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arxiv: 1907.03560 · v1 · pith:2CC2OMTZnew · submitted 2019-07-01 · 📡 eess.IV

Variational Auto-Encoder Based Approximate Bayesian Computation Uncertian Inverse Method for Sheet Metal Forming Problem

Jiaquan Wang , Yang Zeng , Xinchao Jiang , Hu Wang , Enying Li , Guangyao Li This is my paper

Pith reviewed 2026-05-25 11:51 UTC · model grok-4.3

classification 📡 eess.IV
keywords variational auto-encoderapproximate Bayesian computationsheet metal formingparameter identificationinverse methodLSSVR surrogatelatent variablesimage-assisted inference
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The pith

A variational auto-encoder supplies summary statistics for approximate Bayesian computation to identify material and process parameters in sheet metal forming from images.

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

The paper proposes combining a variational auto-encoder with approximate Bayesian computation to identify design parameters in sheet metal forming problems using image data. By mapping images to a low-dimensional latent space, the VAE provides summary statistics that minimize information loss while controlling computational cost. A least squares support vector regression model then links parameters to these latent variables, allowing efficient comparison in the ABC framework. This approach is demonstrated on a sheet forming problem where both material and process parameters are recovered. A sympathetic reader would care because it offers a systematic way to handle inverse problems in manufacturing where direct observation of parameters is difficult but image responses are available.

Core claim

The proposed method maps images to latent variables via VAE for use as summary statistics in ABC, constructs the parameter-latent relationship with LSSVR, and determines parameters by comparing simulated and observed coefficient vectors, showing feasibility for identifying material and process parameters in sheet forming.

What carries the argument

VAE latent variables used as summary statistics in ABC, supported by an LSSVR surrogate that maps design parameters to simulation coefficient vectors

If this is right

  • The method achieves an effective trade-off between information loss and computational cost by using trained VAE latent variables.
  • It overcomes the difficulty of selecting summary statistics in ABC for image-based problems.
  • Processing images directly as the objective function captures response results effectively for practical engineering cases.
  • The identified material parameters of the blank and process parameters of the forming process demonstrate the method on a real sheet forming problem.

Where Pith is reading between the lines

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

  • The same latent-variable replacement for summary statistics could apply to other manufacturing inverse problems that produce image responses.
  • The LSSVR surrogate step might allow the approach to scale to parameter spaces with more variables than direct ABC sampling permits.
  • If the VAE is trained on a broader set of forming images, the method could support parameter identification across different materials or geometries without retraining the full pipeline.

Load-bearing premise

The VAE latent variables retain enough information about the forming response that ABC can reliably distinguish correct from incorrect parameter sets.

What would settle it

Generate synthetic image data from a known set of true material and process parameters, run the full VAE-ABC-LSSVR pipeline, and check whether the resulting posterior concentrates around the known true values.

read the original abstract

In this study, an image-assisted Approximate Bayesian Computation (ABC) parameter inverse method is proposed to identify the design parameters. In the proposed method, the images are mapped to a low-dimensional latent space by Variational Auto-Encoder (VAE), and the information loss is minimized by network training. Therefore, an effective trade-off between information loss and computational cost can be achieved by using the latent variables of VAE as summary statistics of ABC, which overcomes the difficulty of selecting summary statistics in the ABC. Besides, for some practical engineering problems, processing the images as objective function can effective show the response result. Meanwhile, the relationship between design parameters and the latent variables is constructed by Least Squares Support Vector Regression (LSSVR) surrogate model. With the well-constructed LSSVR model, the simulation coefficient vectors under given parameters will be determined effectively. Then, the parameters to be identified are determined by comparing the simulated and observed coefficient vectors in ABC. Finally, a sheet forming problem is investgated by the suggested method. The material parameters of the blank and the process parameters of the forming process are identified. Results show that the method is feasibility and effective for the identification of sheet forming parameters.

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.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The method implicitly assumes that VAE training converges to a useful latent space and that LSSVR generalizes, but these are not quantified.

pith-pipeline@v0.9.0 · 5762 in / 1124 out tokens · 29332 ms · 2026-05-25T11:51:57.597877+00:00 · methodology

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Works this paper leans on

64 extracted references · 64 canonical work pages · 1 internal anchor

  1. [1]

    Experimental Mechanics, 2008

    Cooreman, S., et al., Identification of mechanical material behavior through inverse modeling and DIC. Experimental Mechanics, 2008. 48(4): p. 421-433

    work page 2008

  2. [2]

    Computational Materials Science, 2014

    Sun, G., et al., Determination of mechanical properties of the weld line by combining micro-indentation with inverse modeling. Computational Materials Science, 2014. 85: p. 347-362

    work page 2014

  3. [3]

