author=. Annual Review of Microbiology , volume=

  2. [2]

    International Journal of Food Microbiology , volume=

    A dynamic approach to predicting bacterial growth in food , author=. International Journal of Food Microbiology , volume=

  3. [3]

    Batch process at controlled pH , author=

    A kinetic study of the lactic acid fermentation. Batch process at controlled pH , author=. Journal of Biochemical and Microbiological Technology and Engineering , volume=

  4. [4]

    Applied and Environmental Microbiology , volume=

    Modeling of the bacterial growth curve , author=. Applied and Environmental Microbiology , volume=

  5. [5]

    Journal of Theoretical Biology , volume=

    An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model , author=. Journal of Theoretical Biology , volume=

  6. [6]

    Applied and Environmental Microbiology , volume=

    Convenient model to describe the combined effects of temperature and pH on microbial growth , author=. Applied and Environmental Microbiology , volume=

  7. [7]

    Journal of Bacteriology , volume=

    Relationship between temperature and growth rate of bacterial cultures , author=. Journal of Bacteriology , volume=

  8. [8]

    Journal of Biotechnology , volume=

    The development of an industrial-scale fed-batch fermentation simulation , author=. Journal of Biotechnology , volume=

  9. [9]

    Nature Reviews Drug Discovery , volume=

    Applications of machine learning in drug discovery and development , author=. Nature Reviews Drug Discovery , volume=

  10. [10]

    Scientific Reports , volume=

    Bayesian optimization for materials design with mixed quantitative and qualitative variables , author=. Scientific Reports , volume=

  11. [11]

    Biotechnology and Bioengineering , year=

    Predicting monoclonal antibody titer using machine learning , author=. Biotechnology and Bioengineering , year=

  12. [12]

    Biotechnology and Bioengineering , year=

    Systematic comparison of machine learning methods for bioprocess monitoring , author=. Biotechnology and Bioengineering , year=

  13. [13]

    Biotechnology and Bioengineering , year=

    Online machine learning for industrial cell culture monitoring , author=. Biotechnology and Bioengineering , year=

  14. [14]

    arXiv preprint arXiv:2312.00000 , year=

    Deep Set neural networks for irregular bioprocess time series , author=. arXiv preprint arXiv:2312.00000 , year=

    arXiv

  15. [15]

    Biochemical Engineering Journal , volume=

    A general deep hybrid model for bioreactor systems , author=. Biochemical Engineering Journal , volume=

  16. [16]

    Biotechnology and Bioengineering , year=

    Hybrid LSTM model for HEK293 fed-batch , author=. Biotechnology and Bioengineering , year=

  17. [17]

    Biochemical Engineering Journal , year=

    Deep neural network estimation of Monod kinetics for industrial fermentation , author=. Biochemical Engineering Journal , year=

  18. [18]

    Biotechnology and Bioengineering , year=

    Physics-informed neural networks for CHO cell culture modeling , author=. Biotechnology and Bioengineering , year=

  19. [19]

    Computers & Chemical Engineering , year=

    PINN-based optimization of fed-batch and perfusion bioreactors , author=. Computers & Chemical Engineering , year=

  20. [20]

    coli biomass prediction , author=

    Metabolic constraint PINN for E. coli biomass prediction , author=. NeurIPS Workshop on AI for Science , year=

  21. [21]

    Biotechnology and Bioengineering , year=

    Neural ODE for CHO batch and fed-batch prediction , author=. Biotechnology and Bioengineering , year=

  22. [22]

    Chemical Engineering Science , year=

    Universal differential equations for bioprocess modeling , author=. Chemical Engineering Science , year=

  23. [23]

    Nature Communications , year=

    Sim-to-real reinforcement learning for bioreactor control , author=. Nature Communications , year=

  24. [24]

    AIChE Journal , year=

    Meta-learning foundation model for chemical reactor prediction , author=. AIChE Journal , year=

  25. [25]

    NeurIPS , year=

    Neural ordinary differential equations , author=. NeurIPS , year=

  26. [26]

    ICML , year=

    Conditional neural processes , author=. ICML , year=

  27. [27]

    NeurIPS , year=

    Deep sets , author=. NeurIPS , year=

  28. [28]

    Nature , volume=

    Highly accurate protein structure prediction with AlphaFold , author=. Nature , volume=

  29. [29]

    and others , journal=

    Bonanni, F. and others , journal=. A predictive deep learning framework for

  30. [30]

    Computers & Chemical Engineering , year=

    Causal convolutional autoencoders for bioprocess trajectory prediction , author=. Computers & Chemical Engineering , year=

