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arxiv: 2606.20490 · v1 · pith:IN2UQNVInew · submitted 2026-06-18 · 💻 cs.MS

Software package MaRDI Open Interfaces for improved interoperability in numerical optimization

Dmitry I. Kabanov , Stephan Rave , Mario Ohlberger This is my paper

Pith reviewed 2026-06-26 14:38 UTC · model grok-4.3

classification 💻 cs.MS
keywords interoperabilitynumerical optimizationsoftware interfacesphysics-informed neural networksBurgers equationcomputational experiments
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The pith

MaRDI Open Interfaces provides standardized APIs that reduce the coding effort needed to connect experiment code to different numerical optimization solvers.

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

The paper introduces updates to the MaRDI Open Interfaces software package designed to improve interoperability among numerical solvers in computational science. The package targets the repetitive work of creating bindings and modifying code to match varying solver interfaces, especially when benchmarking or switching solvers for the same problem class. By offering a common interface, it allows users to apply multiple solvers to tasks like optimization problems with less adaptation. The authors illustrate this with a new interface for nonlinear optimization used in training physics-informed neural networks to solve the viscous Burgers' equation.

Core claim

The MaRDI Open Interfaces package supplies a unified interface for nonlinear optimization problems that lets computational experiments incorporate different solvers without rewriting substantial amounts of code for each one.

What carries the argument

The MaRDI Open Interfaces package, with its recently developed nonlinear optimization interface that standardizes calls to solvers.

If this is right

  • Computational scientists spend less time writing and testing bindings to individual numerical solvers.
  • Experiment codes can be adapted more quickly when changing solvers for benchmarking purposes.
  • Researchers can allocate more effort to the core scientific questions in their projects rather than interface maintenance.

Where Pith is reading between the lines

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

  • Adoption of such interfaces might increase the reproducibility of optimization experiments by making solver comparisons more straightforward.
  • Future work could test the interface's performance overhead on large-scale problems to ensure it remains practical.

Load-bearing premise

That the developed interface is general enough to cover a wide range of nonlinear optimization solvers and experiments while adding negligible overhead.

What would settle it

Demonstrating a set of solvers and PINN training tasks where using the MaRDI interface still requires extensive custom code changes or performance penalties compared to direct bindings.

Figures

Figures reproduced from arXiv: 2606.20490 by Dmitry I. Kabanov, Mario Ohlberger, Stephan Rave.

Figure 1
Figure 1. Figure 1: Comparison of the solutions of the problem (5) at 𝑡 = 2: exact solution via the Cole–Hopf transformation versus approximated solutions by physics￾informed neural networks (10) trained until the gradient ∞-norm tolerance gtol is met for gtol ∈ {10−3 , 10−4 , 10−5} via the BFGS method for trial 1. A Using SciPy B Using Optim.jl-HagerZhang C Using Optim.jl-StrongWolfe D Using Optim.jl-BackTracking. for the he… view at source ↗
read the original abstract

To address the challenges of interoperability in computational science, we present the latest updates to the software package MaRDI Open Interfaces. This software package aims to decrease the time and coding/testing efforts spent by computational scientists on tasks such as writing bindings to numerical solvers and adapting experiment codes to the varying interfaces of solvers for the same problem type (e.g., for benchmarking, which solver is better). By streamlining these tasks, this software package helps researchers focus on the actual essence of their computational projects. Here, we demonstrate a recently developed interface for nonlinear optimization and illustrate how it can be applied for computational experiments with optimization problems. As an example of such problem, we consider training of physics-informed neural networks to predict the solutions of viscous Burgers' equation.

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 describes updates to the MaRDI Open Interfaces software package, which provides standardized interfaces for numerical solvers to reduce the time and coding effort required for writing bindings and adapting experiment codes across different solvers for the same problem class. The central contribution is a newly developed interface for nonlinear optimization, illustrated via its application to training a physics-informed neural network on the viscous Burgers' equation.

