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REVIEW 5 major objections 5 minor 44 references

Predicting Wall Thickness Changes in Cold Forging Processes: An Integrated FEM and Neural Network approach

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A graph neural network predicts tube wall thickness changes in nosing as accurately as FEM, at a fraction of the cost.

desk verdict The paper has a real engineering use case and a plausible surrogate, but the headline claim—that separate edge encoders are better—is never tested against the shared-encoder baseline. read the letter →

arxiv 2411.13366 v2 pith:GD2MMKCQ submitted 2024-11-20 cs.LG

Sasa Ilic , Abdulkerim Karaman , Johannes Pöppelbaum , Jan Niclas Reimann , Michael Marré , Andreas Schwung This is my paper · ORCID
classification cs.LG
keywords coldforgingnosingprocessgraphneuralnetworksurrogatemodelfiniteelementmethodwallthicknesspredictionareabetweencurvesreal-timecontrol
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

The paper claims that a purpose-built graph neural network can replace slow finite-element simulations for predicting wall thickness changes in the cold nosing of tubes, with accuracy close to the FEM reference and runtime reduced from about 301 minutes to roughly 3.5 minutes on a GPU. It argues that because nosing involves three distinct contact mechanisms—deformation inside the tube, contact between tube and die, and contact between stamp and tube—the network should use a separate encoder for each interaction type, with edges dynamically added as parts come into contact. The authors also introduce a metric, the area between thickness curves (ABTC), that quantifies how well a predicted wall-thickness profile matches the FEM profile along the tube. If the claim holds, such surrogates could run inside closed-loop production control, where traditional FEM is too slow.

What carries the argument

The central mechanism is a graph neural network with three edge sets and corresponding encoders: internal tube edges model material deformation, dynamic edges between tube and die model forming contact, and dynamic edges between stamp and tube model axial feed. Node encoders include mesh connectivity, positions, and a solid/deformable flag; edge features include relative Cartesian coordinates, Euclidean distance, and the friction coefficient. A shared message-passing processor with k=15 steps updates node features, and a decoder outputs the per-node displacement Δp = $p^{{t+1}}$ − p^t; the trajectory is generated by forward integration. The paper extends the mesh-graph-network baseline by splitting the single edge encoder into three interaction-specific encoders, which is what makes the nosing-specific physics learnable.

What would settle it

Run instrumented physical nosing trials on CuZn39Pb2 tubes spanning the parameter grid (φ from 0.05 to 0.35, α from 5° to 25°, μ = 0.05 and 0.2), measure wall-thickness profiles along the tube after forming, and compare them with both the FEM and the GNN rollouts using the ABTC metric; if the FEM itself deviates substantially from the measured profiles, or if the GNN's ABTC relative to the FEM is much larger than the values reported in Table 3 on the same scale, the surrogate's accuracy claim fails.

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Extended reading notes

Core claim

The core discovery is that a graph-neural-network surrogate—built on an encode-process-decode one-step predictor with three specialized edge encoders (tube-internal, tube-die, tube-stamp) and dynamic distance-based edge insertion—can reproduce the FEM-computed mesh deformation and wall-thickness evolution of a CuZn39Pb2 tube during die nosing. Trained on 207,778 FEM timesteps covering variations in forming degree φ, die opening angle α, and Coulomb friction μ, and tested on 48,045 held-out timesteps, the network rolls out 4,500 steps and matches the FEM thickness profiles well, with deviations concentrated at the collar region that leaves the die and with no catastrophic error growth. The network has 2.88 million trainable parameters and runs the full simulation in about 3.5 minutes on a GPU versus 301 minutes for FEM on a CPU. The authors additionally show that the model learns contact genuinely: when the die is moved out of contact, no forming occurs.

Load-bearing premise

The load-bearing premise is that the FEM simulation itself faithfully represents the real nosing process for CuZn39Pb2 tubes; the network is trained and evaluated only against FEM output, and the authors state that comparison with a real experimental setup is future work.

Editorial extensions

If this is right

  • If the model generalizes as claimed, real-time monitoring and closed-loop control of nosing processes become feasible, since a full 4,500-step rollout takes minutes on a GPU rather than hours on a CPU.
  • The separation of edge types suggests a design recipe for surrogate models of other forging and forming operations with multiple contacting tools: encode each distinct contact pair separately.
  • The ABTC metric gives a physically interpretable error measure for wall-thickness predictions and could become a standard for comparing forming surrogates.
  • The step-size ablation shows that larger time steps are only slightly worse, so the surrogate could be run with coarser steps, trading a little accuracy for additional speed.
  • The model's recovery from initial rollout deviations means short-horizon errors do not necessarily compound into failure over a full forming cycle.