    Eggertsen, P.-A. and K. Mattiasson, An efficient inverse approach for material hardening parameter identification from a three-point bending test. Engineering with Computers, 2010. 26(2): p. 159-170

    work page 2010

  4. [4]

    BelHadjSalah, and R

    Aguir, H., H. BelHadjSalah, and R. Hambli, Parameter identification of an elasto-plastic behaviour using artificial neural networks –genetic algorithm method. Materials & Design, 2011. 32(1): p. 48-53

    work page 2011

  5. [5]

    Zhu, and Y

    Yu, M., P. Zhu, and Y . Ma, Identification of the interface properties of hollow spheres filled syntactic foams: An inverse strategy combining microstructural modeling with Kriging metamodel. Composites Science and Technology, 2013. 74: p. 179-185

    work page 2013

  6. [6]

    Materials Science and Engineering: A, 2011

    Moy, C.K.S., et al., Identification of the material properties of Al 2024 alloy by means of inverse analysis and indentation tests. Materials Science and Engineering: A, 2011. 529: p. 119-130

    work page 2024

  7. [7]

    Coleman, H.W. and W.G. Steele, Experimentation, validation, and uncertainty analysis for engineers. 2018: John Wiley & Sons

    work page 2018

  8. [8]

    Babuška, I. and R.S. Silva, Dealing with uncertainties in engineering problems using only available data. Computer Methods in Applied Mechanics and Engineering, 2014. 270: p. 57-75

    work page 2014

  9. [9]

    A new methodology for the estimation of total uncertainty in computational simulation

    Oberkampf, W., et al. A new methodology for the estimation of total uncertainty in computational simulation . in 40th Structures, Structural Dynamics, and Materials Conference and Exhibit. 1999

    work page 1999

  10. [10]

    International journal for numerical methods in engineering, 2010

    Galbally, D., et al., Non‐linear model reduction for uncertainty q uantification in large‐scale inverse problems. International journal for numerical methods in engineering, 2010. 81(12): p. 1581-1608

    work page 2010

  11. [11]

    Nenarokomov, and A.F

    Fadale, T.D., A.V . Nenarokomov, and A.F. Emery, Uncertainties in parameter estimation: the inverse problem. International Journal of Heat and Mass Transfer, 1995. 38(3): p. 511-518

    work page 1995

  12. [12]

    Savchuk, V . and C.P. Tsokos, Bayesian theory and methods with applications . V ol. 1. 2011: Springer Science & Business Media

    work page 2011

  13. [13]

    Yang, and C.L

    Yan, L., F.L. Yang, and C.L. Fu, A new numerical method for the inverse source problem from a Bayesian perspective. International Journal for Numerical Methods in Engineering, 2015. 85(11): p. 1460-1474

    work page 2015

  14. [14]

    Journal of Sound & Vibration, 2010

    Nichols, J.M., et al., A Bayesian approach to identifying structural nonlinearity using free -decay respons e: Application to damage detection in composites. Journal of Sound & Vibration, 2010. 329(15): p. 2995-3007

    work page 2010

  15. [15]

    Murphy, and J.M

    Moore, E.Z., K.D. Murphy, and J.M. Nichols, Crack identification in a freely vibrating plate using Bayesian parameter estimation. Mechanical Systems & Signal Processing, 2011. 25(6): p. 2125-2134

    work page 2011

  16. [16]

    Venkataraman, and A

    Campillo-Funollet, E., C. Venkataraman, and A. Madzvamuse, A Bayesian approach to parameter identification with an application to Turing systems. 2016

    work page 2016

  17. [17]

    Mechanical Systems & Signal Processing, 2015

    Zhang, W., et al., A hybrid parameter identification method based on Bayesian approach and interval analysis for uncertain structures. Mechanical Systems & Signal Processing, 2015. 60-61: p. 853-865

    work page 2015

  18. [18]

    Liu, P. and S.K. Au, Bayesian parameter identification of hysteretic behavior of composite walls. Probabilistic Engineering Mechanics, 2013. 34(34): p. 101 - 109

    work page 2013

  19. [19]

    Molecular Biology & Evolution, 19 99

    Pritchard, J.K., et al., Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Molecular Biology & Evolution, 19 99. 16(12): p. 1791-1798

    work page

  20. [20]

    Turner, B.M. and T.V . Zandt, A tutorial on approximate Bayesian computation. Journal of Mathematical Psychology, 2012. 56(2): p. 69-85

    work page 2012

  21. [21]

    Fearnhead, P. and D. Prangle, Constructing Summary Statistics for Approximate Bayesian Computation: Semi-automatic ABC. Journal of the Royal Statistical Society, 2011. 74(3): p. 419-474

    work page 2011

  22. [22]

