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REVIEW 3 major objections 5 minor 39 references

A two-phase neural pipeline finds V-beam geometries that hit a target displacement while minimizing stress and volume.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-14 16:27 UTC pith:WX3HC6JT

load-bearing objection Solid engineering application of a known forward-surrogate + GD inverse pattern to V-beam sensors, with honest failure analysis and FEA re-checks; the minimality claim is only partially validated. the 3 major comments →

arxiv 2607.09752 v1 pith:WX3HC6JT submitted 2026-07-04 eess.SP cs.AI

Data-Driven Forward and Inverse Modeling of V-Beam Thermal Sensors

Tudor Bartha , Radu Chiorean , Adrian Groza This is my paper
classification eess.SP cs.AI
keywords V-beam thermal sensorinverse designphysics-informed neural networkforward surrogate modelgradient-descent optimizationMEMSfinite-element analysisill-posed inverse problem
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Direct machine learning cannot invert a V-beam thermal sensor: many beam angles, lengths, and widths produce the same displacement under a temperature load, so regression collapses to constant predictions. The authors show this ill-posedness through five failed trials (random forests, expanded data, correlation checks, physics-penalized nets) and then reverse the direction of the problem. They train a neural forward model that maps geometry plus material constants to displacement, stress, and volume, freeze it, and run multi-restart gradient descent on the geometric parameters alone, driving displacement error, stress, and volume down together. On a 3000-sample finite-element dataset the best variant returns designs that, when re-simulated, match the target displacement with 4.76 percent mean absolute percentage error and place more than 70 percent of cases under the 5 percent engineering threshold. The practical payoff is a rapid, data-driven alternative to repeated finite-element redesign loops for thermal MEMS sensors.

Core claim

The inverse design of V-beam thermal sensors is ill-posed under direct regression, but becomes tractable once a neural network is trained only in the well-posed forward direction and then embedded, with frozen weights, inside a multi-restart gradient-descent loop that jointly matches a target displacement and minimizes stress and volume; the resulting geometries re-validated by finite-element analysis achieve 4.76 percent displacement MAPE, with 71.2 percent of designs under 5 percent error.

What carries the argument

Two-phase workflow: a physics-informed (or plain) multilayer perceptron that maps (β, l, w, ΔT, E, α) to (displacement, stress, volume), followed by multi-restart gradient descent on the geometric variables alone that minimizes a weighted sum of displacement mismatch, predicted stress, and predicted volume.

Load-bearing premise

A neural surrogate trained only on randomly sampled finite-element runs—most of them low-displacement—is accurate enough that geometries optimized against the frozen surrogate stay valid when re-checked by full simulation and, by implication, for real devices.

What would settle it

Fabricate a set of the optimized V-beam sensors and measure their actual displacement under the design temperature; if measured errors systematically exceed the reported 4.76 percent MAPE, the surrogate-based claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper addresses inverse design of V-beam thermal sensors: given target displacement and ΔT, recover beam angle β, length l and width w that also minimize volume and max stress. Direct multi-output regression fails because the map is many-to-one. After five exploratory trials (RF, expanded data, correlation analysis, custom-loss GeometryNet), the authors adopt a two-phase pipeline: (i) train a forward NN/PINN that maps (β,l,w,ΔT,E,α) to (displacement, stress, volume) on a 3000-sample ANSYS FEA set, and (ii) freeze the network and run multi-restart gradient descent on the geometric variables under the composite loss of Eq. (6). Four forward variants are compared; the best inverse designs, when re-simulated in FEA, yield 4.76 % displacement MAPE with 71.2 % of cases under 5 % error (PINN_FILTER, Table IV).

Significance. If the reported FEA-validated accuracy holds, the work supplies a practical, low-cost surrogate for an otherwise expensive multiphysics design loop and documents a transparent failure analysis of direct inverse regression. Strengths include public data/code, systematic ablation of MLP vs PINN and filtered vs unfiltered training, and—most importantly—the external FEA re-run check that breaks pure surrogate circularity. The contribution is applied rather than methodological; its value for MEMS design practice is real provided the joint stress/volume optimality claim can be substantiated.

