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REVIEW 3 major objections 4 minor 61 references

Can ChatGPT implement finite element models for geotechnical engineering applications?

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read ChatGPT can generate working finite element code for coupled geotechnical problems when the target is a high-level library like FEniCS, but in low-level MATLAB its output requires extensive error-driven re-prompting or direct human repair.

desk verdict A genuinely first empirical test of LLM-assisted mixed FEM in geotechnics; the qualitative pass criteria and missing logs make the headline claim hard to audit, but the direction is right and worth refereeing. read the letter →

arxiv 2501.02199 v1 pith:62CN4EVJ submitted 2025-01-04 math.NA cs.AIcs.NA

Taegu Kim , Tae Sup Yun , Hyoung Suk Suh This is my paper · ORCID
classification math.NAcs.AIcs.NA MSC 65N3074S0576S05
keywords finiteelementmethodlargelanguagemodelChatGPTcodegenerationpromptengineeringhydro-mechanicalcouplingunsaturatedsoilFEniCS
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether a general-purpose large language model, ChatGPT, can write working finite element code for coupled geotechnical problems from natural-language prompts that supply the governing equations, geometry, boundary conditions, and discretization details but deliberately omit the variational weak form. Three hydromechanically coupled problems of escalating difficulty are used as tests: one-dimensional consolidation, differential settlement of a strip footing, and gravity-driven seepage in unsaturated soil, each run in both the FEniCS and MATLAB environments. The paper's central finding is that the model performs very well when the target is FEniCS — all 100 consolidation trials passed on the first attempt, and the hardest coupled problem never required direct human coding — while MATLAB output needed many rounds of error-message re-prompting and, for the footing problem, consistently ended in manual repair. The conclusion argued for is that ChatGPT does not yet replace human programmers but can substantially assist finite element implementation, provided the target library is high-level and the user understands the mathematics behind the errors.

What carries the argument

The carrying mechanism is the three-stage GPT-based workflow — initial prompting, prompt augmentation, and direct human involvement — measured against a difficulty gradient of three model problems. The initial prompt supplies the strong-form balance and constitutive equations, geometry, material properties, initial and boundary conditions, mesh size, timestep, time integration scheme, and requested output plots; the weak form is deliberately withheld so that the test includes whether the model can derive the variational statement itself. When execution fails, the user feeds the error message back to ChatGPT and repeats, up to ten times. The decisive variable is the abstraction level of the target language: FEniCS accepts a near-mathematical statement of the weak form and automates element assembly, interpolation, and solving, so the generated scripts stay short and correct, whereas MATLAB requires the model to write shape functions, element matrices, and global assembly line by line, which is where its output turns unstable or wrong. The three problems — single-field diffusion, two-field saturated poroelasticity with LBB-stable Taylor-Hood elements (a standard stable pairing of displacement and pressure spaces), and pseudo-three-phase unsaturated flow with the van Genuchten retention model (a standard closed-form water retention curve) — provide the ordered test beds against which augmentation counts are compared.

What would settle it

Re-run the three model problems with a pre-registered quantitative acceptance rule — for example, an $L^2$ relative error below 1% against the Terzaghi analytical solution, the GeoStudio results, and the Liakopoulos data, computed by the same GPT-generated codes — and recount how many trials pass on the first attempt; if the first-try pass rates drop substantially, the headline capability claim was an artifact of visual matching.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that ChatGPT o1 can infer the Galerkin weak form from a strong-form statement of a coupled initial boundary value problem and convert it into executable finite element code, and that the abstraction level of the programming interface decides whether this happens with almost no revision or not at all. In FEniCS the model produced error-free scripts with zero to a handful of prompt augmentations: Naug = 0 in all 100 trials of the consolidation problem, usually six or fewer for the Taylor-Hood u-pw footing problem, and between 1 and 10 for the van Genuchten seepage problem, with no trial in any problem requiring direct human intervention. In MATLAB the same prompts produced code that was numerically unstable, mishandled boundary conditions, or failed to assemble, requiring prompt augmentations in 27 of 100 trials for the simplest problem and direct human code repair in all 30 trials of the coupled footing problem. The authors take this as evidence that large language models are currently assistive tools: they remove the bulk of low-level programming only when the target library already supplies that machinery.

