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arxiv: 2605.24275 · v1 · pith:BXGQSS3Xnew · submitted 2026-05-22 · 📡 eess.SY · cs.SY

Learning regime-dependent governing equations: A symbolic decision tree approach

Ilias Mitrai , Tongjia Liu , Gabriel E. Sanoja This is my paper

Pith reviewed 2026-06-30 14:14 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords symbolic decision treesregime-dependent governing equationsmixed-integer optimizationhybrid dynamical modelspolymer melts viscositydata-driven discoveryinterpretable modelschemical engineering systems
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The pith

Symbolic decision trees jointly learn regime partitions and local governing equations by solving a mixed-integer optimization problem.

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

Chemical engineering systems often switch between different governing mechanisms depending on operating conditions. The paper develops symbolic decision trees that discover both the conditions splitting data into regimes and the equations holding inside each regime at the same time. Parametrizing the splits and the local equations with basis functions converts the task into a mixed-integer optimization problem solvable from data. The resulting models are intended to be more accurate than a single global equation and more interpretable than conventional decision trees, with demonstrations on hybrid dynamical systems and polymer-melt viscosity.

Core claim

Symbolic decision trees identify physically interpretable regimes and local governing equations while improving predictive accuracy relative to approaches that learn a single global model or use existing decision tree models. The method simultaneously learns interpretable splitting conditions to partition the input domain and local governing equations that describe each regime. Both the splitting conditions and governing equations are parametrized using basis functions, resulting in a mixed-integer optimization learning problem.

What carries the argument

Symbolic decision trees that parametrize splitting conditions for regime partitions and local governing equations with basis functions and solve the resulting mixed-integer optimization problem.

If this is right

  • The learned models support predictive modeling, optimization, and control in chemical engineering systems with regime switches.
  • The partitions and equations recovered are physically interpretable.
  • The same procedure applies to learning hybrid dynamical models.
  • The same procedure applies to learning constitutive equations such as zero-shear viscosity of polymer melts.

Where Pith is reading between the lines

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

  • The framework could be tested on regime-switching data from domains outside chemical engineering where labeled regime data are scarce.
  • Changing the choice or number of basis functions might allow the same optimization structure to handle qualitatively different regime transitions without altering the algorithm.

Load-bearing premise

Parametrizing both splitting conditions and local governing equations with basis functions yields a tractable mixed-integer optimization problem whose solution correctly recovers the underlying regime partitions and equations from data.

What would settle it

Apply the method to data generated from a known regime-switching system with documented boundaries and equations; the recovered partitions or equations should match the known structure or at least reduce prediction error below that of a single global model.

Figures

Figures reproduced from arXiv: 2605.24275 by Gabriel E. Sanoja, Ilias Mitrai, Tongjia Liu.

Figure 1
Figure 1. Figure 1: Decision trees with nonlinear expressions in the leaves and splitting [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mean absolute error on the testing set as a function of the number of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Mean absolute error on the testing set as a function of the distance from the origin for the di [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of the interacting two-tank system. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: We simulate the system for t ∈ [0, 20] using [h1(0) h2(0)] = [0.1 1.2] as initial condition. From the results, we observe that the model discovered with the proposed approach tracks the evolution of height more accurately than the model discovered using sparse regression. Specifically, the root mean squared er￾ror with the proposed approach is 9.6 × 10−4 , whereas with the sparse regression model it is 2.5… view at source ↗
Figure 6
Figure 6. Figure 6: Inlet flow rates and liquid level evolution [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of the liquid level in the first tank using the model discovered with the proposed approach and with sparse regression. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Polymer viscosity as a function of molecular weight for [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: L2 error for the identified coefficients as a function of the noise level. 0.01 0.1 0.2 0.5 Noise level 10 3 10 2 10 1 Splitting condition coefficient recovery error [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: L2 error for the identified coefficients in the splitting conditions as a function of the noise level. 6. Conclusions In this paper, we propose a data-driven framework for dis￾covering regime-dependent governing equations. The major challenge in such learning tasks is the need to simultaneously identify distinct regimes and the governing equations within each regime. To address this challenge, we represen… view at source ↗
read the original abstract