Reading between the lines

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

  • The same encoder-splitting architecture could be extended to other tube-forming operations such as expanding, necking with a mandrel, or flow forming by adding edge types for the new tool contacts, and to different materials by adding material parameters as node or edge features.
  • Because the model is trained only on FEM data, its practical value depends on FEM fidelity; a physical validation campaign comparing measured wall-thickness profiles to both FEM and GNN outputs would be the decisive test, and the ABTC metric could be reused as the evaluation measure.
  • The noisy predictions at high deformation degrees (φ = 0.35) suggest the dataset's edge-of-distribution region is a bottleneck; adding training simulations near process limits or using uncertainty-aware predictors could improve reliability where failures such as buckling are most likely.
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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

5 major / 5 minor

Summary. The paper proposes a graph neural network (GNN) surrogate for finite element method (FEM) simulations of tube nosing in cold forging. It first presents a domain analysis and a 2D axisymmetric FEM model to study how the deformation degree, die opening angle, and friction coefficient affect wall thickness. The GNN follows the encode-process-decode framework of Pfaff et al. but introduces separate edge encoders for three interaction types (tube–tube, tube–die, tube–stamp) with dynamically added contact edges, and a new evaluation metric called the area between thickness curves (ABTC). The model is trained on multi-step rollout targets from FEM and tested on nine held-out parameter configurations, showing visually plausible mesh predictions and thickness profiles that track FEM results, with a considerable computation-time reduction compared with FEM. The authors conclude that the separation of edge types into dedicated encoders improves accuracy and enables real-time process use.

Significance. If the central claims are substantiated, this work would be a useful contribution to surrogate modeling in metal forming, offering a domain-tuned GNN architecture and a concrete evaluation metric (ABTC) for comparing thickness profiles. The paper provides a reasonably thorough FEM preprocessing study, a pragmatic use of dynamic edges for contact, and a clear speed comparison. The ABTC metric is a sensible addition for this application. However, the main advertised novelty—the multi-encoder separation—is not tested against a shared-encoder baseline, and the evaluation omits variance measures, full-profile reporting, and experimental validation. The work is therefore promising but currently does not establish its central architectural claim.

major comments (5)
  1. [Section 5 and Section 4.3] The conclusion states that "the separation of edge types into their corresponding encoders resulted in more accurate models," but no experiment in the paper tests this assertion against the single-encoder baseline of [35] or any equivalent shared-encoder architecture. The ablation studies in Section 4.3 cover step width, removal of die contact, and full-dataset rollouts, but none isolates the effect of the proposed multi-encoder design. Since this separation is the main architectural novelty advertised in the abstract and introduction, the central claim is currently unsupported. Please add a controlled comparison, e.g., the proposed architecture vs. a GraphNet with a single shared edge encoder, on the same training/testing split and metrics.
  2. [Section 4.2.1, Figure 16] The wall-thickness evaluation is truncated at 0.8 relative tube length, which is precisely where the model is reported to show its largest deviations (the collar/funnel region). The authors state that the prediction "tends to deviate at the beginning of the tube" and that the deviation occurs in the collar area, yet the quantitative ABTC results in Table 3 and Figure 20 appear to be computed on the truncated profiles. To avoid overstating accuracy, please present the full thickness profiles or explicitly justify why the excluded region is irrelevant to downstream process-monitoring tasks, and report ABTC on the full tube length as a secondary result.
  3. [Table 4] The execution-time comparison is not rigororous because the FEM and NN timings are measured on different hardware (FEM on an Intel Core i9-7980XE with GTX 1070; NN on an Intel Core i7-11700 with RTX 5000). The claimed speedup is therefore confounded by hardware differences. Please report timings on matched hardware, or at least provide per-simulation-step timings, CPU-only and GPU-only results, and state the assumptions that make the comparison meaningful.
  4. [Section 2.2.3, Section 4.3.3] The test set consists of only nine hand-picked configurations, and all reported ABTC and RMSE values appear to be single deterministic rollouts. Because the model includes noise injection during training and random initialization, repeated runs will produce different results. Please report means and standard deviations over multiple training seeds and/or multiple rollouts for the test configurations, so the generalization claims in Section 4.3.3 are supported statistically.
  5. [Section 5] The paper correctly lists comparison with real experimental setups as future work, but the abstract and introduction frame the surrogate as predicting wall thickness changes in nosing processes generally. The GNN is trained and evaluated only against FEM output, so its accuracy is contingent on the validity of the FEM model (2D axisymmetric assumption, Hollomon flow-curve parameters, Coulomb friction model, and material database). Please add an explicit scope statement that the surrogate is a model of the specific FEM setup, and discuss how FEM discretization and constitutive-model uncertainties might affect the predicted thickness profiles in real production.
minor comments (5)
  1. [Section 3.2, Eq. (9)] In the sentence "Within the processor, f d, f d, f p and f n are also MLPs," the second "f d" should be "f t"; the equation itself correctly uses f^d, f^t, f^p, and f^n.
  2. [Section 2.2.1] There are typos: "rigit element" should be "rigid element," "visibible" should be "visible," and "paramters" should be "parameters."
  3. [Figure 15] The legend labels "ground truth, tube, die" do not indicate which colors correspond to predicted versus ground-truth tube and die. Please clarify the color/line mapping in the caption.
  4. [Section 4.4] The phrase "the general different is still big enough" should read "the general difference is still big enough." Also, the hardware comparison is described only in the text; a supplementary table listing CPU/GPU models, memory, and software versions would improve reproducibility.
  5. [Data and Code Availability] The manuscript states "Data availability: Not applicable" and "Code availability: Not applicable." For a machine-learning paper with a custom dataset and architecture, providing the FEM dataset, preprocessing scripts, and model code would greatly strengthen reproducibility and should be considered.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the GNN surrogate is trained and evaluated against FEM outputs as an external target, and the missing single-encoder baseline is an experimental gap, not a circular argument.