Load-bearing premise

The load-bearing premise is that 'passing' means what the authors judged it to mean — a trial passes when its plots closely match a benchmark solution, with no numerical tolerance or pre-registered acceptance rule, so the reported pass rates inherit whatever subjectivity that judgment carries.

Editorial extensions

If this is right

  • Engineers who know the equations but are not FEM programmers can realistically delegate the implementation of mixed finite element codes to an LLM when the target is a high-level library such as FEniCS.
  • Error-message-driven prompt augmentation is a workable debugging loop: ChatGPT fixed syntax errors, solver tolerance failures, weak-form mistakes, and unphysical saturation values from a few lines of feedback.
  • The programming environment, not just the model, determines automation success; low-level targets shift the bottleneck back to the human programmer.
  • Consolidation, settlement, and seepage analyses — routine geotechnical tasks — are the near-term practical beneficiaries of this assistive workflow.
  • Users still need domain expertise to diagnose failures and point at the right lines, so the immediate payoff is faster coding, not expert-free modeling.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the pass criterion is visual agreement with benchmarks rather than a numerical tolerance, the reported first-try pass rates are likely an upper bound; re-measuring with, say, a 1% relative-error rule would probably reduce them, especially for the seepage problem where ChatGPT had to be guided to clamp $S_w$ and $k_r$ to $[0,1]$.
  • The same prompt-augmentation loop could be tested across other high-level finite element interfaces, which would show whether FEniCS's specific API or the high-level paradigm in general is what rescues the model.
  • The workflow assumes the user can still diagnose what is wrong; a natural follow-up is to measure how far a user without finite element knowledge gets before the loop stalls — the weak-form corrections in the paper required the authors to point at specific code lines.
  • If this trend continues across future model generations, the augmentation-count distributions reported here (mode 0 for the simple problem, 1–10 for the complex one) become a convenient benchmark for tracking the progress of automated numerical-code generation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper evaluates whether ChatGPT (specifically o1) can generate finite element code for three hydro-mechanically coupled geotechnical problems: 1D consolidation (Model Problem 1), coupled settlement of a strip footing (Model Problem 2), and gravity-driven unsaturated seepage (Model Problem 3). The authors prompt ChatGPT with strong-form equations, constitutive laws, geometry, boundary conditions, and discretization details in both MATLAB and FEniCS environments, then iteratively re-prompt using error messages and user-specified debugging instructions until the generated code "passes" a verification/validation exercise. They report that FEniCS-based code required zero augmentations in all 100 trials of Model Problem 1 and few augmentations in most trials of Model Problems 2 and 3, whereas MATLAB-based code frequently required many augmentations or direct human intervention. The paper concludes that LLMs cannot yet replace human programmers but can substantially assist in numerical implementation. Appendix A provides the poromechanics derivations for the three model problems.

Significance. The manuscript has several genuine strengths: the poromechanics derivations in Appendix A are standard and internally consistent; the benchmarks are external (Terzaghi's analytical solution, GeoStudio, and Liakopoulos's experiments) with no fitted parameters; the study uses repeated trials (100, 30, and 30) and reports Naug histograms; and the conclusion is appropriately modest, framing ChatGPT as an assistive tool rather than a full replacement. However, the central empirical claim is not independently checkable as reported. Success is defined only qualitatively in §3.2 as a code that "runs without any issues and yields results that are reasonably accurate," and the verification/validation sections report visual agreement without any numerical tolerance or pre-registered acceptance rule. In addition, several counted "prompt augmentations" are human-authored fixes (for example, supplying the specific line of code to change in §4.2 and instructing the model to impose Sw ≤ 1 and kr ≤ 1 in §4.3).