Many chemical engineering systems are governed by mechanisms that switch across operating regimes, making the data-driven discovery of regime-dependent governing equations essential for predictive modeling, optimization, and control. We propose symbolic decision trees for the data-driven discovery of regime-dependent governing equations. The method simultaneously learns interpretable splitting conditions to partition the input domain and local governing equations that describe each regime. To improve tractability, both the splitting conditions and governing equations are parametrized using basis functions, resulting in a mixed-integer optimization learning problem. We use the proposed approach to learn hybrid dynamical models and a constitutive equation for the zero-shear viscosity of polymer melts. Symbolic decision trees identify physically interpretable regimes and local governing equations while improving predictive accuracy relative to approaches that learn a single global model or use existing decision tree models. This framework provides an interpretable and generalizable route for discovering regime-dependent models in chemical engineering systems.

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 / 1 minor

Summary. The paper proposes symbolic decision trees to discover regime-dependent governing equations by simultaneously learning interpretable splitting conditions and local governing equations. Both are parametrized with basis functions to yield a mixed-integer optimization problem, which is applied to hybrid dynamical models and a constitutive equation for zero-shear viscosity of polymer melts. The central claim is that this identifies physically interpretable regimes, recovers local equations, and improves predictive accuracy over single global models or existing decision-tree approaches.

Significance. If the mixed-integer program reliably recovers the true regime partitions and equations, the framework would offer a practical, interpretable route to hybrid models for switching systems in chemical engineering, with direct relevance to modeling, optimization, and control. The basis-function parametrization for tractability and the concrete applications to dynamical systems and polymer rheology are strengths.

major comments (2)
  1. [Methods and Results sections (formulation and validation)] The central claim requires that the mixed-integer program recovers the underlying physical regime boundaries and equations (not merely fits the data). The manuscript supplies no synthetic-data experiments with known ground-truth partitions, no recovery guarantees, and no analysis of multiple optima with comparable training loss; without these, improved predictive accuracy does not establish correct regime identification.
  2. [Methods (optimization formulation)] § on the mixed-integer formulation: the claim that parametrizing splits and local models with basis functions produces a tractable problem whose global solution recovers the regimes is load-bearing, yet no details on the exact MINLP, solver behavior, or sensitivity to initialization are provided to support that the recovered partitions are the physically correct ones rather than alternative partitions with similar loss.
minor comments (1)
  1. [Abstract and Results] The abstract states accuracy gains but supplies no quantitative error metrics, cross-validation details, or comparison baselines; these should be added to the results section for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects of validating the method's ability to recover true regimes. We address each point below and will make revisions to strengthen the paper accordingly.

read point-by-point responses

  1. Referee: [Methods and Results sections (formulation and validation)] The central claim requires that the mixed-integer program recovers the underlying physical regime boundaries and equations (not merely fits the data). The manuscript supplies no synthetic-data experiments with known ground-truth partitions, no recovery guarantees, and no analysis of multiple optima with comparable training loss; without these, improved predictive accuracy does not establish correct regime identification.

    Authors: We agree that demonstrating recovery of known regimes on synthetic data would strengthen the central claim. The current manuscript focuses on real-world applications where the learned regimes are interpretable and align with physical understanding in hybrid systems and polymer rheology, and shows superior predictive accuracy. However, to directly address this, we will add synthetic experiments with ground-truth partitions in the revised version. We will also include an analysis of multiple local optima by reporting results from different initializations or solver settings to assess consistency of the recovered partitions. revision: yes

  2. Referee: [Methods (optimization formulation)] § on the mixed-integer formulation: the claim that parametrizing splits and local models with basis functions produces a tractable problem whose global solution recovers the regimes is load-bearing, yet no details on the exact MINLP, solver behavior, or sensitivity to initialization are provided to support that the recovered partitions are the physically correct ones rather than alternative partitions with similar loss.