    W, and B

    MA, B., Z. W, and B. DJ, Approximate Bayesian computation in population genetics. Genetics, 2002. 162(4): p. 2025-2035

    work page 2002

  23. [23]

    Joyce, P. and P. Marjoram, Approximately sufficient statis tics and bayesian computation. Stat Appl Genet Mol Biol, 2008. 7(1): p. Article26

    work page 2008

  24. [24]

    Leuenberger, and L

    Wegmann, D., C. Leuenberger, and L. Excoffier, Efficient approximate Bayesian computation coupled with Markov chain Monte Carlo without likelihood. Genetics, 2009. 182(4): p. 1207-1218

    work page 2009

  25. [25]

    Blum, M.G.B. and O. François, Non-linear regression models for Approximate Bayesian Computation. Statistics and Computing, 2010. 20(1): p. 63-73

    work page 2010

  26. [26]

    Statistics, 2015

    Prangle, D., Summary Statistics in Approximate Bayesia n Computation. Statistics, 2015. 9279: p. 50-61

    work page 2015

  27. [27]

    Kingma, D.P. and M. Welling, Auto-Encoding Variational Bayes. 2013

    work page 2013

  28. [28]

    Li, P., et al., Salience Estimation via Variational Auto -Encoders for Multi - Document Summarization. 2017

    work page 2017

  29. [29]

    Plis, and V .C

    Hjelm, R.D., S.M. Plis, and V .C. Calhoun, Variational Autoencoders for Feature Detection of Magnetic Resonance Imaging Data. 2016

    work page 2016

  30. [30]

    Pekhovsky, T. and M. Korenevsky, Investigation of Using VAE for i -V ector Speaker Verification. 2017

    work page 2017

  31. [31]

    Variational Gaussian Process Auto-Encoder for Ordinal Prediction of Facial Action Units

    Eleftheriadis, S., et al. Variational Gaussian Process Auto-Encoder for Ordinal Prediction of Facial Action Units . in Asian Conference on Computer Vision . 2016

    work page 2016

  32. [32]

    Suykens, J.A.K. and J. Vandewalle, Least Squares Support Vector Machine Classifiers. 1999: Kluwer Academic Publishers. 293-300

    work page 1999

  33. [33]

    Proceedings of the National Academy of Sciences of the United States of America, 2003

    Marjoram, P., et al., Markov Chain Monte Carlo without Likelihoods. Proceedings of the National Academy of Sciences of the United States of America, 2003. 100(26): p. 15324-15328

    work page 2003

  34. [34]

    Statistics & Computing, 2012

    Moral, P.D., An adaptive sequential Monte Carlo method for approxima te Bayesian computation. Statistics & Computing, 2012. 22(5): p. 1009-1020

    work page 2012

  35. [35]

    Y , and T

    SA, S., F. Y , and T. MM, Sequential Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences of the United States of America, 2007. 104(6): p. 1760-1765

    work page 2007

  36. [36]

    Jones, M.C. and A. Pewsey, Adaptive approximate Bayesian computation. Biometrika, 2009. 96(4): p. 983-990

    work page 2009

  37. [37]

    Journal of the Royal Society Interface, 2009

    Toni, T., et al., Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface, 2009. 6(31): p. 187-202

    work page 2009

  38. [38]

    Yang, Z., Reanalysis based Approximate Bayesian Computation for Inverse Heat Conduction Problem. 2017

    work page 2017

  39. [39]

    Liu, and Z

    Zhang, Q., Y . Liu, and Z. Zhang, A new optimization method for sheet metal forming processes ba sed on an iterative learning control model. The International Journal of Advanced Manufacturing Technology, 2016. 85(5-8): p. 1063-1075

    work page 2016

  40. [40]

    Li, and Q

    Sun, G., G. Li, and Q. Li, Variable fidelity design based surrogate and artificial bee colony algorithm for sheet m etal forming process. Finite Elements in Analysis and Design, 2012. 59: p. 76-90

    work page 2012

  41. [41]

    Materials & Design, 2010

    Sun, G., et al., Multiobjective robust optimization method for drawbead design in sheet metal forming. Materials & Design, 2010. 31(4): p. 1917-1929

    work page 2010

  42. [42]

    Herdy, and M

    Jakumeit, J., M. Herdy, and M. Nitsche, Parameter optimization of the sheet metal forming process using an iterative parallel Kriging algorithm. Structural and Multidisciplinary Optimization, 2005. 29(6): p. 498-507

    work page 2005

  43. [43]

    Peng, C. -Y . and C.J. Wu, On the choice of nugget in kriging modeling for deterministic computer experiments. Journal of Computational and Graphical Statistics, 2014. 23(1): p. 151-168

    work page 2014

  44. [44]