major comments (3)
  1. [§4.2; §4.3; §3.2] The acceptance criterion for a "passing" code is not well defined. §3.2 defines success as a code that "runs without any issues and yields results that are reasonably accurate," and the verification/validation sections report only qualitative agreement ("closely matched," "closely aligned") with the Terzaghi solution, GeoStudio, and Liakopoulos data, without a single quantitative error tolerance or pre-registered acceptance rule (§4.1, §4.2, §4.3, Figs. 5, 10, 14). Consequently, the histograms of Naug in Figures 6, 8, and 12 are not independently checkable: whether a trial passes depends on the authors' visual judgment, not on a measurable outcome. This undermines the central claim in the Abstract that FEniCS required "minimal code revisions" while MATLAB required "extensive prompt augmentations." Please specify a quantitative error metric (e.g., relative L2 error of pore pressure or settlement, with a stated threshold) and pre-register the acceptance rule before interpreting the reported trial counts.
  2. [Figures 6, 8, 12; §4.1–§4.3] Human-specified corrections are counted as prompt augmentations, conflating the model's capability with the human's programming effort. In Model Problem 2, the third FEniCS augmentation was "we instructed ChatGPT to correct this part by providing the specific line of code that required modification" (§4.2, Fig. 10). In Model Problem 3, the authors instructed ChatGPT to impose the constraints Sw ≤ 1 and kr ≤ 1 (§4.3). These are human-authored fixes, not autonomous model debugging, yet they are included in the measure Naug that underlies the FEniCS-versus-MATLAB comparison. The paper itself notes in §3.2 that "diagnosing errors may require an understanding of the formulation," and §5 concedes that domain experts remain essential. Please separate trials in which the model resolved an error from the error message alone from trials in which a human supplied the specific fix; otherwise "minimal code revisions" is not a clean measure of ChatGPT's capability.
  3. The empirical evaluation is not reproducible. The paper shows only exemplary initial prompts and generated code (Figs. 3, 9, 13) and does not provide the complete prompt history, error messages, human instructions, and generated code for all 100/30/30 trials. Because ChatGPT is a stochastic model and because the acceptance rule is qualitative (see Major Comment 1), an independent party cannot verify the reported Naug counts or rerun the benchmark exercise. Please include a supplementary archive with the full prompt log, the output code for each trial, and a script that computes the proposed error metric for each pass/fail decision.
minor comments (4)
  1. [§5] The word "relevent" in the first sentence of Section 5 is misspelled and should be "relevant."
  2. [Figures 6, 8, 12] The histograms do not clearly label the horizontal axis or the categories of Naug in the text or captions; for example, the numerical values "73 100 21 0 6 0" in Figure 6 are not explained. Please label the horizontal axis as "Naug" and describe each bar in the caption or in the surrounding text.
  3. [§4.2] The text refers to the GeoStudio comparison as a "verification test," but comparing against another numerical code is a code-to-code comparison rather than verification against an exact solution. Please use a term such as "benchmark comparison" or clarify what is being verified.
  4. [§3.2] For reproducibility, please report the exact ChatGPT model version, sampling/temperature settings, and the number of independent runs used for each environment; the paper states only "ChatGPT o1," which is not sufficient for an independent replication.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: benchmarks are external and no equation is fitted to force agreement; the qualitative pass criterion and human-in-the-loop fixes are methodological limitations, not circular derivations.

full rationale

The paper's load-bearing comparisons are made against external benchmarks: the Terzaghi analytical solution for Model Problem 1, GeoStudio results for Model Problem 2, and the Liakopoulos experimental data for Model Problem 3. None of these benchmarks is constructed from the ChatGPT output, and no model parameter or equation is fitted to force agreement with them. The governing equations are standard poromechanical balances (Terzaghi, Biot, van Genuchten) derived and cited from the literature; the appendix re-derives the simplified model forms from those standard equations rather than from the later numerical results. The iterative prompt-augmentation loop is a code-debugging procedure, not a derivation: the paper does not claim that the benchmark agreement follows from its prompts by construction, and it explicitly frames ChatGPT as an assistive tool requiring human expertise (Section 5: 'the involvement of domain experts remains essential, particularly in diagnosing errors'). The qualitative 'reasonably accurate' pass criterion is a real falsifiability and reproducibility limitation, but it is not a circularity: it makes the capability claim harder to verify, not equivalent to its inputs. The paper's self-citations (Kim et al. 2024; Suh and Sun 2021a,b; Suh et al. 2024) are used for context, notation, and prior framework reference; none is a load-bearing uniqueness theorem or an assumed result that the present conclusion reduces to. For these reasons, no specific circular step can be exhibited, and the appropriate score is low.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no fitted parameters and no new postulated entities. Its central claim is empirical. The load-bearing inputs are the correctness of external benchmarks, the implicit subjective pass criterion, the boundary between human and model contribution, and the representativeness of one LLM.