major comments (3)
  1. [§IV.C, Table IV, Eq. (6)] Table IV and §IV.C report only displacement error of the re-simulated geometries. The central claim is that the GD solutions simultaneously minimize stress and volume. No comparison is given against other FEA-feasible geometries that meet the same displacement target (or against a direct FEA optimizer). Without such a check, the “minimum-stress, minimum-volume” assertion remains unverified; the surrogate may simply return a local argmin of its own stress/volume surfaces.
  2. [§II.5, Table III–IV] The training distribution is heavily skewed (2726/3000 samples with displacement < 0.15 µm, §II.5). Filtering at 0.15 µm improves inverse MAPE (Table IV) but further restricts the domain. The paper should quantify how surrogate accuracy and the quality of the recovered optima degrade outside the dense region, or enlarge the design-of-experiments coverage before claiming general utility.
  3. [§IV.A–B, Eqs. (2)–(4), Fig. 5] Analytical formulas used as soft PINN targets exhibit 27.91 % displacement MAPE and 21.63 % stress MAPE on the same data (Fig. 5, §IV.A). While the authors note that qualitative trends are preserved, the magnitude of the discrepancy raises the possibility that the physics residual systematically biases the learned gradients. A sensitivity study on λ (or an ablation that removes the physics term entirely for the inverse stage) is needed to confirm that the PINN advantage is not an artifact of this mismatch.
minor comments (5)
  1. [Table I] Table I lists Displacement as an “Input” and β,l,w as “Outputs,” which matches the inverse view but confuses the forward-model description that follows. Clarify roles per phase.
  2. [Table I, Fig. 1] Units for displacement appear as µm while beam lengths are given in mm; a brief consistency note would help readers.
  3. [Eq. (6)–(7)] The inverse loss weights λ2=λ3=0.001 are stated without justification or sensitivity analysis; a short ablation would strengthen reproducibility.
  4. [throughout] Several typographical issues: “V olume” spacing, “sensordisplacement” concatenation, and inconsistent capitalization of model names (MLP FILTER vs MLP_FILTER).
  5. [Fig. 6, Table II] Figure 6 is referenced as the MLP_FILTER architecture but the caption and surrounding text do not state whether residual connections or batch-norm are present; a one-line architectural summary would suffice.

Circularity Check

1 steps flagged

No major circularity: inverse geometries are re-validated by independent FEA re-runs (Table IV), breaking surrogate self-consistency; only mild non-load-bearing self-citation of co-author analytical formulas as optional PINN soft targets.

specific steps
  1. self citation load bearing [Section IV.A (Analytical Formulas) and IV.B (PINN loss Eqs. 2–4)]
    "The analytical formulas presented in [6] have a reported accuracy of under 6%. However, testing has been performed on only 12 structures... The MAPE of the formula for sensor displacement is of 27.91%... The results guide towards the usage of the formulas as a soft constraint in the loss function of the PINN... L_PINN = L_data + λ · L_physics ... L_physics = 1/N ∑ ||f_θ(x̃_i) − ỹ_analytical,i||²"

    The soft physics target inside the best-reported forward model (PINN_FILTER) is taken from analytical expressions whose sole citation is co-author Chiorean’s prior paper [6]. The present work itself demonstrates those expressions are inaccurate (27.91% MAPE), yet still inserts them into the loss that shapes the surrogate later used for inverse GD. This is a mild self-referential element, not a full reduction of the main claim (FEA re-runs remain independent and MLP without physics also works).

full rationale

The derivation chain is standard surrogate-based inverse design, not circular by construction. A forward NN/PINN is trained on 3000 FEA samples to map (β,l,w,ΔT,E,α) → (displacement, stress, volume); weights are frozen; multi-restart GD then optimizes geometry variables under the composite loss of Eq. (6) to hit a target displacement while softly minimizing predicted stress/volume. Success is not scored against the frozen surrogate alone: optimized geometries are re-simulated in ANSYS FEA and displacement MAPE is reported (Table IV, best 4.76% for PINN_FILTER with 71.2% of cases <5%). This external check prevents the classic fitted-surrogate-as-prediction loop. Direct inverse regression trials (Sections III.A–D) correctly failed due to ill-posedness and were abandoned. The sole mild issue is the optional physics term in the PINN loss (Eqs. 2–4), which soft-targets analytical formulas from co-author Chiorean [6]; the paper itself measures those formulas at 27.91% displacement MAPE (Section IV.A, Fig. 5) yet still uses them. This is ordinary self-citation of prior work by an overlapping author and is not load-bearing—the MLP variants without physics also produce usable inverse designs, and final claims rest on FEA re-runs rather than the analytical expressions. No self-definitional identities, no uniqueness theorems imported from the authors, no ansatz smuggled as theorem, and no renaming of known results appear. Score 2 reflects only that residual self-citation; the central two-phase claim remains independently supported by the FEA validation loop.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 1 invented entities

