pith. sign in

arxiv: 2604.03354 · v1 · submitted 2026-04-03 · 🧮 math.OC · stat.CO

Optimal Experimental Design using Eigenvalue-Based Criteria with Pyomo.DoE

Daniel J. Laky , Shammah Lilonfe , Shawn B. Martin , Katherine A. Klise , Bethany L. Nicholson , John D. Siirola , Alexander W. Dowling This is my paper

Pith reviewed 2026-05-13 18:15 UTC · model grok-4.3

classification 🧮 math.OC stat.CO
keywords optimal experimental designPyomoE-optimalityeigenvalue criteriaequation-oriented optimizationdigital twinsuncertainty quantification
0
0 comments X

The pith

Pyomo.DoE now supports E-optimality and ME-optimality criteria inside equation-oriented optimization problems.

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

Digital twins depend on high-quality data, which makes efficient model-based design of experiments essential for high-fidelity first-principles models. Pyomo.DoE already handles optimal experimental design in equation-oriented frameworks, but it could not directly incorporate linear algebra operations such as matrix inversion and eigenvalue computation. The paper adds callback mechanisms that let the solver evaluate eigenvalue-based metrics during optimization. This change makes it possible to optimize directly for the minimum eigenvalue of the information matrix or for the condition number of that matrix. The work also introduces a modeling abstraction that reduces effort when setting up intrusive uncertainty quantification.

Core claim

This work extends Pyomo.DoE with callback-based capabilities that enable rigorous computation of eigenvalue-based design metrics, including minimum eigenvalue optimality (E-optimality) and condition number optimality (ME-optimality), within equation-oriented optimization frameworks. These additions allow experimental design to focus directly on poorly informed or numerically problematic parameter directions. We also present a new experiment-creation modeling abstraction for intrusive uncertainty quantification in Pyomo that reduces user modeling effort by aligning model and software abstractions across the digital twin workflow.

What carries the argument

Callback interface that embeds matrix inversion and eigenvalue decomposition operations into the equation-oriented optimization problem.

If this is right

  • Designs can now maximize the smallest eigenvalue of the Fisher information matrix to improve the worst-case parameter uncertainty.
  • Designs can minimize the condition number of the information matrix to reduce numerical sensitivity in parameter estimation.
  • The new abstraction lets users build uncertainty-quantification workflows with less manual model reformulation.
  • Eigenvalue criteria become available for any first-principles model already expressible in Pyomo.

Where Pith is reading between the lines

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

  • The same callback pattern could be reused to embed other linear-algebra diagnostics, such as singular-value thresholds, without changing the core modeling language.
  • Users working on large-scale digital twins might now iterate between design and calibration steps more tightly because the optimality metric is evaluated inside the same optimization run.
  • The approach may encourage development of hybrid criteria that combine eigenvalue information with traditional A- or D-optimality in a single problem.

Load-bearing premise

The callback mechanism for eigenvalue and matrix operations integrates into the equation-oriented solver without numerical instability or prohibitive computational cost.

What would settle it

Apply the extended Pyomo.DoE to a small linear parameter estimation problem whose E-optimal design is known analytically and verify that the computed design matches the known solution while the solver converges normally.

Figures

Figures reproduced from arXiv: 2604.03354 by Alexander W. Dowling, Bethany L. Nicholson, Daniel J. Laky, John D. Siirola, Katherine A. Klise, Shammah Lilonfe, Shawn B. Martin.

Figure 1
Figure 1. Figure 1: General workflow for model building and identification using Pyomo, [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Parallelism between the physical experiment that a scientist performs with the [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example connecting the elements of a small model (in Case Study 1, Eq. 32) to [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Objective function values, Ψ (D-, E-, ME-, A-opt), and related values (maximum eigenvalue and trace of the FIM) plotted as a function of the experimental design decision, sample time (days). The star represents the optimal point found for each criterion using Pyomo.DoE with a Grey Box objective [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Data for the sine wave (left) and step test (right) experiments using the TCLab [PITH_FULL_IMAGE:figures/full_fig_p028_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Pairwise covariance of parameters with preliminary data only (a) and additional [PITH_FULL_IMAGE:figures/full_fig_p029_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Optimal profiles for D-optimality (top left), A-optimality (top right), ME [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Proposed three-stage membrane cascade to recover critical minerals and ma [PITH_FULL_IMAGE:figures/full_fig_p034_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Pairwise covariance of parameters with preliminary data only (a) and additional [PITH_FULL_IMAGE:figures/full_fig_p039_9.png] view at source ↗
read the original abstract