Significance. If the interfaces are shown to be sufficiently general and low-overhead, the package would address a recurring practical bottleneck in computational science by enabling easier solver interchange for benchmarking and experimentation. The open-interface approach is a positive step toward reproducibility. However, the manuscript supplies only a single descriptive example without supporting metrics, so the claimed effort reduction remains an assertion rather than a demonstrated result.

major comments (2)
  1. [Abstract / demonstration] Abstract and demonstration section: the claim that the package 'decreases the time and coding/testing efforts' is load-bearing for the paper's purpose, yet the manuscript provides no quantitative support such as lines-of-code comparisons, timing data, or multi-solver benchmarks for the PINN training task. The single Burgers-equation example alone does not establish the asserted savings.
  2. [Nonlinear optimization interface] Nonlinear optimization interface description: the assertion that the interface is 'general enough' to avoid substantial user adaptation is not tested beyond one problem; no additional test cases, overhead measurements, or comparisons to direct bindings are reported, leaving the weakest assumption unexamined.
minor comments (1)
  1. The manuscript would benefit from an explicit statement of the software repository URL, license, and installation instructions to support immediate use and verification by readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on the manuscript. We address each major comment below, clarifying the scope and intent of the work while noting where revisions can be made.

read point-by-point responses

  1. Referee: [Abstract / demonstration] Abstract and demonstration section: the claim that the package 'decreases the time and coding/testing efforts' is load-bearing for the paper's purpose, yet the manuscript provides no quantitative support such as lines-of-code comparisons, timing data, or multi-solver benchmarks for the PINN training task. The single Burgers-equation example alone does not establish the asserted savings.

    Authors: The abstract states that the package 'aims to decrease' the time and coding/testing efforts, reflecting the design goal of standardized interfaces rather than an empirical claim of measured savings. The demonstration section illustrates the application of the new nonlinear optimization interface to the PINN training task on the viscous Burgers' equation as a representative use case. We agree that the single example does not constitute a quantitative benchmark study. We will revise the manuscript to ensure the abstract and text consistently frame effort reduction as a motivating objective of the interface design without implying demonstrated quantitative results in this work. revision: partial

  2. Referee: [Nonlinear optimization interface] Nonlinear optimization interface description: the assertion that the interface is 'general enough' to avoid substantial user adaptation is not tested beyond one problem; no additional test cases, overhead measurements, or comparisons to direct bindings are reported, leaving the weakest assumption unexamined.

    Authors: The nonlinear optimization interface was designed with generality in mind to support a range of solvers and problem formulations. The Burgers' equation PINN example was chosen as a non-trivial, real-world optimization task to demonstrate practical usage. We acknowledge that additional test cases, overhead measurements, and direct binding comparisons would provide further validation of generality and performance. However, such extensive benchmarking lies outside the scope of this software description paper, which focuses on presenting the interface and its initial application. No revision to add these elements is planned. revision: no

Circularity Check

0 steps flagged

No circularity: purely descriptive software paper with no derivations or predictions

full rationale

The manuscript presents a software package for numerical solver interoperability and demonstrates its nonlinear optimization interface on a single PINN training example for Burgers' equation. No equations, fitted parameters, predictions, or uniqueness theorems appear; the central claim is an engineering assertion about reduced coding effort that is not derived from any internal construction or self-citation chain. The work is self-contained as a descriptive account of interfaces and usage, with no load-bearing steps that reduce to their own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are involved; the paper is a software tool description rather than a mathematical or physical derivation.

pith-pipeline@v0.9.1-grok · 5655 in / 987 out tokens · 29197 ms · 2026-06-26T14:38:24.345085+00:00 · methodology

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Reference graph

Works this paper leans on

44 extracted references · 24 canonical work pages

  1. [1]

    B. Azmi, A. Petrocchi, and S. Volkwein. In:Error Control, Adaptive Discretizations, and Applications, Part 2. Elsevier, 2024. Chap. Parameter optimization for elliptic- parabolic systems by an adaptive trust-region reduced basis method, pp. 109–

    2024

  2. [2]

    doi: 10.1016/bs.aams.2024.07.001

    work page doi:10.1016/bs.aams.2024.07.001 2024

  3. [3]

    Die mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative)