    Authors: The manuscript presents the mixed-integer optimization formulation in the Methods section, where both splitting conditions and local models are parametrized with basis functions to enable tractability. We acknowledge that additional details on the specific MINLP structure, the solver employed, and empirical sensitivity to initialization would be beneficial. In the revision, we will expand this section to include the full mathematical formulation, solver information, and results from multiple optimization runs to demonstrate robustness and that the identified regimes are consistent rather than arbitrary alternatives with similar loss. revision: yes

Circularity Check

0 steps flagged

No circularity: standard optimization-based learning procedure

full rationale

The paper formulates symbolic decision trees as a mixed-integer program that parametrizes splitting conditions and local governing equations via basis functions, then solves for regime partitions and models from data. The claimed outputs (improved predictive accuracy and interpretable regimes) are the direct numerical results of this optimization rather than quantities defined by construction to equal the inputs. No self-citation chains, uniqueness theorems, or ansatzes are invoked in the provided abstract or description to justify core steps; the method is presented as an empirical discovery tool whose validity rests on solver performance and data fit, not on internal redefinition. This is a conventional data-driven modeling pipeline with no load-bearing reduction of predictions to fitted inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so specific free parameters, axioms, and invented entities cannot be extracted or verified from the full text.

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discussion (0)

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Reference graph

Works this paper leans on

47 extracted references · 5 canonical work pages · 1 internal anchor

  1. [1]

    Learning surrogate models for simulation-based optimization,

    A. Cozad, N. V . Sahinidis, and D. C. Miller, “Learning surrogate models for simulation-based optimization,”AIChE J., vol. 60, no. 6, pp. 2211– 2227, 2014

    2014

  2. [2]

    Discovering governing equations from data by sparse identification of nonlinear dynamical sys- tems,

    S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical sys- tems,”Proceedings of the national academy of sciences, vol. 113, no. 15, pp. 3932–3937, 2016

    2016

  3. [3]

    Data-driven identification of inter- pretable reduced-order models using sparse regression,

    A. Narasingam and J. S.-I. Kwon, “Data-driven identification of inter- pretable reduced-order models using sparse regression,”Computers& Chemical Engineering, vol. 119, pp. 101–111, 2018

    2018

  4. [4]

    Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results,

    F. Abdullah and P. D. Christofides, “Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results,”Computers&Chemical Engineering, vol. 174, p. 108247, 2023

    2023

  5. [5]

    Symantic: An efficient symbolic regression method for interpretable and parsimo- nious model discovery in science and beyond,

    M. R. Muthyala, F. Sorourifar, Y . Peng, and J. A. Paulson, “Symantic: An efficient symbolic regression method for interpretable and parsimo- nious model discovery in science and beyond,”Industrial&Engineering Chemistry Research, vol. 64, no. 6, pp. 3354–3369, 2025

    2025

  6. [6]

    Distilling free-form natural laws from exper- imental data,

    M. Schmidt and H. Lipson, “Distilling free-form natural laws from exper- imental data,”Science, vol. 324, no. 5923, pp. 81–85, 2009

    2009

  7. [7]

    A global minlp approach to symbolic re- gression,

    A. Cozad and N. V . Sahinidis, “A global minlp approach to symbolic re- gression,”Mathematical Programming, vol. 170, no. 1, pp. 97–119, 2018

    2018

  8. [8]

    Globally Optimal Symbolic Regression

    V . Austel, S. Dash, O. Gunluk, L. Horesh, L. L, G. Nan- nicini, and B. Schieber, “Globally optimal symbolic regression,” https://arxiv.org/abs/1710.10720, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  9. [9]

    Learning symbolic expressions: Mixed-integer formulations, cuts, and heuristics,

    J. Kim, S. Leyffer, and P. Balaprakash, “Learning symbolic expressions: Mixed-integer formulations, cuts, and heuristics,”INFORMS Journal on Computing, vol. 35, pp. 1383–1403, 2023. 8