The central claim rests on FEA as ground truth, a randomly sampled and skewed geometry dataset, hand-chosen inverse and PINN loss weights, and soft use of approximate analytical formulas. No new physical entities are postulated; the method reuses standard NNs, PINN soft constraints, and gradient descent. Free parameters and domain assumptions dominate the ledger; independent physical evidence is absent.

free parameters (5)
  • inverse loss weights λ1, λ2, λ3 = 1, 0.001, 0.001
    Set by hand to 1, 0.001, 0.001 to balance displacement fit against stress and volume; no systematic sensitivity study reported.
  • PINN physics weight λ
    Relative weight of analytical soft constraint in L_PINN = L_data + λ L_physics; must be >0 but specific tuned value not fixed in text.
  • displacement filter threshold 0.15 µm = 0.15 µm
    Post-hoc training filter for FILTER models that drops high-displacement samples; chosen from observed skew rather than physical bound.
  • GD restarts and iteration budget = 10 restarts × 1000 iters
    10 independent random restarts, up to 1000 iterations each; chosen to reduce local minima without proof of global optimality.
  • NN architecture and training hyperparameters = e.g. MLP_FILTER 512→256→128, dropout 0.1, LR 1e-3, batch 128
    Hidden widths, dropout, LR, batch size selected by grid search over 60 combinations per model family; free design choices that affect reported MAPE.
axioms (5)
  • domain assumption ANSYS FEA under uniform thermal load is an accurate enough ground truth for displacement, max stress, and volume of the V-beam sensor.
    Entire dataset and re-validation loop treat FEA outputs as labels; no experimental calibration is provided (Sections II, IV.C).
  • ad hoc to paper Analytical formulas from Chiorean et al. [6], despite 27.91% displacement MAPE and 21.63% stress MAPE on this dataset, still capture correct qualitative trends and are useful as soft PINN constraints.
    Section IV.A explicitly notes large MAPE yet proceeds to use the formulas in L_physics.
  • domain assumption The inverse map from (displacement, ΔT) to (β, l, w) is ill-posed with multiple geometries per target, so direct multi-output regression cannot recover a unique minimum-stress/volume design.
    Motivated by correlation analysis and scatter plots in Section III.C; underpins abandoning direct inverse models.
  • domain assumption Random sampling of β∈[10,40]°, l∈[20,35] mm, w∈[1,2] mm and ΔT∈[20,70] K adequately covers the design space of interest.
    Dataset construction in Section II; authors note non-uniform displacement distribution as a limitation.
  • standard math Standard supervised learning assumptions (i.i.d. train/val/test split, MSE/MAPE as fidelity metrics, Adam with weight decay and early stopping) suffice for a reliable surrogate.
    Training protocol in Section IV.B.
invented entities (1)
  • GeometryNet (custom multi-output inverse network with composite physics penalties) no independent evidence
    purpose: Early failed attempt to predict (β,l,w) directly with MSE plus analytical volume/stress penalties.
    Named architecture in Section III.D; not retained in the final pipeline and has no independent evidence outside this study.

pith-pipeline@v1.1.0-grok45 · 13039 in / 3844 out tokens · 47280 ms · 2026-07-14T16:27:56.462102+00:00 · methodology

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read the original abstract

This paper presents a machine learning framework for data-driven inverse design of V-beam thermal sensors. The goal is to determine the optimal sensor geometry: beam inclination angle, beam length and beam width that achieves a target displacement under a given temperature. The design should also provide the geometry with minimum structure volume and minimum mechanical stress the sensor must support. This problem is ill-posed as for a given displacement there are multiple possible geometric configurations, causing direct regression methods to fail. We document a series of five exploratory trials that progressively revealed the nature of the problem culminating in a two-phase solution: a neural network forward model trained to map geometry and material constants to sensor responses, a gradient-descent inverse optimization over the frozen forward model, minimizing stress and volume simultaneously. The proposed pipeline utilizes a 3000-sample dataset and achieves a MAPE of 4.76% for predicting the displacement, more than 70% of predictions having MAPE of under 5%.