  31. [31]

    Journal of Applied Bacteriology , volume=

    Indices for performance evaluation of predictive models in food microbiology , author=. Journal of Applied Bacteriology , volume=

  32. [32]

    and others , journal=

    Katipoglu-Yazan, T. and others , journal=. A high-throughput dataset of

  33. [33]

    and others , journal=

    Faure, L. and others , journal=. Compositional growth response of

  34. [34]

    Buchanan, R. L. and Phillips, J. G. , journal=. Predictive models for the effects of temperature, p

  35. [35]

    Zaika, L. L. and others , journal=. Modeling the growth of

  36. [36]

    Eifert, J. D. and others , journal=. Growth of

  37. [37]

    ComBase: a combined database of microbial growth and survival responses , author=

  38. [38]

    Computers & Chemical Engineering , year=

    Reinforcement learning for batch bioprocess optimization , author=. Computers & Chemical Engineering , year=

  39. [39]

    Biochemical Engineering Journal , year=

    Process control for industrial fermentation: a review of recent advances , author=. Biochemical Engineering Journal , year=

  40. [40]

    Bioresource Technology , year=

    Physics-informed neural networks for microbial growth modeling , author=. Bioresource Technology , year=

  41. [41]

    and others , journal=

    Riezzo, R. and others , journal=. Hybrid neural--mechanistic models for

  42. [42]

    Computers & Chemical Engineering , year=

    The development of an industrial-scale fed-batch fermentation simulation , author=. Computers & Chemical Engineering , year=

  43. [43]

    Cell , volume=

    How to build the virtual cell with artificial intelligence: priorities and opportunities , author=. Cell , volume=

  44. [44]

    Biochemical Engineering Journal , volume=

    Machine learning for biochemical engineering: A review , author=. Biochemical Engineering Journal , volume=

  45. [45]

    Trends in Biotechnology , year=

    Machine learning in bioprocess development: From promise to practice , author=. Trends in Biotechnology , year=

  46. [46]

    Benchmarking biopharmaceutical process development and manufacturing cost contributions to

    Farid, Suzanne S and Baron, Maria and Stamatis, Christos and Nie, Wendy and Coffman, Jonathan , journal=. Benchmarking biopharmaceutical process development and manufacturing cost contributions to

  47. [47]

    Biotechnology and Bioengineering , year=

    Transfer Learning Approaches in Bioprocess Engineering: Opportunities and Challenges , author=. Biotechnology and Bioengineering , year=

  48. [48]

    Trends in Biotechnology , year=

    A snapshot of biomanufacturing and the need for enabling research infrastructure , author=. Trends in Biotechnology , year=

  49. [49]

    arXiv preprint arXiv:2310.09991 , year=

    Applications of Machine Learning in Biopharmaceutical Process Development and Manufacturing: Current Trends, Challenges, and Opportunities , author=. arXiv preprint arXiv:2310.09991 , year=

    Pith/arXiv arXiv

  50. [50]

    Nature Reviews Physics , volume=

    Physics-informed machine learning , author=. Nature Reviews Physics , volume=

  51. [51]

    International Conference on Learning Representations (ICLR) , year=

    Hollmann, Noah and M. International Conference on Learning Representations (ICLR) , year=

  52. [52]

    Cell , volume=

    A Deep Learning Approach to Antibiotic Discovery , author=. Cell , volume=

  53. [53]

    and Bambrick, Joshua and others , journal=

    Abramson, Josh and Adler, Jonas and Dunger, Jack and Evans, Richard and Green, Tim and Pritzel, Alexander and Ronneberger, Olaf and Willmore, Lindsay and Ballard, Andrew J. and Bambrick, Joshua and others , journal=. Accurate structure prediction of biomolecular interactions with

  54. [54]

    Science , volume=

    Evolutionary-scale prediction of atomic-level protein structure , author=. Science , volume=

  55. [55]

    and Juergens, David and Bennett, Nathaniel R

    Watson, Joseph L. and Juergens, David and Bennett, Nathaniel R. and Trippe, Brian L. and Yim, Jason and Eisenach, Helen E. and Ahern, Woody and Borst, Andrew J. and Ragotte, Robert J. and Milles, Lukas F. and others , journal=. De novo design of protein structure and function with

  56. [56]

    Journal of Computational Physics , volume=

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations , author=. Journal of Computational Physics , volume=

  57. [57]

    Nature Machine Intelligence , volume=

    Drug discovery with explainable artificial intelligence , author=. Nature Machine Intelligence , volume=