assumptions (4)
  • domain assumption The benchmark solutions used for verification and validation are correct and appropriate for the target problems.
    Terzaghi analytical solution, GeoStudio simulation, and Liakopoulos experimental data are treated as ground truth in Section 4. If any benchmark is wrong or inapplicable, the pass/fail judgments lose meaning.
  • ad hoc to paper A code 'passes' when its output agrees with the benchmark to an unspecified, authors-judged degree.
    Sections 4.1 to 4.3 describe passing without a stated error tolerance or quantitative metric. This makes the success criterion partly subjective.
  • ad hoc to paper During prompt augmentation, the human role is limited to supplying error messages and high-level debugging instructions, not writing the finite element code.
    The claim that ChatGPT 'implemented' the models depends on this separation. The paper admits direct human intervention was needed for MATLAB in Model Problem 2.
  • domain assumption ChatGPT o1 outputs are representative of current large language model code generation capabilities.
    Only one LLM is tested, and the authors note other models may perform differently. Generalizing beyond ChatGPT o1 is an unstated leap.

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Cite this review

Pith. "Pith review of Can ChatGPT implement finite element models for geotechnical engineering applications?." pith.science (2026). https://pith.science/paper/62CN4EVJ

@misc{pith2026250102199,
  author       = {Pith},
  title        = {Pith review of: Can ChatGPT implement finite element models for geotechnical engineering applications?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/62CN4EVJ}},
  note         = {Machine review of arXiv:2501.02199}
}
read the original abstract

This study assesses the capability of ChatGPT to generate finite element code for geotechnical engineering applications from a set of prompts. We tested three different initial boundary value problems using a hydro-mechanically coupled formulation for unsaturated soils, including the dissipation of excess pore water pressure through fluid mass diffusion in one-dimensional space, time-dependent differential settlement of a strip footing, and gravity-driven seepage. For each case, initial prompting involved providing ChatGPT with necessary information for finite element implementation, such as balance and constitutive equations, problem geometry, initial and boundary conditions, material properties, and spatiotemporal discretization and solution strategies. Any errors and unexpected results were further addressed through prompt augmentation processes until the ChatGPT-generated finite element code passed the verification/validation test. Our results demonstrate that ChatGPT required minimal code revisions when using the FEniCS finite element library, owing to its high-level interfaces that enable efficient programming. In contrast, the MATLAB code generated by ChatGPT necessitated extensive prompt augmentations and/or direct human intervention, as it involves a significant amount of low-level programming required for finite element analysis, such as constructing shape functions or assembling global matrices. Given that prompt engineering for this task requires an understanding of the mathematical formulation and numerical techniques, this study suggests that while a large language model may not yet replace human programmers, it can greatly assist in the implementation of numerical models.

Figures

Figures reproduced from arXiv: 2501.02199 by the authors.

Figure 1
Figure 1. Schematic of geometry and boundary conditions for the numerical examples considered in this work: (a) [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Schematic representation of the workflow for GPT-based finite element implementation. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. GPT-based finite element code generation for Model Problem (1). (a) The initial prompts given to GPT; (b) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Exemplary prompt augmentation process for GPT-MATLAB for Model Problem (1). [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Comparison of the final numerical results from GPT-MALAB and GPT-FEniCS against the analytical solution. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Number of additional prompts required to pass the verification test for Model Problem (1). [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: The initial prompt given to GPT to generate mixed finite element code that can solve Model Problem (2). [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Number of additional prompts required to pass the verification test for Model Problem (2). [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Exemplary prompt augmentation process for GPT-FEniCS used to solve Model Problem (2). [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Numerical results from GPT-FEniCS after the (a) second and (b) third-round prompt augmentations, [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: The initial prompt given to GPT to generate mixed finite element code that can solve Model Problem (3). [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Number of additional prompts required to pass the validation test for Model Problem (3). [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 13
Figure 13. Figure 13: Exemplary prompt augmentation process for GPT-FEniCS used to solve Model Problem (3). [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]
Figure 14
Figure 14. Figure 14: Numerical results from GPT-FEniCS after the three consecutive prompt augmentations, compared to the [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.