Figures

Figures reproduced from arXiv: 2607.09752 by Adrian Groza, Radu Chiorean, Tudor Bartha.

Figure 1
Figure 1. Figure 1: V-beam thermal sensor response and geometrical parameters [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pearson correlation matrix Three-dimensional scatter plots of ∆T and displacement colored by each geometric parameter revealed no structured mapping. For the same value of ∆T and displacement there were many values of β, l and w present. This confirmed the ill-posed nature of direct inverse regression and motivated a fundamental rethinking of the approach [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 3D scatter plot of Beam width by ∆T and displacement close to the target displacement. The best results came from a combination where the weights of the value and stress were only around 0.15 each, while the fit weight 0.7. This provided MAE of around 12%. However, this result was deceptive as the NN always predicted a constant value (the mean) and because of the data distribution it seemed to give good re… view at source ↗
Figure 4
Figure 4. Figure 4: Error vs sensor displacement IV. TWO-PHASE WORKFLOW The failure of direct inverse regression motivated a two￾phase strategy that sidesteps the ill-posedness by working in the forward direction. A. Analytical Formulas The analytical formulas presented in [6] have a reported accuracy of under 6%. However, testing has been performed on only 12 structures and this leads to the need of performing further resear… view at source ↗
Figure 5
Figure 5. Figure 5: Analytical formulas analysis [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: MLP FILTER Forward Neural Network Architecture loss function chosen for this model is MSE - trying to be as close as possible to the ground truth. MSE = 1 n Xn i=1 (yi − yˆi) 2 (1) • MLP_FILTER - the same model as before, but this time training is performed on a filtered dataset and only includes samples that have sensordisplacement ∈ (0, 0.15). This is done in order to eliminate the outlier high-displacem… view at source ↗

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Reference graph

Works this paper leans on

39 extracted references · 3 linked inside Pith

  1. [1]

    A high force low area mems thermal actuator,

    M. J. Sinclair, “A high force low area mems thermal actuator,” inITHERM 2000. The Seventh Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (Cat. No. 00CH37069), vol. 1. IEEE, 2000, pp. 127–132

    2000

  2. [2]

    L. M. Phinney, M. S. Baker, J. R. Serrano, and I. Nazul,Thermal microactuators. InTech, 2012

    2012

  3. [3]

    Macro modeling of v-shaped electro-thermal mems actuator with human error factor,

    D. Zhang, A. Cai, Y . Zhao, and T. Hu, “Macro modeling of v-shaped electro-thermal mems actuator with human error factor,”Micromachines, vol. 12, no. 6, p. 622, 2021

    2021

  4. [4]

    Iterative learning control for v-shaped electrothermal microactuator,

    N. T. Dzung, P. H. Phuc, N. Q. Dich, and N. D. Phuoc, “Iterative learning control for v-shaped electrothermal microactuator,”Electronics, vol. 8, no. 12, p. 1410, 2019

    2019

  5. [5]

    Fabrication and characterization of high-sensitivity, wide- range, and flexible mems thermal flow velocity sensors,

    M. Li, G. Qin, C. Jia, D. Zhang, Z. Li, X. Han, S. Xu, L. Zhao, G. Luo, C. Liuet al., “Fabrication and characterization of high-sensitivity, wide- range, and flexible mems thermal flow velocity sensors,”Microsystems & Nanoengineering, vol. 10, no. 1, p. 102, 2024

    2024

  6. [6]

    Analytical and numerical study on the maximum force developed by a v-beam thermal actuator,

    R. S. Chiorean, M. C. Dudescu, M. Pustan, and M. Hardau, “Analytical and numerical study on the maximum force developed by a v-beam thermal actuator,”Procedia Technology, vol. 12, pp. 359–363, 2014

    2014

  7. [7]

    Physics- informed neural networks (pinns) for fluid mechanics: A review,

    S. Cai, Z. Mao, Z. Wang, M. Yin, and G. E. Karniadakis, “Physics- informed neural networks (pinns) for fluid mechanics: A review,”Acta Mechanica Sinica, vol. 37, no. 12, pp. 1727–1738, 2021

    2021

  8. [8]

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

    M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” Journal of Computational physics, vol. 378, pp. 686–707, 2019

    2019

  9. [9]

    Machine learning-based inverse design for functional materials: Methods, challenges, and engineering applications,