    P. Benner et al. “Die mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative)”. In: GAMM Rundbrief 1 (2022), pp. 40–43. doi: 21.11116/0000-000A-BC70-4 . 11

    2022

  4. [4]

    Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization

    L. Biegler and V. Zavala. “Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization”. In: Com- puters & Chemical Engineering 33.3 (2009), pp. 575–582. doi: 10 . 1016 / j . compchemeng.2008.08.006

    2009

  5. [5]

    C. M. Bishop. Pattern Recognition and Machine Learning . Springer New York, 2006

    2006

  6. [6]

    Bradbury et al

    J. Bradbury et al. JAX: composable transformations of Python+NumPy programs . Version 0.3.13. 2018. url: http://github.com/jax-ml/jax

    2018

  7. [7]

    The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations

    C. G. Broyden. “The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations”. In: IMA Journal of Applied Mathematics 6.1 (1970), pp. 76–90. doi: 10.1093/imamat/6.1.76

    work page doi:10.1093/imamat/6.1.76 1970

  8. [8]

    The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm

    C. G. Broyden. “The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm”. In:IMA Journal of Applied Mathematics 6.3 (1970), pp. 222–231. doi: 10.1093/imamat/6.3.222

    work page doi:10.1093/imamat/6.3.222 1970

  9. [9]

    Spin-Free Quantum Chemistry

    J. M. Burgers. “A Mathematical Model Illustrating the Theory of Turbulence”. In: Advances in Applied Mechanics 1 (1948), pp. 171–199. doi: 10.1016/S0065- 2156(08)70100-5

    work page doi:10.1016/s0065- 1948

  10. [10]

    A. R. Conn, N. I. M. Gould, and P. L. Toint. Trust Region Methods. Society for Industrial and Applied Mathematics, 2000. doi: 10.1137/1.9780898719857

    work page doi:10.1137/1.9780898719857 2000

  11. [11]

    Cyipopt: Cython wrapper for the Interior Point Optimizer Ipopt

    Cyipopt contributors. Cyipopt: Cython wrapper for the Interior Point Optimizer Ipopt. https://github.com/mechmotum/cyipopt. Accessed in April 2026

    2026

  12. [12]

    Truncated-Newton algorithms for large-scale un- constrained optimization

    R. S. Dembo and T. Steihaug. “Truncated-Newton algorithms for large-scale un- constrained optimization”. In: Mathematical Programming 26.2 (1983), pp. 190–

    1983

  13. [13]

    doi: 10.1007/bf02592055

    work page doi:10.1007/bf02592055

  14. [14]

    JuMP: A Modeling Language for Mathe- matical Optimization

    I. Dunning, J. Huchette, and M. Lubin. “JuMP: A Modeling Language for Mathe- matical Optimization”. In: SIAM Review 59.2 (2017), pp. 295–320. doi: 10.1137/ 15m1020575

    2017

  15. [15]

    A new approach to variable metric algorithms

    R. Fletcher. “A new approach to variable metric algorithms”. In:The Computer Journal 13.3 (1970), pp. 317–322. doi: 10.1093/comjnl/13.3.317

    work page doi:10.1093/comjnl/13.3.317 1970

  16. [16]

    Computational Optimization and Applications , volume=

    F. Gao and L. Han. “Implementing the Nelder-Mead simplex algorithm with adap- tive parameters”. In: Computational Optimization and Applications 51.1 (2012), pp. 259–277. doi: 10.1007/s10589-010-9329-3. 12

    work page doi:10.1007/s10589-010-9329-3 2012

  17. [17]

    Understanding the difficulty of training deep feedfor- ward neural networks

    X. Glorot and Y. Bengio. “Understanding the difficulty of training deep feedfor- ward neural networks”. In:Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics . Ed. by Y. W. Teh and M. Titterington. Vol. 9. Proceedings of Machine Learning Research. Chia Laguna Resort, Sardinia, Italy: PMLR, 2010, pp. 249–256

    2010

  18. [18]