    2023

  10. [10]

    Perspectives on the integration be- tween first-principles and data-driven modeling,

    W. Bradley, J. Kim, Z. Kilwein, L. Blakely, M. Eydenberg, J. Jalvin, C. Laird, and F. Boukouvala, “Perspectives on the integration be- tween first-principles and data-driven modeling,”Comput. Chem. Eng., p. 107898, 2022

    2022

  11. [11]

    arXiv preprint arXiv:2011.03902 , year=

    R. T. Chen, B. Amos, and M. Nickel, “Learning neural event functions for ordinary differential equations,”arXiv preprint arXiv:2011.03902, 2020

    work page arXiv 2011

  12. [12]

    Neural hybrid automata: Learning dynamics with multiple modes and stochastic transitions,

    M. Poli, S. Massaroli, L. Scimeca, S. Chun, S. J. Oh, A. Yamashita, H. Asama, J. Park, and A. Garg, “Neural hybrid automata: Learning dynamics with multiple modes and stochastic transitions,”Advances in Neural Information Processing Systems, vol. 34, pp. 9977–9989, 2021

    2021

  13. [13]

    Industrial, large-scale model predictive control with structured neural networks,

    P. Kumar, J. B. Rawlings, and S. J. Wright, “Industrial, large-scale model predictive control with structured neural networks,”Comput. Chem. Eng., vol. 150, p. 107291, 2021

    2021

  14. [14]

    Learning an approx- imate model predictive controller with guarantees,

    M. Hertneck, J. K ¨ohler, S. Trimpe, and F. Allg¨ower, “Learning an approx- imate model predictive controller with guarantees,”IEEE Control Syst. Lett., vol. 2, no. 3, pp. 543–548, 2018

    2018

  15. [15]

    Learning for online mixed-integer model predictive control with parametric optimality cer- tificates,

    L. Russo, S. H. Nair, L. Glielmo, and F. Borrelli, “Learning for online mixed-integer model predictive control with parametric optimality cer- tificates,”IEEE Control Systems Letters, vol. 7, pp. 2215 – 2220, 2023

    2023

  16. [16]

    Deep learning-based embedded mixed-integer model predictive control,

    B. Karg and S. Lucia, “Deep learning-based embedded mixed-integer model predictive control,” in2018 European Control Conference (ECC), pp. 2075–2080, IEEE, 2018

    2075

  17. [17]

    PRISM: Re- current neural networks and presolve methods for fast mixed-integer opti- mal control,

    A. Cauligi, A. Chakrabarty, S. Di Cairano, and R. Quirynen, “PRISM: Re- current neural networks and presolve methods for fast mixed-integer opti- mal control,” inLearning for Dynamics and Control Conference, pp. 34– 46, PMLR, 2022

    2022

  18. [18]

    Identification of piecewise affine systems based on statistical clustering technique,

    H. Nakada, K. Takaba, and T. Katayama, “Identification of piecewise affine systems based on statistical clustering technique,”Automatica, vol. 41, no. 5, pp. 905–913, 2005

    2005

  19. [19]

    Model selection for hybrid dynamical systems via sparse regression,

    N. M. Mangan, T. Askham, S. L. Brunton, J. N. Kutz, and J. L. Proctor, “Model selection for hybrid dynamical systems via sparse regression,” Proceedings of the Royal Society A: Mathematical, Physical and Engi- neering Sciences, vol. 475, no. 2223, 2019

    2019

  20. [20]

    A clustering technique for the identification of piecewise affine systems,

    G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari, “A clustering technique for the identification of piecewise affine systems,”Automatica, vol. 39, no. 2, pp. 205–217, 2003

    2003

  21. [21]

    Identification of hybrid systems a tutorial,

    S. Paoletti, A. L. Juloski, G. Ferrari-Trecate, and R. Vidal, “Identification of hybrid systems a tutorial,”European journal of control, vol. 13, no. 2- 3, pp. 242–260, 2007

    2007

  22. [22]

