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Computation
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Synergy between Multiphysics/Multiscale Modeling and Machine Learning
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Synergy between Multiphysics/Multiscale Modeling and Machine Learning

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Engineering".

Deadline for manuscript submissions: closed (15 December 2024) | Viewed by 3270

Special Issue Editor

Prof. Dr. Adnan Ibrahimbegovic

E-Mail Website
Guest Editor
Center for Research Royallieu, UTC, 60200 Compiegne, France
Interests: computational solid mechanics; computational structural mechanics; computational fluid mechanics; multi-scale and multi-physics problem; combined mechanics-probability

Special Issue Information

Dear Colleagues,

The proposed special issue aims to explore recent advancements in mechanics and applied mathematics within the dynamic research area of multi-scale modeling and computations applied to various domains, including solids, fluids, structures, systems, and multi-physics problems. A key objective of this thematic issue is to investigate the synergies between traditional multi-physics/multi-scale methodologies and model construction techniques utilizing machine learning algorithms. Drawing upon the expertise of computational mechanics specialists, this special issue endeavors to identify efficient reduced models developed with appropriate assumptions and kinematic constraints. Additionally, classical structural models are highlighted for their utility in constructing relevant multi-scale and multi-physics models. Concurrently, there is a burgeoning interest in leveraging Artificial Intelligence (AI) and statistical data analysis algorithms, including machine learning approaches, for mechanics modeling. How can these approaches be harmonized? Can they leverage each other's advancements? Can model construction proficiency be simplified to the application of AI algorithms?

Therefore, the special issue also welcomes submissions from the fields of aerospace engineering, civil engineering, mechanical engineering, materials science, and applied mathematics for the design and analysis of numerical algorithms.

Prof. Dr. Adnan Ibrahimbegovic
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Computation is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • heterogeneous materials
  • complex structures
  • multibody systems
  • machine learning
  • biomechanics
  • material and structure failures
  • adaptive modeling
  • mechanics of porous media
  • fluid-structure interaction
  • multi-phase flows
  • wave propagation
  • stochastic processes
  • uncertainty propagation