    A family of variable-metric methods derived by variational means

    D. Goldfarb. “A family of variable-metric methods derived by variational means”. In: Mathematics of Computation 24.109 (1970), pp. 23–26. doi: 10.1090/s0025- 5718-1970-0258249-6

    work page doi:10.1090/s0025- 1970

  19. [19]

    Algorithm 851: CGDESCENT, a conjugate gradi- ent method with guaranteed descent

    W. W. Hager and H. Zhang. “Algorithm 851: CGDESCENT, a conjugate gradi- ent method with guaranteed descent”. In: ACM Transactions on Mathematical Software 32.1 (2006), pp. 113–137. doi: 10.1145/1132973.1132979

    work page doi:10.1145/1132973.1132979 2006

  20. [20]

    Polytopic Autoencoders for Very Low-Dimensional Parametrizations of Fluid Flow Models

    J. Heiland and Y. Kim. “Polytopic Autoencoders for Very Low-Dimensional Parametrizations of Fluid Flow Models”. In: PAMM 25.2 (2025). doi: 10.1002/ pamm.70008

    2025

  21. [21]

    IEEE Std 754-2019 (2019)

    IEEE. IEEE Standard for Floating-Point Arithmetic. Tech. rep. Institute of Electrical and Electronics Engineers, 2019. doi: 10.1109/IEEESTD.2019.8766229

    work page doi:10.1109/ieeestd.2019.8766229 2019

  22. [22]

    S. G. Johnson. The NLopt nonlinear-optimization package. https://github.com/ stevengj/nlopt. 2007

    2007

  23. [23]

    Improving Interoperability in Sci- entific Computing via MaRDI Open Interfaces

    D. I. Kabanov, S. Rave, and M. Ohlberger. “Improving Interoperability in Sci- entific Computing via MaRDI Open Interfaces”. In: Journal of Open Research Software 13 (2025). doi: 10.5334/jors.569

    work page doi:10.5334/jors.569 2025

  24. [24]

    A relaxed localized trust-region reduced basis ap- proach for optimization of multiscale problems

    T. Keil and M. Ohlberger. “A relaxed localized trust-region reduced basis ap- proach for optimization of multiscale problems”. In: ESAIM: Mathematical Mod- elling and Numerical Analysis 58.1 (2024), pp. 79–105. doi: 10 . 1051 / m2an / 2023089

    2024

  25. [25]

    D. P. Kingma and J. Ba. Adam: A Method for Stochastic Optimization . https: //arxiv.org/abs/1412.6980. 2017

    Pith/arXiv arXiv 2017

  26. [26]

    Newton’s Method for Large Bound-Constrained Opti- mization Problems

    C.-J. Lin and J. J. Mor´e. “Newton’s Method for Large Bound-Constrained Opti- mization Problems”. In: SIAM Journal on Optimization 9.4 (1999), pp. 1100–1127. doi: 10.1137/s1052623498345075

    work page doi:10.1137/s1052623498345075 1999

  27. [27]

    Mathematical Programming , author =

    D. C. Liu and J. Nocedal. “On the limited memory BFGS method for large scale optimization”. In: Mathematical Programming 45.1–3 (1989), pp. 503–528. doi: 10.1007/bf01589116

    work page doi:10.1007/bf01589116 1989

  28. [28]

    JSOSolvers.jl: Unconstrained and bound-constrained optimiza- tion solvers

    T. Migot et al. “JSOSolvers.jl: Unconstrained and bound-constrained optimiza- tion solvers”. In: Journal of Open Source Software 11.117 (2026), p. 9467. doi: 10.21105/joss.09467. 13

    work page doi:10.21105/joss.09467 2026

  29. [29]

    Optim: A mathematical optimization package for Julia

    P. K. Mogensen and A. N. Riseth. “Optim: A mathematical optimization package for Julia”. In: Journal of Open Source Software 3.24 (2018), p. 615. doi: 10.21105/ joss.00615

    2018

  30. [30]

    A Simplex Method for Function Minimization

    J. A. Nelder and R. Mead. “A Simplex Method for Function Minimization”. In: The Computer Journal 7.4 (1965), pp. 308–313. doi: 10.1093/comjnl/7.4.308

    work page doi:10.1093/comjnl/7.4.308 1965

  31. [31]