    Journal of Offshore Mechanics and Arctic Engineering, 2016

    Chen, J., et al., Flexible riser configuration design for extremely shallow water with surrogate-model-based optimization. Journal of Offshore Mechanics and Arctic Engineering, 2016. 138(4): p. 041701

    work page 2016

  45. [45]

    Optimization for Stamping Process Parameters of Front Fender Based on Numerical Simulation Technology

    Liu, Z.F., et al. Optimization for Stamping Process Parameters of Front Fender Based on Numerical Simulation Technology. in Advanced Materials Research

    work page

  46. [46]

    Journal of Central South University,

    Zhou, J., et al., Multi-objective optimization of stamping forming process of head using Pareto-based genetic algorithm. Journal of Central South University,

    work page

  47. [47]

    The i nverse approach and mathematica l programming techniques for optimum design of sheet forming parts

    Barlet, O., et al. The i nverse approach and mathematica l programming techniques for optimum design of sheet forming parts. in ASME. 1996

    work page 1996

  48. [48]

    Chinese Journal of Mechanical Engineering, 2015

    Dong, G., et al., Hot granules medium pressure forming process of AA7075 conical parts. Chinese Journal of Mechanical Engineering, 2015. 28(3): p. 580- 591

    work page 2015

  49. [49]

    Computers & Structures, 2005

    Breitkopf, P., et al., Moving least squares response surface approximation: Formulation and metal forming applications. Computers & Structures, 2005. 83(17-18): p. 1411-1428

    work page 2005

  50. [50]

    Doersch, C., Tutorial on Variational Autoencoders. 2016

    work page 2016

  51. [51]

    Severyn , and E

    Semeniuta, S., A. Severyn , and E. Barth, A Hybrid Convolutional Variational Autoencoder for Text Generation. 2017

    work page 2017

  52. [52]

    Inoue, T., et al., Transfer learning from synthetic to real images using variational autoencoders for robotic applications. 2017

    work page 2017

  53. [53]

    Bourinet, and T

    Steiner, M., J.M. Bourinet, and T. Lahmer, An adaptive sampling method for global sensitivity analysis based on least -squares support vector regression. Reliability Engineering & System Safety, 2019. 183: p. 323-340

    work page 2019

  54. [54]

    Chinese Journal of Mechanical Engineering, 2017

    Wang, H., et al., Sheet metal forming optimization by using surrogate modeling techniques. Chinese Journal of Mechanical Engineering, 2017. 30(1): p. 22-36

    work page 2017

  55. [55]

    Marciniak, and J

    Hu, J., Z. Marciniak, and J. Duncan, Mechanics of sheet metal forming . 2002: Elsevier

    work page 2002

  56. [56]

    Chinese Journal of Mechanical Engineering, 2015

    Teng, F., et al., Springback prediction and optimization of variable stretch force trajectory in three -dimensional stretch bending process. Chinese Journal of Mechanical Engineering, 2015. 28(6): p. 1132-1140

    work page 2015

  57. [57]

    Cui, and J

    Wei, D., Z. Cui, and J. Chen, Optimization and tolerance prediction of sheet metal forming process using response surface model. Computational Materials Science, 2008. 42(2): p. 228-233

    work page 2008

  58. [58]

    Ioffe, S. and C. Szegedy, Batch normalization: accelerating deep network training by reducing internal covariate shift , in Proceedings of the 3 2nd International Conference on International Conference on Machine Learning - Volume 37. 2015, JMLR.org: Lille, France. p. 448-456

    work page 2015

  59. [59]

    Wang, and X

    Li, Y ., H. Wang, and X. Deng, Image-based reconstruction for a 3D-PFHS heat transfer problem by ReConNN. International Journal of Heat and Mass Transfer,

    work page

  60. [60]

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

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  61. [61]

    Tieleman, T. and G. Hinton, Lecture 6.5-rmsprop: Divide the gradient by a running av erage of its recent magnitude. COURSERA: Neural networks for machine learning, 2012. 4(2): p. 26-31

    work page 2012

  62. [62]

    Nigam, and E

    Hadgu, A.T., A. Nigam, and E. Diaz-Aviles. Large-scale learning with AdaGrad on Spark. in 2015 IEEE International Conference on Big Data (Big Data). 2015. IEEE

    work page 2015

  63. [63]

    IEEE Trans Image Process, 2004

    Zhou, W., et al., Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process, 2004. 13(4): p. 600-612

    work page 2004

  64. [64]

    Ma, and M.H

    Yang, C.Y ., C. Ma, and M.H. Yang. Single-Image Super -Resolution: A Benchmark. in European Conference on Computer Vision. 2014

    work page 2014