Digital twins require high-quality data to achieve predictive capability, but time and resource limitations make efficient experiment design essential. Model-based design of experiments can address this challenge, especially when coupled with equation-oriented optimization and first-principles models. Pyomo.DoE is a software package for optimal experimental design of high-fidelity, equation-oriented models; however, embedding linear algebra operations such as matrix inversion and eigenvalue computation within these optimization problems remains difficult. This work extends Pyomo.DoE with callback-based capabilities that enable rigorous computation of eigenvalue-based design metrics, including minimum eigenvalue optimality (E-optimality) and condition number optimality (ME-optimality), within equation-oriented optimization frameworks. These additions allow experimental design to focus directly on poorly informed or numerically problematic parameter directions. We also present a new experiment-creation modeling abstraction for intrusive uncertainty quantification in Pyomo that reduces user modeling effort by aligning model and software abstractions across the digital twin workflow. In addition, a brief tutorial on experimental design metrics is provided in the methodology and supplementary information. Overall, this work expands the range of practical optimal design criteria available in Pyomo.DoE and improves the workflow for building and refining high-value digital twins.

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

0 major / 1 minor

Summary. The manuscript extends Pyomo.DoE with callback-based mechanisms to incorporate eigenvalue-based optimality criteria (E-optimality via minimum eigenvalue and ME-optimality via condition number) directly into equation-oriented optimization models. It also introduces a new experiment-creation modeling abstraction to support intrusive uncertainty quantification and provides a tutorial on experimental design metrics for digital-twin workflows.

Significance. If the callback integration functions as described, the work meaningfully expands the set of usable design criteria in Pyomo for high-fidelity, first-principles models, allowing direct optimization over poorly conditioned parameter directions. The new abstraction reduces modeling overhead and aligns software and model structures, which is a practical contribution for users building digital twins. The engineering reuse of existing linear-algebra primitives inside the optimization framework is a clear strength.

minor comments (1)
  1. [Abstract] The abstract states that the callbacks enable 'rigorous computation,' yet the manuscript text does not include numerical benchmarks, error analysis, or solver-compatibility tests that would confirm stability and cost for realistic model sizes.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive review and recommendation to accept the manuscript. We appreciate the recognition of the callback-based support for E- and ME-optimality criteria as well as the new experiment-creation abstraction for uncertainty quantification in high-fidelity models.

Circularity Check

0 steps flagged

No significant circularity; software extension of existing primitives

full rationale

The manuscript presents an engineering extension to Pyomo.DoE that adds callback support for eigenvalue-based optimality criteria (E- and ME-optimality) inside equation-oriented models. No load-bearing mathematical derivation is claimed; the work consists of new modeling abstractions, callback implementations, and a tutorial on standard design metrics. All steps rely on standard linear-algebra operations and Pyomo primitives rather than any self-referential fit, self-citation chain, or ansatz that reduces to the target result by construction. The central claim remains externally verifiable through code execution and does not loop back to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard assumptions of model-based optimal experimental design and the numerical stability of callbacks inside Pyomo solvers; no new free parameters or invented entities are introduced.

axioms (2)
  • domain assumption The information matrix derived from the model is positive semi-definite and its eigenvalues meaningfully quantify parameter identifiability.
    Invoked when defining E-optimality and ME-optimality criteria.
  • domain assumption Callback functions for linear-algebra operations can be evaluated reliably inside the equation-oriented optimization loop.
    Central to the claimed extension.

pith-pipeline@v0.9.0 · 5536 in / 1282 out tokens · 32390 ms · 2026-05-13T18:15:40.012470+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

86 extracted references · 86 canonical work pages

  1. [1]

    The Na- tional Academies Press, Washington, DC, 2024.doi:10.17226/26894

    National Academy of Engineering, National Academies of Sciences, Engineering, and Medicine, Foundational Research Gaps and Future Directions for Digital Twins, The National Academies Press, Washing- ton, DC, 2024.doi:10.17226/26894. URLhttps://nap.nationalacademies.org/catalog/26894/ foundational-research-gaps-and-future-directions-for- digital-twins

    work page doi:10.17226/26894 2024

  2. [2]

    rep., AIAA, AIA (2020)

    AIAA Digital Engineering Integration Committee, Digital twin: Defini- tion & value, Tech. rep., AIAA, AIA (2020)

    work page 2020

  3. [3]

    Macías, D

    A. Macías, D. Muñoz, E. Navarro, P. González, Data fabric and digital twins: An integrated approach for data fusion design and evaluation of pervasive systems, Information Fusion 103 (2024) 102139. doi:https://doi.org/10.1016/j.inffus.2023.102139. URLhttps://www.sciencedirect.com/science/article/pii/ S1566253523004554

    work page doi:10.1016/j.inffus.2023.102139 2024

  4. [4]