    Nocedal and S

    J. Nocedal and S. J. Wright. Numerical Optimization. 2nd ed. Springer New York,

  32. [32]

    doi: 10.1007/978-0-387-40065-5

    work page doi:10.1007/978-0-387-40065-5

  33. [33]

    A direct search optimization method that models the objective and constraint functions by linear interpolation

    M. J. D. Powell. “A direct search optimization method that models the objective and constraint functions by linear interpolation”. In: Advances in Optimization and Numerical Analysis. Ed. by S. Gomez and J.-P. Hennart. Kluwer Academic: Dordrecht, 1994, pp. 51–67

    1994

  34. [34]

    M. J. D. Powell. The BOBYQA algorithm for bound constrained optimization without derivatives. Tech. rep. NA2009/06. Department of Applied Mathematics and Theoretical Physics, Cambridge England, 2009

    2009

  35. [35]

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.J

    M. Raissi, P. Perdikaris, and G. E. Karniadakis. “Physics-informed neural net- works: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations”. In: Journal of Computational Physics 378 (2019), pp. 686–707. doi: 10.1016/j.jcp.2018.10.045

    work page doi:10.1016/j.jcp.2018.10.045 2019

  36. [36]

    Riemannian Shape Optimization of Thin Shells Using Isogeometric Analysis

    R. Rosandi and B. Simeon. “Riemannian Shape Optimization of Thin Shells Using Isogeometric Analysis”. In: PAMM 25.1 (2025). doi: 10.1002/pamm.202400204

    work page doi:10.1002/pamm.202400204 2025

  37. [37]

    Functional Stability Analysis of Numerical Algorithms

    T. Rowan. “Functional Stability Analysis of Numerical Algorithms”. PhD thesis. Department of Computer Sciences, University of Texas at Austin, 1990

    1990

  38. [38]

    2023.Dissolving the Causal-Constitution Fallacy: Diachronic Constitution and the Metaphysics of Extended Cognition

    S. Salsa and G. Verzini. Partial Differential Equations in Action: From Modelling to Theory. Springer International Publishing, 2022. doi: 10.1007/978-3-031- 21853-8

    work page doi:10.1007/978-3-031- 2022

  39. [39]

    SOBMOR: Structured Optimization-Based Model Order Reduction

    P. Schwerdtner and M. Voigt. “SOBMOR: Structured Optimization-Based Model Order Reduction”. In: SIAM Journal on Scientific Computing 45.2 (2023), A502– A529. doi: 10.1137/20m1380235

    work page doi:10.1137/20m1380235 2023

  40. [40]

    Conditioning of quasi-Newton methods for function minimiza- tion

    D. F. Shanno. “Conditioning of quasi-Newton methods for function minimiza- tion”. In: Mathematics of Computation 24.111 (1970), pp. 647–656. doi: 10.1090/ s0025-5718-1970-0274029-x

    1970

  41. [41]

    Sivia and J

    D. Sivia and J. Skilling. Data analysis: a Bayesian tutorial . OUP Oxford, 2006

    2006

  42. [42]

    Nature Methods 17:261--272, ://dx.doi.org/10.1038/s41592-019-0686-2

    P. Virtanen, R. Gommers, T. E. Oliphant, et al. “SciPy 1.0: Fundamental Algo- rithms for Scientific Computing In Python”. In: Nature Methods 17.3 (2020), pp. 261–272. doi: 10.1038/s41592-019-0686-2. 14

    work page doi:10.1038/s41592-019-0686-2 2020

  43. [43]

    Wasserman

    L. Wasserman. All of Statistics. Springer New York, 2004. doi: 10.1007/978-0- 387-21736-9

    work page doi:10.1007/978-0- 2004

  44. [44]

    A Trust-Region Method for p-Harmonic Shape Optimization

    H. Wyschka and W. Wollner. “A Trust-Region Method for p-Harmonic Shape Optimization”. In: PAMM 25.1 (2025). doi: 10.1002/pamm.70000. 15

    work page doi:10.1002/pamm.70000 2025