    Identification of hybrid systems via mixed-integer programming,

    A. Bemporad, J. Roll, and L. Ljung, “Identification of hybrid systems via mixed-integer programming,” inProceedings of the 40th IEEE Confer- ence on Decision and Control (Cat. No. 01CH37228), vol. 1, pp. 786– 792, IEEE, 2001

    2001

  23. [23]

    Mathematical pro- gramming for piecewise linear regression analysis,

    L. Yang, S. Liu, S. Tsoka, and L. G. Papageorgiou, “Mathematical pro- gramming for piecewise linear regression analysis,”Expert systems with applications, vol. 44, pp. 156–167, 2016

    2016

  24. [24]

    Breiman, J

    L. Breiman, J. Friedman, R. A. Olshen, and C. J. Stone,Classification and regression trees. Chapman and Hall/CRC, 2017

    2017

  25. [25]

    Learning with continuous classes,

    J. R. Quinlanet al., “Learning with continuous classes,” in5th Australian joint conference on artificial intelligence, vol. 92, pp. 343–348, World Scientific, 1992

    1992

  26. [26]

    Near-optimal nonlinear regression trees,

    D. Bertsimas, J. Dunn, and Y . Wang, “Near-optimal nonlinear regression trees,”Operations Research Letters, vol. 49, no. 2, pp. 201–206, 2021

    2021

  27. [27]

    Approximate model predictive building control via machine learning,

    J. Drgo ˇna, D. Picard, M. Kvasnica, and L. Helsen, “Approximate model predictive building control via machine learning,”Applied energy, vol. 218, pp. 199–216, 2018

    2018

  28. [28]

    Building temper- ature control by simple mpc-like feedback laws learned from closed-loop data,

    M. Klau ˇco, J. Drgoˇna, M. Kvasnica, and S. Di Cairano, “Building temper- ature control by simple mpc-like feedback laws learned from closed-loop data,”IFAC Proceedings Volumes, vol. 47, no. 3, pp. 581–586, 2014

    2014

  29. [29]

    Learning ap- proximate semi-explicit hybrid mpc with an application to microgrids,

    D. Masti, T. Pippia, A. Bemporad, and B. De Schutter, “Learning ap- proximate semi-explicit hybrid mpc with an application to microgrids,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 5207–5212, 2020

    2020

  30. [30]

    A piecewise linear regression and classification algorithm with application to learning and model predictive control of hybrid sys- tems,

    A. Bemporad, “A piecewise linear regression and classification algorithm with application to learning and model predictive control of hybrid sys- tems,”IEEE Transactions on Automatic Control, vol. 68, no. 6, pp. 3194– 3209, 2022

    2022

  31. [31]

    Piecewise linear trees as surrogate models for system design and planning under high-frequency temporal variabil- ity,

    Y . Wu and C. T. Maravelias, “Piecewise linear trees as surrogate models for system design and planning under high-frequency temporal variabil- ity,”European Journal of Operational Research, vol. 315, no. 2, pp. 541– 552, 2024

    2024

  32. [32]

    Hyperplane decision trees as piecewise linear surrogate models for chemical process design,

    E. M. Sunshine, C. C. Tedesco, S. A. Akhade, M. J. McNenly, J. R. Kitchin, and C. D. Laird, “Hyperplane decision trees as piecewise linear surrogate models for chemical process design,”Computers&Chemical Engineering, vol. 202, p. 109204, 2025

    2025

  33. [33]

    Learning symbolic representations of hybrid dynamical systems,

    D. L. Ly and H. Lipson, “Learning symbolic representations of hybrid dynamical systems,”The Journal of Machine Learning Research, vol. 13, no. 1, pp. 3585–3618, 2012

    2012

  34. [34]

    Ps-tree: A piecewise sym- bolic regression tree,

    H. Zhang, A. Zhou, H. Qian, and H. Zhang, “Ps-tree: A piecewise sym- bolic regression tree,”Swarm and Evolutionary Computation, vol. 71, p. 101061, 2022