    J. Yan, Q. Lu, N. Li, M. Pitt, Developing data requirements for city-level digital twins: Stakeholder perspective, Journal of Management in Engineering 41 (2) (2025) 04024068.arXiv: https://ascelibrary.org/doi/pdf/10.1061/JMENEA.MEENG-6434, doi:10.1061/JMENEA.MEENG-6434. 46 URLhttps://ascelibrary.org/doi/abs/10.1061/JMENEA.MEENG- 6434

    work page doi:10.1061/jmenea.meeng-6434 2025

  5. [5]

    R. A. Fisher, R. A. Fisher, The design of experiments, Springer, 1971

    work page 1971

  6. [6]

    Nature Synthesis , author =

    M. Abolhasani, E. Kumacheva, The rise of self-driving labs in chem- ical and materials sciences, Nature Synthesis 2 (2023) 483–492.doi: 10.1038/s44160-022-00231-0

    work page doi:10.1038/s44160-022-00231-0 2023

  7. [7]

    G. Tom, S. P. Schmid, S. G. Baird, Y. Cao, K. Darvish, H. Hao, S. Lo, S. Pablo-García, E. M. Rajaonson, M. Skreta, N. Yoshikawa, S. Corapi, G. D. Akkoc, F. Strieth-Kalthoff, M. Seifrid, A. Aspuru-Guzik, Self-driving laboratories for chemistry and mate- rials science, Chemical Reviews 124 (16) (2024) 9633–9732, pMID: 39137296.arXiv:https://doi.org/10.1021/...

    work page doi:10.1021/acs.chemrev.4c00055 2024

  8. [8]

    Accounts of Chemical Research , author =

    M. Seifrid, R. Pollice, A. Aguilar-Granda, Z. Morgan Chan, K. Hotta, C. T. Ser, J. Vestfrid, T. C. Wu, A. Aspuru-Guzik, Autonomous chemical experiments: Challenges and perspectives on establish- ing a self-driving lab, Accounts of Chemical Research 55 (17) (2022) 2454–2466, pMID: 35948428.arXiv:https://doi.org/10.1021/ acs.accounts.2c00220,doi:10.1021/acs...

    work page doi:10.1021/acs.accounts.2c00220 2022

  9. [9]

    Quaglio, C

    M. Quaglio, C. Waldron, A. Pankajakshan, E. Cao, A. Gavriilidis, E. S. Fraga, F. Galvanin, An online reparametrisation approach for robust parameter estimation in automated model identification platforms, Computers & Chemical Engineering 124 (2019) 270–284. doi:https://doi.org/10.1016/j.compchemeng.2019.01.010. URLhttps://www.sciencedirect.com/science/art...

    work page doi:10.1016/j.compchemeng.2019.01.010 2019

  10. [10]

    Waldron, A

    C. Waldron, A. Pankajakshan, M. Quaglio, E. Cao, F. Galvanin, A. Gavriilidis, Model-based design of transient flow experiments for the identification of kinetic parameters, React. Chem. Eng. 5 (2020) 112– 123.doi:10.1039/C9RE00342H. URLhttp://dx.doi.org/10.1039/C9RE00342H 47

    work page doi:10.1039/c9re00342h 2020

  11. [11]

    Agunloye, P

    E. Agunloye, P. Petsagkourakis, M. Yusuf, R. Labes, T. Chamberlain, F. L. Muller, R. A. Bourne, F. Galvanin, Automated kinetic model iden- tification via cloud services using model-based design of experiments, React. Chem. Eng. 9 (2024) 1859–1876.doi:10.1039/D4RE00047A. URLhttp://dx.doi.org/10.1039/D4RE00047A

    work page doi:10.1039/d4re00047a 2024

  12. [12]

    F. M. Gomes, F. M. Pereira, A. F. Silva, M. B. Silva, Multiple response optimization: Analysis of genetic programming for symbolic regression and assessment of desirability functions, Knowledge-Based Systems 179 (2019) 21–33.doi:https://doi.org/10.1016/j.knosys.2019.05.002. URLhttps://www.sciencedirect.com/science/article/pii/ S0950705119302096

    work page doi:10.1016/j.knosys.2019.05.002 2019

  13. [13]

    B. Can, C. Heavey, Comparison of experimental designs for simulation-based symbolic regression of manufacturing systems, Computers & Industrial Engineering 61 (3) (2011) 447–462. doi:https://doi.org/10.1016/j.cie.2011.03.012. URLhttps://www.sciencedirect.com/science/article/pii/ S036083521100088X

    work page doi:10.1016/j.cie.2011.03.012 2011

  14. [14]