    W. Lin, L. Jin, Z. Jiang, M. Cai, Z. Lai, D. Yurchenko, B. Yan, S. Zhou, K. S. Novoselov, W.-H. Liaoet al., “Machine learning-based inverse design for functional materials: Methods, challenges, and engineering applications,”Advanced Functional Materials, p. e75070, 2026

    2026

  10. [10]

    Machine learning-based inverse design methods considering data characteristics and design space size in materials design and manufacturing: a review,

    J. Lee, D. Park, M. Lee, H. Lee, K. Park, I. Lee, and S. Ryu, “Machine learning-based inverse design methods considering data characteristics and design space size in materials design and manufacturing: a review,” Materials horizons, vol. 10, no. 12, pp. 5436–5456, 2023

    2023

  11. [11]

    Multilayer perceptron and neural networks,

    M.-C. Popescu, V . E. Balas, L. Perescu-Popescu, and N. Mastorakis, “Multilayer perceptron and neural networks,”WSEAS transactions on circuits and systems, vol. 8, no. 7, pp. 579–588, 2009

    2009

  12. [12]

    Solving ill-posed inverse problems using iterative deep neural networks,

    J. Adler and O. ¨Oktem, “Solving ill-posed inverse problems using iterative deep neural networks,”Inverse Problems, vol. 33, no. 12, p. 124007, 2017

    2017

  13. [13]

    H. W. Engl and C. W. Groetsch,Inverse and ill-posed problems. Elsevier, 2014, vol. 4

    2014

  14. [14]

    An overview of gradient descent optimization algorithms,

    S. Ruder, “An overview of gradient descent optimization algorithms,” arXiv preprint arXiv:1609.04747, 2016

    Pith/arXiv arXiv 2016

  15. [15]

    Machine learning and computation-enabled intelligent sensor design,

    Z. Ballard, C. Brown, A. M. Madni, and A. Ozcan, “Machine learning and computation-enabled intelligent sensor design,”Nature Machine Intelligence, vol. 3, no. 7, pp. 556–565, 2021

    2021

  16. [16]

    Machine learning predictive models for mineral prospectivity: An evaluation of neural networks, random forest, regres- sion trees and support vector machines,

    V . Rodriguez-Galiano, M. Sanchez-Castillo, M. Chica-Olmo, and M. Chica-Rivas, “Machine learning predictive models for mineral prospectivity: An evaluation of neural networks, random forest, regres- sion trees and support vector machines,”Ore geology reviews, vol. 71, pp. 804–818, 2015

    2015

  17. [17]

    Cira guide to custom loss functions for neural networks in environmental sciences–version 1,

    I. Ebert-Uphoff, R. Lagerquist, K. Hilburn, Y . Lee, K. Haynes, J. Stock, C. Kumler, and J. Q. Stewart, “Cira guide to custom loss functions for neural networks in environmental sciences–version 1,”arXiv preprint arXiv:2106.09757, 2021

    Pith/arXiv arXiv 2021

  18. [18]

    Finite element method: an overview,

    V . Jagota, A. P. S. Sethi, and K. Kumar, “Finite element method: an overview,”Walailak Journal of Science and Technology (WJST), vol. 10, no. 1, pp. 1–8, 2013

    2013

  19. [19]

    Artificial intelligence and machine learning in design of mechanical materials,

    K. Guo, Z. Yang, C.-H. Yu, and M. J. Buehler, “Artificial intelligence and machine learning in design of mechanical materials,”Materials Horizons, vol. 8, no. 4, pp. 1153–1172, 2021

    2021

  20. [20]

    Definitions and examples of inverse and ill- posed problems,

    S. I. Kabanikhinet al., “Definitions and examples of inverse and ill- posed problems,”J. Inverse Ill-Posed Probl, vol. 16, no. 4, pp. 317–357, 2008

    2008

  21. [21]

    Overview of inverse problems,

    P. Argoul, “Overview of inverse problems,” Ph.D. dissertation, Modes, 2012

    2012

  22. [22]

    Tikhonov regularization for large scale problems,

    G. H. Golub 1 and U. V on Matt, “Tikhonov regularization for large scale problems,” inScientific Computing: Proceedings of the Workshop, 10-12 March 1997, Hong Kong. Springer Science & Business Media, 1998, p. 3

    1997

  23. [23]

    Nanophotonic particle simulation and inverse design using artificial neural networks,