    2022

  35. [35]

    Identification of hybrid systems with dynamics-based modeling through symbolic regression,

    S. Plambeck, M. Schmidt, A. Subias, L. Trav ´e-Massuy`es, and G. Fey, “Identification of hybrid systems with dynamics-based modeling through symbolic regression,”Journal of Systems and Software, p. 112639, 2025

    2025

  36. [36]

    Symbolic regression enhanced decision trees for classification tasks,

    K. S. Fong and M. Motani, “Symbolic regression enhanced decision trees for classification tasks,” inProceedings of the AAAI Conference on Arti- ficial Intelligence, vol. 38, pp. 12033–12042, 2024

    2024

  37. [37]

    Discovering interpretable piecewise nonlinear model pre- dictive control laws via symbolic decision trees,

    I. Mitrai, “Discovering interpretable piecewise nonlinear model pre- dictive control laws via symbolic decision trees,”arXiv preprint arXiv:2510.10411, 2025

    work page arXiv 2025

  38. [38]

    Optimal classification trees,

    D. Bertsimas and J. Dunn, “Optimal classification trees,”Machine Learn- ing, vol. 106, no. 7, pp. 1039–1082, 2017

    2017

  39. [39]

    Strong optimal classification trees,

    S. Aghaei, A. G ´omez, and P. Vayanos, “Strong optimal classification trees,”Operations Research, vol. 73, no. 4, pp. 2223–2241, 2025

    2025

  40. [40]

    Gurobi Optimizer Reference Manual,

    Gurobi Optimization, LLC, “Gurobi Optimizer Reference Manual,” 2021. Accessed: 2023-08-31

    2021

  41. [41]

    Scikit-learn: Machine learning in Python,

    F. Pedregosa, G. Varoquaux, A. Gramfort, V . Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V . Dubourg, J. Van- derplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duch- esnay, “Scikit-learn: Machine learning in Python,”Journal of Machine Learning Research, vol. 12, pp. 2825–2830, 2011

    2011

  42. [42]

    Col- umn generation based heuristic for learning classification trees,

    M. Firat, G. Crognier, A. F. Gabor, C. A. Hurkens, and Y . Zhang, “Col- umn generation based heuristic for learning classification trees,”Comput- ers&Operations Research, vol. 116, p. 104866, 2020

    2020

  43. [43]

    An improved column- generation-based matheuristic for learning classification trees,

    K. K. Patel, G. Desaulniers, and A. Lodi, “An improved column- generation-based matheuristic for learning classification trees,”Comput- ers&Operations Research, vol. 165, p. 106579, 2024

    2024

  44. [44]

    Acceleration techniques for learning optimal classification trees with integer program- ming,

    M. Keegan, M. Forbes, P. Corry, and M. Abolghasemi, “Acceleration techniques for learning optimal classification trees with integer program- ming,”arXiv preprint arXiv:2511.18791, 2025

    work page arXiv 2025

  45. [45]

    Quant-bnb: A scalable branch- and-bound method for optimal decision trees with continuous features,

    R. Mazumder, X. Meng, and H. Wang, “Quant-bnb: A scalable branch- and-bound method for optimal decision trees with continuous features,” inInternational Conference on Machine Learning, pp. 15255–15277, PMLR, 2022

    2022

  46. [46]

    A scalable deterministic global optimization algorithm for training optimal decision tree,

    K. Hua, J. Ren, and Y . Cao, “A scalable deterministic global optimization algorithm for training optimal decision tree,”Advances in Neural Infor- mation Processing Systems, vol. 35, pp. 8347–8359, 2022

    2022

  47. [47]

    Rs-ort: A reduced-space branch-and-bound algorithm for optimal regression trees,

    C. Heredia, P. Chumpitaz-Flores, and K. Hua, “Rs-ort: A reduced-space branch-and-bound algorithm for optimal regression trees,”arXiv preprint arXiv:2510.23901, 2025. 9

    work page arXiv 2025