    Castillo, K

    F. Castillo, K. Marshall, J. Green, A. Kordon, A methodology for com- bining symbolic regression and design of experiments to improve empiri- cal model building, in: E. Cantú-Paz, J. A. Foster, K. Deb, L. D. Davis, R. Roy, U.-M. O’Reilly, H.-G. Beyer, R. Standish, G. Kendall, S. Wil- son, M. Harman, J. Wegener, D. Dasgupta, M. A. Potter, A. C. Schultz, K....

    work page 2003

  15. [15]

    A. W. Rogers, A. Lane, C. Mendoza, S. Watson, A. Kowalski, P. Mar- tin, D. Zhang, Integrating knowledge-guided symbolic regression and model-based design of experiments to accelerate process flow diagram development, IFAC-PapersOnLine 58 (14) (2024) 127–132, 12th IFAC Symposium on Advanced Control of Chemical Processes ADCHEM 2024.doi:https://doi.org/10.1...

    work page doi:10.1016/j.ifacol.2024.08.325 2024

  16. [16]

    Saidi, M

    M. Saidi, M. A. R. Fallah, N. Nemati, M. R. Rahimpour, Model-based design of experiments for kinetic study of anisole upgrading process 48 over pt/γal2o3: Model development and optimization by application of response surface methodology and artificial neural network, Chemical Product and Process Modeling 12 (3) (2017) 20160071 [cited 2025-01- 14].doi:doi:...

    work page doi:10.1515/cppm-2016-0071 2017

  17. [17]

    Heinisch, Y

    J. Heinisch, Y. Lockner, C. Hopmann, Comparison of design of experiment methods for modeling injection molding experiments using artificial neural networks, Journal of Manufacturing Processes 61 (2021) 357–368.doi:https://doi.org/10.1016/j.jmapro.2020.11.011. URLhttps://www.sciencedirect.com/science/article/pii/ S1526612520307982

    work page doi:10.1016/j.jmapro.2020.11.011 2021

  18. [18]

    Sangoi, M

    E. Sangoi, M. Quaglio, F. Bezzo, F. Galvanin, Optimal design of experiments based on artificial neural network classifiers for fast kinetic model recognition, in: Y. Yamashita, M. Kano (Eds.), 14th International Symposium on Process Systems Engineering, Vol. 49 of Computer Aided Chemical Engineering, Elsevier, 2022, pp. 817–822. doi:https://doi.org/10.101...

    work page doi:10.1016/b978-0-323-85159-6.50136-6 2022

  19. [19]

    In: 2020 American Control Conference (ACC), pp

    M. Imani, S. F. Ghoreishi, Bayesian optimization objective-based ex- perimental design, in: 2020 American Control Conference (ACC), 2020, pp. 3405–3411.doi:10.23919/ACC45564.2020.9147824

    work page doi:10.23919/acc45564.2020.9147824 2020

  20. [20]

    Imani, S

    M. Imani, S. F. Ghoreishi, Graph-based bayesian optimization for large- scale objective-based experimental design, IEEE Transactions on Neu- ral Networks and Learning Systems 33 (10) (2022) 5913–5925.doi: 10.1109/TNNLS.2021.3071958

    work page doi:10.1109/tnnls.2021.3071958 2022

  21. [21]

    X. Cao, X. Chen, L. T. Biegler, Integrated bayesian parameter estimation with model-based design of experiments for dynamic processes, AIChE Journal 70 (7) (2024) e18418.arXiv:https: //aiche.onlinelibrary.wiley.com/doi/pdf/10.1002/aic.18418, doi:https://doi.org/10.1002/aic.18418. URLhttps://aiche.onlinelibrary.wiley.com/doi/abs/10.1002/ aic.18418 49

    work page doi:10.1002/aic.18418 2024

  22. [22]

    Tulsyan, J

    A. Tulsyan, J. Fraser Forbes, B. Huang, Designing priors for ro- bust bayesian optimal experimental design, Journal of Process Control 22 (2) (2012) 450–462.doi:https://doi.org/10.1016/ j.jprocont.2011.12.004. URLhttps://www.sciencedirect.com/science/article/pii/ S0959152411002411

    work page 2012

  23. [23]

    B. Lei, T. Q. Kirk, A. Bhattacharya, D. Pati, X. Qian, R. Arroyave, B. K. Mallick, Bayesian optimization with adaptive surrogate models for automated experimental design, npj Computational Materials 7 (194) (2021)

    work page 2021

  24. [24]