full rationale

The paper's central derivation chain is supervised surrogate modeling: the GNN takes mesh node positions and edge features from FEM simulations as inputs and is trained to predict one-step node displacements, with held-out FEM parameter configurations used as test data. This is standard learning against an external target, not a reduction of the prediction to its own inputs. The wall-thickness claims are evaluated with the proposed ABTC metric and rollouts, and the reported accuracy is an empirical result rather than a definitional consequence. The main architectural claim, that separating edge-type encoders improves accuracy, is asserted in the conclusion but is not tested against a shared-encoder baseline in the Section 4.3 ablations; however, this is a missing experiment, not a circular step. The only self-citations ([26], [27]) appear in related-work descriptions of GNN usage and carry no load in the derivation. No equation defines the predicted quantity in terms of itself, no fitted parameter is renamed as a prediction, and no load-bearing result is imported solely from the authors' own prior work. Thus, no significant circularity is present; the relevant limitation is external experimental validation, which the authors acknowledge as future work.

Assumptions & free parameters 5 free parameters · 6 assumptions · 1 invented entities

The central modeling burden is placed on FEM-generated data. The model parameters are standard hyperparameters chosen by hand rather than derived from theory, and the key domain assumptions are the validity of the FEM model and the chosen evaluation window.

free parameters (5)
  • contact radius r = 0.8 mm
    Hyperparameter controlling dynamic edge insertion between tube and die or stamp meshes; set by hand in Section 3.4.3.
  • number of message passing steps k = 15
    Processor depth chosen in Section 3.4.1.
  • encoder and processor hidden size = 128
    MLP width for all encoders and processor blocks, Section 3.4.1.
  • training noise scale factor = 1e-3
    Rollout stabilization noise multiplier, Section 3.4.3.
  • initial learning rate = 1e-4 with decay to 1e-5
    Adam optimizer settings, Section 3.4.3.
assumptions (6)
  • domain assumption FEM simulation is an accurate ground truth for the real nosing process.
    No experimental validation is provided; the authors state that comparing FEM with real setups is future work (Section 5).
  • domain assumption The 2D axisymmetric FEM model captures the relevant physics of nosing.
    The simulation uses a 2D axisymmetric plane instead of a 3D body, justified by radial symmetry (Section 2.2.1), but no experimental check is reported.
  • domain assumption The material model for CuZn39Pb2 (Hollomon parameters C=794.965 MPa, n=0.334) is valid for the process.
    Properties come from the Simufact material database and are not independently measured here (Section 2.2.1).
  • domain assumption Evaluation up to 0.8 relative tube length is representative of production-relevant errors.
    Section 4.2.1 truncates the thickness plots because the tube has left the die contact region, which also excludes the collar region where the model deviates most.
  • domain assumption The hand-picked test configurations represent the parameter space fairly.
    Table 2 shows a small, non-random held-out set; several parameter combinations were excluded because the FEM produced out-of-spec workpieces.
  • domain assumption The proposed ABTC metric is a valid measure of prediction quality.
    ABTC is introduced in Section 3.3.2 and used throughout the evaluation, but its validity is not compared with other metrics or external benchmarks.
invented entities (1)
  • Area Between Thickness Curves (ABTC) metric
    purpose: Evaluation metric to quantify the difference between predicted and FEM wall-thickness profiles.
    Defined and used only in this paper; no external validation or established benchmark yet, so it does not yet provide independent evidence.

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Cite this review

Pith. "Pith review of Predicting Wall Thickness Changes in Cold Forging Processes: An Integrated FEM and Neural Network approach." pith.science (2026). https://pith.science/paper/GD2MMKCQ

@misc{pith2026241113366,
  author       = {Pith},
  title        = {Pith review of: Predicting Wall Thickness Changes in Cold Forging Processes: An Integrated FEM and Neural Network approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GD2MMKCQ}},
  note         = {Machine review of arXiv:2411.13366}
}
read the original abstract

This study presents a novel approach for predicting wall thickness changes in tubes during the nosing process. Specifically, we first provide a thorough analysis of nosing processes and the influencing parameters. We further set-up a Finite Element Method (FEM) simulation to better analyse the effects of varying process parameters. As however traditional FEM simulations, while accurate, are time-consuming and computationally intensive, which renders them inapplicable for real-time application, we present a novel modeling framework based on specifically designed graph neural networks as surrogate models. To this end, we extend the neural network architecture by directly incorporating information about the nosing process by adding different types of edges and their corresponding encoders to model object interactions. This augmentation enhances model accuracy and opens the possibility for employing precise surrogate models within closed-loop production processes. The proposed approach is evaluated using a new evaluation metric termed area between thickness curves (ABTC). The results demonstrate promising performance and highlight the potential of neural networks as surrogate models in predicting wall thickness changes during nosing forging processes.

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Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.