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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Predicting the Non-Deterministic Response of a Micro-Scale Mechanical Model Using Generative Adversarial Networks.

Albert Argilaga1, Duanyang Zhuang1,2

  • 1MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058, China.

Materials (Basel, Switzerland)
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Summary

Machine learning (ML) models, specifically Generative Adversarial Networks (GANs), can now predict non-deterministic micro-scale geomechanical responses. This data-driven approach significantly reduces computational costs in multiscale modeling.

Keywords:
Gaussian Process RegressionGenerative Adversarial NetworksSelf-Organizing Mapasymptotic homogenizationconstitutive lawmachine learningmicro-scale

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Area of Science:

  • Geomechanics
  • Computational Material Science
  • Machine Learning

Background:

  • Advanced micro-scale material descriptions enhance geomechanical multiscale models but increase computational expense.
  • The non-deterministic nature of micro-scale responses presents a significant challenge for surrogate modeling.
  • Existing machine learning algorithms struggle to integrate non-determinism in material response prediction.

Purpose of the Study:

  • To investigate the feasibility of training machine learning algorithms using micro-scale data for cost-effective geomechanical response prediction.
  • To develop a surrogate model capable of capturing the non-deterministic behavior of micro-scale material responses.

Main Methods:

  • A data-driven approach was employed to train various machine learning algorithms, including Gaussian Process Regression (GPR), Self-Organizing Maps (SOM), and Generative Adversarial Networks (GANs).
  • Generative Adversarial Networks (GANs) were selected due to superior performance in reproducing non-deterministic micro-scale responses.
  • A modified GAN architecture with reduced network depth was specifically tested for generating failure probability maps.

Main Results:

  • Generative Adversarial Networks (GANs) demonstrated superior performance in learning and predicting non-deterministic micro-scale material responses compared to GPR and SOM.
  • A modified, shallower GAN architecture effectively generated failure probability maps, accurately capturing the inherent non-determinism.
  • The trained GAN generator showed potential for integration into existing multiscale models.

Conclusions:

  • Machine learning, particularly GANs, offers a viable solution to reduce the computational burden of micro-scale simulations in geomechanics.
  • The developed GAN-based surrogate model can partially replace costly physics-based micro-scale computations within multiscale frameworks.
  • This approach enables more efficient and refined geomechanical multiscale modeling by leveraging micro-scale data.