    Attia, S

    A. Attia, S. Leyffer, T. S. Munson, Stochastic learning approach for binary optimization: Application to bayesian optimal design of exper- iments, SIAM Journal on Scientific Computing 44 (2) (2022) B395– B427.arXiv:https://doi.org/10.1137/21M1404363,doi:10.1137/ 21M1404363. URLhttps://doi.org/10.1137/21M1404363

    work page doi:10.1137/21m1404363 2022

  25. [25]

    Ziyao Guo, Kai Wang, George Cazenavette, Hui Li, Kaipeng Zhang, and Yang You

    S. Greenhill, S. Rana, S. Gupta, P. Vellanki, S. Venkatesh, Bayesian optimization for adaptive experimental design: A review, IEEE Access 8 (2020) 13937–13948.doi:10.1109/ACCESS.2020.2966228

    work page doi:10.1109/access.2020.2966228 2020

  26. [26]

    Franceschini, S

    G. Franceschini, S. Macchietto, Model-based design of experiments for parameter precision: State of the art, Chemical Engineering Science 63 (19) (2008) 4846–4872

    work page 2008

  27. [27]

    Galvanin, M

    F. Galvanin, M. Barolo, F. Bezzo, S. Macchietto, A backoff strat- egy for model-based experiment design under parametric uncer- tainty, AIChE Journal 56 (8) (2010) 2088–2102.arXiv:https: //aiche.onlinelibrary.wiley.com/doi/pdf/10.1002/aic.12138, doi:https://doi.org/10.1002/aic.12138. URLhttps://aiche.onlinelibrary.wiley.com/doi/abs/10.1002/ aic.12138

    work page doi:10.1002/aic.12138 2010

  28. [28]

    Galvanin, E

    F. Galvanin, E. Cao, N. Al-Rifai, A. Gavriilidis, V. Dua, A joint model-based experimental design approach for the iden- tification of kinetic models in continuous flow laboratory re- actors, Computers & Chemical Engineering 95 (2016) 202–215. doi:https://doi.org/10.1016/j.compchemeng.2016.05.009. 50 URLhttps://www.sciencedirect.com/science/article/pii/ S...

    work page doi:10.1016/j.compchemeng.2016.05.009 2016

  29. [29]

    Geremia, S

    M. Geremia, S. Macchietto, F. Bezzo, A review on model-based design of experiments for parameter precision – open challenges, trends and future perspectives, Chemical Engineering Science 319 (2026) 122347. doi:https://doi.org/10.1016/j.ces.2025.122347. URLhttps://www.sciencedirect.com/science/article/pii/ S0009250925011686

    work page doi:10.1016/j.ces.2025.122347 2026

  30. [30]

    Chowdhary, S

    A. Chowdhary, S. E. Ahmed, A. Attia, Pyoed: An extensible suite for data assimilation and model-constrained optimal design of experiments, ACM Trans. Math. Softw. 50 (2) (Jun. 2024).doi:10.1145/3653071. URLhttps://doi.org/10.1145/3653071

    work page doi:10.1145/3653071 2024

  31. [31]

    Lee, pydoe: The experimental design package for python

    A. Lee, pydoe: The experimental design package for python. URLhttps://pythonhosted.org/pyDOE/

    work page

  32. [32]

    S. Z. B. Tabrizi, E. Barbera, W. R. L. da Silva, F. Bezzo, A python/numpy-based package to support model discrimination and identification, Systems and Control Transactions (2025) 1282–1287

    work page 2025

  33. [33]

    Foracchia, A

    M. Foracchia, A. Hooker, P. Vicini, R. Alfredo, poped, a software for optimal experiment design in population kinetics, Computer Methods and Programs in Biomedicine 74 (1) (2022) 29–46.doi:10.1016/S0169- 2607(03)00073-7

    work page doi:10.1016/s0169- 2022

  34. [34]

    Butler, B

    D. Butler, B. Cullis, On model based design of comparative experiments in r, National Institute for Applied Statistics Research Australia, Uni- versity of Wollongong: Wollongong, NSW, Australia (2022)

    work page 2022

  35. [35]

    D. T. Agi, K. D. Jones, M. J. Watson, H. G. Lynch, M. Dougher, X. Chen, M. N. Carlozo, A. W. Dowling, Com- putational toolkits for model-based design and optimization, Current Opinion in Chemical Engineering 43 (2024) 100994. doi:https://doi.org/10.1016/j.coche.2023.100994. URLhttps://www.sciencedirect.com/science/article/pii/ S2211339823000989 51

    work page doi:10.1016/j.coche.2023.100994 2024

  36. [36]