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

24 pages, 1543 KiB  
Article
Stochastic Up-Scaling of Discrete Fine-Scale Models Using Bayesian Updating
by Muhammad Sadiq Sarfaraz, Bojana V. Rosić and Hermann G. Matthies
Computation 2025, 13(3), 68; https://doi.org/10.3390/computation13030068 - 7 Mar 2025
Viewed by 500
Abstract
In this work, we present an up-scaling framework in a multi-scale setting to calibrate a stochastic material model. In particular with regard to application of the proposed method, we employ Bayesian updating to identify the probability distribution of continuum-based coarse-scale model parameters from [...] Read more.
In this work, we present an up-scaling framework in a multi-scale setting to calibrate a stochastic material model. In particular with regard to application of the proposed method, we employ Bayesian updating to identify the probability distribution of continuum-based coarse-scale model parameters from fine-scale measurements, which is discrete and also inherently random (aleatory uncertainty) in nature. Owing to the completely dissimilar nature of models for the involved scales, the energy is used as the essential medium (i.e., the predictions of the coarse-scale model and measurements from the fine-scale model) of communication between them. This task is realized computationally using a generalized version of the Kalman filter, employing a functional approximation of the involved parameters. The approximations are obtained in a non-intrusive manner and are discussed in detail especially for the fine-scale measurements. The demonstrated numerical examples show the utility and generality of the presented approach in terms of obtaining calibrated coarse-scale models as reasonably accurate approximations of fine-scale ones and greater freedom to select widely different models on both scales, respectively. Full article
(This article belongs to the Special Issue Synergy between Multiphysics/Multiscale Modeling and Machine Learning)
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24 pages, 12859 KiB  
Article
A DNN-Based Surrogate Constitutive Equation for Geometrically Exact Thin-Walled Rod Members
by Marcos Pires Kassab, Eduardo de Morais Barreto Campello and Adnan Ibrahimbegovic
Computation 2025, 13(3), 63; https://doi.org/10.3390/computation13030063 - 3 Mar 2025
Viewed by 501
Abstract
Kinematically exact rod models were a major breakthrough to evaluate complex frame structures undergoing large displacements and the associated buckling modes. However, they are limited to the analysis of global effects, since the underlying kinematical assumptions typically take into account only cross-sectional rigid-body [...] Read more.
Kinematically exact rod models were a major breakthrough to evaluate complex frame structures undergoing large displacements and the associated buckling modes. However, they are limited to the analysis of global effects, since the underlying kinematical assumptions typically take into account only cross-sectional rigid-body motion and ocasionally torsional warping. For thin-walled members, local effects can be notably important in the overall behavior of the rod. In the present work, high-fidelity simulations using elastic 3D-solid finite elements are employed to provide input data to train a Deep Neural Newtork-(DNN) to act as a surrogate model of the rod’s constitutive equation. It is capable of indirectly representing local effects such as web/flange bending and buckling at a stress-resultant level, yet using only usual rod degrees of freedom as inputs, given that it is trained to predict the internal energy as a function of generalized rod strains. A series of theoretical constraints for the surrogate model is elaborated, and a practical case is studied, from data generation to the DNN training. The outcome is a successfully trained model for a particular choice of cross-section and elastic material, that is ready to be employed in a full rod/frame simulation. Full article
(This article belongs to the Special Issue Synergy between Multiphysics/Multiscale Modeling and Machine Learning)
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29 pages, 481 KiB  
Article
Reduced-Order Models and Conditional Expectation: Analysing Parametric Low-Order Approximations
by Hermann G. Matthies
Computation 2025, 13(2), 58; https://doi.org/10.3390/computation13020058 - 19 Feb 2025
Viewed by 241
Abstract
Systems may depend on parameters that can be controlled, serve to optimise the system, are imposed externally, or are uncertain. This last case is taken as the “Leitmotiv” for the following discussion.A reduced-order model is produced from the full-order model through some kind [...] Read more.
Systems may depend on parameters that can be controlled, serve to optimise the system, are imposed externally, or are uncertain. This last case is taken as the “Leitmotiv” for the following discussion.A reduced-order model is produced from the full-order model through some kind of projection onto a relatively low-dimensional manifold or subspace. The parameter-dependent reduction process produces a function mapping the parameters to the manifold.One now wants to examine the relation between the full and the reduced state for all possible parameter values of interest. Similarly, in the field of machine learning, a function mapping the parameter set to the image space of the machine learning model is learned from a training set of samples, typically minimising the mean square error. This set may be seen as a sample from some probability distribution, and thus the training is an approximate computation of the expectation, giving an approximation of the conditional expectation—a special case of Bayesian updating, where the Bayesian loss function is the mean square error. This offers the possibility of having a combined view of these methods and also of introducing more general loss functions. Full article
(This article belongs to the Special Issue Synergy between Multiphysics/Multiscale Modeling and Machine Learning)
24 pages, 5846 KiB  
Article
Enhanced Drag Force Estimation in Automotive Design: A Surrogate Model Leveraging Limited Full-Order Model Drag Data and Comprehensive Physical Field Integration
by Kalinja Naffer-Chevassier, Florian De Vuyst and Yohann Goardou
Computation 2024, 12(10), 207; https://doi.org/10.3390/computation12100207 - 16 Oct 2024
Cited by 2 | Viewed by 1571
Abstract
In this paper, a novel surrogate model for shape-parametrized vehicle drag force prediction is proposed. It is assumed that only a limited dataset of high-fidelity CFD results is available, typically less than ten high-fidelity CFD solutions for different shape samples. The idea is [...] Read more.
In this paper, a novel surrogate model for shape-parametrized vehicle drag force prediction is proposed. It is assumed that only a limited dataset of high-fidelity CFD results is available, typically less than ten high-fidelity CFD solutions for different shape samples. The idea is to take advantage not only of the drag coefficients but also physical fields such as velocity, pressure, and kinetic energy evaluated on a cutting plane in the wake of the vehicle and perpendicular to the road. This additional “augmented” information provides a more accurate and robust prediction of the drag force compared to a standard surface response methodology. As a first step, an original reparametrization of the shape based on combination coefficients of shape principal components is proposed, leading to a low-dimensional representation of the shape space. The second step consists in determining principal components of the x-direction momentum flux through a cutting plane behind the car. The final step is to find the mapping between the reduced shape description and the momentum flux formula to achieve an accurate drag estimation. The resulting surrogate model is a space-parameter separated representation with shape principal component coefficients and spatial modes dedicated to drag-force evaluation. The algorithm can deal with shapes of variable mesh by using an optimal transport procedure that interpolates the fields on a shared reference mesh. The Machine Learning algorithm is challenged on a car concept with a three-dimensional shape design space. With only two well-chosen samples, the numerical algorithm is able to return a drag surrogate model with reasonable uniform error over the validation dataset. An incremental learning approach involving additional high-fidelity computations is also proposed. The leading algorithm is shown to improve the model accuracy. The study also shows the sensitivity of the results with respect to the initial experimental design. As feedback, we discuss and suggest what appear to be the correct choices of experimental designs for the best results. Full article
(This article belongs to the Special Issue Synergy between Multiphysics/Multiscale Modeling and Machine Learning)
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