    J. Peurifoy, Y . Shen, L. Jing, Y . Yang, F. Cano-Renteria, B. G. DeLacy, J. D. Joannopoulos, M. Tegmark, and M. Solja ˇci´c, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Science advances, vol. 4, no. 6, p. eaar4206, 2018

    2018

  24. [24]

    A survey on deep learning tools dealing with data scarcity: definitions, challenges, solutions, tips, and applications,

    L. Alzubaidi, J. Bai, A. Al-Sabaawi, J. Santamar ´ıa, A. S. Albahri, B. S. N. Al-Dabbagh, M. A. Fadhel, M. Manoufali, J. Zhang, A. H. Al-Timemyet al., “A survey on deep learning tools dealing with data scarcity: definitions, challenges, solutions, tips, and applications,” Journal of Big Data, vol. 10, no. 1, p. 46, 2023

    2023

  25. [25]

    Mesh-free surrogate models for structural mechanic fem simulation: A comparative study of approaches,

    J. G. Hoffer, B. C. Geiger, P. Ofner, and R. Kern, “Mesh-free surrogate models for structural mechanic fem simulation: A comparative study of approaches,”Applied Sciences, vol. 11, no. 20, p. 9411, 2021

    2021

  26. [26]

    A survey of optimization methods from a machine learning perspective,

    S. Sun, Z. Cao, H. Zhu, and J. Zhao, “A survey of optimization methods from a machine learning perspective,”IEEE transactions on cybernetics, vol. 50, no. 8, pp. 3668–3681, 2019

    2019

  27. [27]

    Incorporating nesterov momentum into adam,

    T. Dozat, “Incorporating nesterov momentum into adam,” 2016

    2016

  28. [28]

    Inverse optimization: Theory and applications,

    T. C. Chan, R. Mahmood, and I. Y . Zhu, “Inverse optimization: Theory and applications,”Operations Research, vol. 73, no. 2, pp. 1046–1074, 2025

    2025

  29. [29]

    A proposed iteration optimiza- tion approach integrating backpropagation neural network with genetic algorithm,

    H.-X. Huang, J.-C. Li, and C.-L. Xiao, “A proposed iteration optimiza- tion approach integrating backpropagation neural network with genetic algorithm,”Expert Systems with Applications, vol. 42, no. 1, pp. 146– 155, 2015

    2015

  30. [30]

    Beeby,MEMS mechanical sensors

    S. Beeby,MEMS mechanical sensors. Artech House, 2004

    2004

  31. [31]

    Choudhary and K

    V . Choudhary and K. Iniewski,Mems: fundamental technology and applications. CRC Press, 2017

    2017

  32. [32]

    Mems design and verification,

    T. Mukherjee, “Mems design and verification,” inINTERNATIONAL TEST CONFERENCE, 2003, pp. 681–690

    2003

  33. [33]

    Deflection de- termination of v-beam thermal sensors using digital image correlation,

    R. Chiorean, C. Dudescu, M. Pustan, and M. H ˘ard˘au, “Deflection de- termination of v-beam thermal sensors using digital image correlation,” Key engineering materials, vol. 601, pp. 41–44, 2014

    2014

  34. [34]

    M. K. Thompson and J. M. Thompson,ANSYS mechanical APDL for finite element analysis. Butterworth-Heinemann, 2017

    2017

  35. [35]

    Learning surrogate models for simulation-based optimization,

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

    2014

  36. [36]

    Electro-thermal dynamics in mems with v- beam actuators,

    EMWorks, “Electro-thermal dynamics in mems with v- beam actuators,” https://www.emworks.com/application/ electro-thermal-dynamics-in-mems-with-v-beam-actuators, 2026, accessed: 2026-06-04

    2026

  37. [37]

    Leakage in data mining: Formulation, detection, and avoidance,

    S. Kaufman, S. Rosset, C. Perlich, and O. Stitelman, “Leakage in data mining: Formulation, detection, and avoidance,”ACM Transactions on Knowledge Discovery from Data (TKDD), vol. 6, no. 4, pp. 1–21, 2012

    2012

  38. [38]

    Adam: A method for stochastic optimization,

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980, 2014

    Pith/arXiv arXiv 2014

  39. [39]

    Alloygraph: A knowledge-graph-grounded multi-agent system for nickel-based super- alloy design,

    A. Lecu, L. Hawizy, S. Birosca, and A. Groza, “Alloygraph: A knowledge-graph-grounded multi-agent system for nickel-based super- alloy design,”Available at SSRN 7022006