    P. S. E. Ltd., gPROMS Advanced User Guide, Process Systems Enter- prise Ltd., London, United Kingdom, 2025. URLhttp://www.psenterprise.com/

    work page 2025

  37. [37]

    M. L. Bynum, G. A. Hackebeil, W. E. Hart, C. D. Laird, B. L. Nichol- son, J. D. Siirola, J.-P. Watson, D. L. Woodruff, Pyomo–optimization modeling in python, 3rd Edition, Vol. 67, Springer Science & Business Media, 2021

    work page 2021

  38. [38]

    J. Wang, A. W. Dowling, Pyomo. doe: An open-source package for model-based design of experiments in python, AIChE Journal 68 (12) (2022) e17813

    work page 2022

  39. [39]

    Nicholson, J

    B. Nicholson, J. D. Siirola, J.-P. Watson, V. M. Zavala, L. T. Biegler, pyomo. dae: A modeling and automatic discretization framework for op- timization with differential and algebraic equations, Mathematical Pro- gramming Computation 10 (2) (2018) 187–223

    work page 2018

  40. [40]

    S. P. Boyd, L. Vandenberghe, Convex optimization, Cambridge univer- sity press, 2004

    work page 2004

  41. [41]

    D. C. Montgomery, Design and analysis of experiments, John wiley & sons, 2017

    work page 2017

  42. [42]

    B. P. M. Duarte, A. C. Atkinson, J. F. O. Granjo, N. M. C. O. and, Optimal design of experiments for implicit models, Journal of the American Statistical Association 117 (539) (2022) 1424– 1437.arXiv:https://doi.org/10.1080/01621459.2020.1862670,doi: 10.1080/01621459.2020.1862670. URLhttps://doi.org/10.1080/01621459.2020.1862670

    work page doi:10.1080/01621459.2020.1862670 2022

  43. [43]

    Ruffini, Riflessioni intorno alla soluzione delle equazioni algebraiche generali, Società tipografica, 1813

    P. Ruffini, Riflessioni intorno alla soluzione delle equazioni algebraiche generali, Società tipografica, 1813

    work page

  44. [44]

    N. H. Abel, Démonstration de l’impossibilité de la résolution algébrique des équations générales qui passent le quatrieme degré, Journal für die reine und angewandte Mathematik 1 (1826) 65–96

    work page

  45. [45]

    Telen, N

    D. Telen, N. Van Riet, F. Logist, J. Van Impe, A differentiable reformulation for e-optimal design of experiments in nonlinear dynamic biosystems, Mathematical Biosciences 264 (2015) 1–7. 52 doi:https://doi.org/10.1016/j.mbs.2015.02.006. URLhttps://www.sciencedirect.com/science/article/pii/ S0025556415000401

    work page doi:10.1016/j.mbs.2015.02.006 2015

  46. [46]

    J. J. Ye, J. Zhou, W. Z. and, Computing a-optimal and e-optimal designs for regression models via semidefinite programming, Commu- nications in Statistics - Simulation and Computation 46 (3) (2017) 2011–2024.arXiv:https://doi.org/10.1080/03610918.2015.1030414, doi:10.1080/03610918.2015.1030414. URLhttps://doi.org/10.1080/03610918.2015.1030414

    work page doi:10.1080/03610918.2015.1030414 2017

  47. [47]

    J. S. Rodriguez, C. D. Laird, V. M. Zavala, Scalable pre- conditioning of block-structured linear algebra systems using admm, Computers & Chemical Engineering 133 (2020) 106478. doi:https://doi.org/10.1016/j.compchemeng.2019.06.003. URLhttps://www.sciencedirect.com/science/article/pii/ S0098135419304454

    work page doi:10.1016/j.compchemeng.2019.06.003 2020

  48. [48]

    D. J. Laky, D. Casas-Orozco, C. D. Laird, G. V. Reklaitis, Z. K. Nagy, Simulation–optimization framework for the digital design of pharma- ceutical processes using pyomo and pharmapy, Industrial & Engineer- ing Chemistry Research 61 (43) (2022) 16128–16140.arXiv:https:// doi.org/10.1021/acs.iecr.2c01636,doi:10.1021/acs.iecr.2c01636. URLhttps://doi.org/10....

    work page doi:10.1021/acs.iecr.2c01636 2022

  49. [49]

    J. Wang, Z. Peng, R. Hughes, D. Bhattacharyya, D. E. Bernal Neira, A. W. Dowling, Measure this, not that: Optimizing the cost and model-based information content of measure- ments, Computers & Chemical Engineering 189 (2024) 108786. doi:https://doi.org/10.1016/j.compchemeng.2024.108786. URLhttps://www.sciencedirect.com/science/article/pii/ S0098135424002047

    work page doi:10.1016/j.compchemeng.2024.108786 2024

  50. [50]

    Lynch, A

    H. Lynch, A. Bjarnason, D. Laky, C. Brown, A. Dowling, Optimizing batch crystallization with model-based design of experiments, Systems and Control Transactions 3 (2024) 308–315.doi:https://doi.org/ 10.69997/sct.152239

    work page doi:10.69997/sct.152239 2024

  51. [51]

    Wächter, L

    A. Wächter, L. T. Biegler, On the implementation of an interior-point 53 filter line-search algorithm for large-scale nonlinear programming, Math- ematical programming 106 (2006) 25–57

    work page 2006

  52. [52]

    A. S. Drud, Conopt—a large-scale grg code, ORSA Journal on comput- ing 6 (2) (1994) 207–216

    work page 1994

  53. [53]

    R. H. Byrd, J. Nocedal, R. A. Waltz, K nitro: An integrated package for nonlinear optimization, Large-scale nonlinear optimization (2006) 35–59

    work page 2006

  54. [54]

    N. V. Sahinidis, Baron: A general purpose global optimization software package, Journal of global optimization 8 (1996) 201–205

    work page 1996

  55. [55]

    Bard, Nonlinear parameter estimation, Vol

    Y. Bard, Nonlinear parameter estimation, Vol. 1209, Academic press New York, 1974

    work page 1974

  56. [56]

    C. R. Rao, et al., Information and the accuracy attainable in the esti- mation of statistical parameters, Bull. Calcutta Math. Soc 37 (3) (1945) 81–91

    work page 1945

  57. [57]

    Nielsen, Cramér-Rao Lower Bound and Information Geometry, Hin- dustan Book Agency, Gurgaon, 2013, pp

    F. Nielsen, Cramér-Rao Lower Bound and Information Geometry, Hin- dustan Book Agency, Gurgaon, 2013, pp. 18–37.doi:10.1007/978-93- 86279-56-9_2. URLhttps://doi.org/10.1007/978-93-86279-56-9_2

    work page doi:10.1007/978-93- 2013

  58. [58]

    C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Vir- tanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del Río, M. Wiebe, P. Peterson, P. Gérard-Marchant, K. Shep- pard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, T. E. Oliphant, Array programmin...

    work page doi:10.1038/s41586-020-2649-2 2020

  59. [59]

    URLhttps://cyipopt.readthedocs.io/en/stable/

    cyipopt developers, cyipopt: Python wrapper for the ipopt optimization package, written in cython. URLhttps://cyipopt.readthedocs.io/en/stable/

    work page

  60. [60]

    D. M. Bates, D. G. Watts, Nonlinear regression analysis and its appli- cations, Vol. 2, Wiley New York, 1988. 54

    work page 1988

  61. [61]

    Marske, Biochemical oxygen demand data interpretation using sum of squares surface, Master’s thesis, University of Wisconsin-Madison (1967)

    work page 1967

  62. [62]

    R. N. GUTENKUNST, F. P. CASEY, J. J. WATERFALL, C. R. MYERS, J. P. SETHNA, Extracting falsifiable predictions from sloppy models, Annals of the New York Academy of Sciences 1115 (1) (2007) 203–211.arXiv:https://nyaspubs.onlinelibrary.wiley.com/ doi/pdf/10.1196/annals.1407.003,doi:https://doi.org/10.1196/ annals.1407.003. URLhttps://nyaspubs.onlinelibrary....

    work page doi:10.1196/annals.1407.003 2007

  63. [63]

    P. M. Oliveira, J. D. Hedengren, An apmonitor temperature lab pid con- trol experiment for undergraduate students, in: 2019 24th IEEE Inter- national Conference on Emerging Technologies and Factory Automation (ETFA), 2019, pp. 790–797.doi:10.1109/ETFA.2019.8869247

    work page doi:10.1109/etfa.2019.8869247 2019

  64. [64]

    J. Park, R. A. Martin, J. D. Kelly, J. D. Hedengren, Bench- mark temperature microcontroller for process dynamics and control, Computers & Chemical Engineering 135 (2020) 106736. doi:https://doi.org/10.1016/j.compchemeng.2020.106736. URLhttps://www.sciencedirect.com/science/article/pii/ S0098135419310129

    work page doi:10.1016/j.compchemeng.2020.106736 2020

  65. [65]

    Hedengren, J

    J. Hedengren, J. Kantor, Computer programming and process control take-home lab, Computer (2020)

    work page 2020

  66. [66]

    de Moura Oliveira, J

    P. de Moura Oliveira, J. D. Hedengren, J. Rossiter, Introducing digital controllers to undergraduate students using the tclab arduino kit, IFAC-PapersOnLine 53 (2) (2020) 17524–17529, 21st IFAC World Congress.doi:https://doi.org/10.1016/j.ifacol.2020.12.2662. URLhttps://www.sciencedirect.com/science/article/pii/ S2405896320334224

    work page doi:10.1016/j.ifacol.2020.12.2662 2020

  67. [67]

    A. W. Dowling, M. Dougher, M. J. Watson, H. G. Lynch, Z. Lu, D. J. Laky, Teaching digital twins in process control using the temperature control lab, Systems and Control Transactions (2025) 2215–2221. 55

    work page 2025

  68. [68]

    T.-Y. Kim, T. Gould, S. Bennet, F. Briens, A. Dasgupta, P. Gonzales, A. Gouy, G. Kamiya, M. Karpiniski, J. Lagelee, et al., The role of crit- ical minerals in clean energy transitions, International Energy Agency: Washington, DC, USA (2021) 70–71

    work page 2021

  69. [69]

    Gaustad, E

    G. Gaustad, E. Williams, A. Leader, Rare earth metals from secondary sources: Review of potential supply from waste and byproducts, Re- sources, Conservation and Recycling 167 (2021) 105213

    work page 2021

  70. [70]

    A. K. Hamzat, M. S. Murad, B. Subeshan, R. Asmatulu, E. Asmatulu, Rare earth element recycling: a review on sustainable solutions and im- pacts on semiconductor and chip industries, Journal of Material Cycles and Waste Management (2025) 1–24

    work page 2025

  71. [71]

    Liang, J

    B. Liang, J. Gu, X. Zeng, W. Yuan, M. Rao, B. Xiao, H. Hu, A review of the occurrence and recovery of rare earth elements from electronic waste, Molecules 29 (19) (2024) 4624

    work page 2024

  72. [72]

    L. Lair, J. A. Ouimet, M. Dougher, B. W. Boudouris, A. W. Dowling, W. A. Phillip, Critical mineral separations: Opportunities for membrane materials and processes to advance sustainable economies and secure supplies, Annual Review of Chemical and Biomolecular Engineering 15 (2024)

    work page 2024

  73. [73]

    Gebreslassie, H

    G. Gebreslassie, H. G. Desta, Y. Dong, X. Zheng, M. Zhao, B. Lin, Advanced membrane-based high-value metal recovery from wastewater, Water Research 265 (2024) 122122

    work page 2024

  74. [74]

    Alemrajabi, J

    M. Alemrajabi, J. Ricknell, S. Samak, R. Rodriguez Varela, J. Martinez, F. Hedman, K. Forsberg, Å. C. Rasmuson, Separation of rare-earth ele- ments using supported liquid membrane extraction in pilot scale, Indus- trial & Engineering Chemistry Research 61 (50) (2022) 18475–18491

    work page 2022

  75. [75]

    N. P. Wamble, E. A. Eugene, W. A. Phillip, A. W. Dowling, Optimal diafiltration membrane cascades enable green recycling of spent lithium- ion batteries, ACS Sustainable Chemistry & Engineering 10 (37) (2022) 12207–12225.doi:10.1021/acssuschemeng.2c03483

    work page doi:10.1021/acssuschemeng.2c03483 2022

  76. [76]

    Z. W. Muetzel, J. A. Ouimet, W. A. Phillip, Device for the acquisition of dynamic data enables the rapid characterization of polymer membranes, ACS Applied Polymer Materials 4 (5) (2022) 3438–3447. 56

    work page 2022

  77. [77]

    J. A. Ouimet, X. Liu, D. J. Brown, E. A. Eugene, T. Popps, Z. W. Muetzel, A. W. Dowling, W. A. Phillip, Data: Diafiltration apparatus for high-throughput analysis, Journal of membrane science 641 (2022) 119743

    work page 2022

  78. [78]

    J. G. Wijmans, R. W. Baker, The solution-diffusion model: a review, Journal of membrane science 107 (1-2) (1995) 1–21

    work page 1995

  79. [79]

    R. W. Baker, Membrane technology and applications, John Wiley & Sons, 2023

    work page 2023

  80. [80]

    Bartels, R

    C. Bartels, R. Franks, S. Rybar, M. Schierach, M. Wilf, The effect of feed ionic strength on salt passage through reverse osmosis membranes, Desalination 184 (1-3) (2005) 185–195

    work page 2005

Showing first 80 references.