Documents published in Scipedia

• A new approach to combine physics-based and data-driven models using a localised trustworthiness metric

  L. Bogaerts, A. Persoons, M. Faes, D. Moens

  WCCM2024.

  
  

  Abstract

  Artificial Neural Networks (ANNs) can solve many (un)supervised learning tasks by virtue of the universal approximation theorem. In the context of on-line process control for manufacturing processes, ANNs are an ideal approach for e.g., on-line monitoring or prediction tasks. However, since they are trained on experimental input-output pairs, the governing physical relations are only implicitly included. This, for instance, can cause inaccuracies when extrapolating to out-of-sample data-points [1]. On the other hand, the numerical approximation of the governing physical laws via numerical methods holds strong potential for the accurate simulation of physical phenomena that occur during manufacturing processes. However, the corresponding computational effort is an impediment that arises with the need for numerous simulations [2]. This makes the application of such numerical schemes computationally intractable within an on-line monitoring context. As such, it is clear that ANNs and numerical simulation models have strong potential, but are fundamentally different models. However, their combination serves as a potentially efficient and accurate aggregated predictor, the so called grey-box model. Such grey-box model is based on highly efficient machine learning algorithms, the black-box member, and backed by validated data with respect to physics generated by the numerical model, the white-box member. A grey-box model capable of defining a trustworthy prediction, including a measurement of uncertainty on the estimator, remains challenging.

  Abstract
  Artificial Neural Networks (ANNs) can solve many (un)supervised learning tasks by virtue of the universal approximation theorem. In the context of on-line process control [...]

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• Enhancing predictive modeling in reactor building dose distribution: A neural network-aided approach

  J. Liu, K. Koyamada, H. Natsukawa, S. Kamioka

  WCCM2024.

  
  

  Abstract

  Ensuring the safety of nuclear reactor decommissioning workers requires accurate, real-time predictions of radiation dose rates within reactor buildings. However, due to the complexity of these structures, such predictions are computationally intensive and time consuming. In this paper, we propose constructing a surrogate model using deep learning to predict radiation dose rates based on simulation results in a space containing a square pillar and a radiation source. The accuracy of the surrogate model's predictions was verified and visualized. Additionally, by applying the principle of superposition, we demonstrated that the distribution of radiation dose rates in spaces with a pillar and multiple radiation sources can be obtained by summing the surrogate model results for each radiation source. We also examined the application of the surrogate model to predicting radiation dose rates in spaces containing multiple square pillars and multiple radiation sources. This approach shows the potential for surrogate models to accurately and efficiently predict radiation dose rates in reactor buildings with complex structures and multiple radiation sources in real time.

  Abstract
  Ensuring the safety of nuclear reactor decommissioning workers requires accurate, real-time predictions of radiation dose rates within reactor buildings. However, due to the [...]

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• Fuzzy statistics-aided inference in experimental design

  R. Dwornicka, A. Gądek-Moszczak, R. Ulewicz, N. Radek

  WCCM2024.

  
  

  Abstract

  Conducting research based on active influence on the examined object or process requires distinguishing an explained quantity, measured quantitatively, the possible changes of which will be considered as influencing it through a group of quantities considered as explanatory quantities. This approach implicitly postulates the existence of a cause-and-effect relationship between the explanatory quantities and the explained quantity. In practice, especially industrial practice, explanatory quantities are often called controlled factors. Knowledge of possible cause-and-effect relationships can be graded, from the most comfortable situation of the existence of appropriate binding equations and their exact solutions, through the existence of binding equations but without knowing the exact solutions, to the absence of such equations. While in the first case, experimental research serves to refine the results originally calculated for idealized models, in the second case, it is a necessary stage of identifying the parameters of the postulated model, and in the third case, it is a necessary stage of collecting data for which the simplest possible forecasting model will be constructed

  Abstract
  Conducting research based on active influence on the examined object or process requires distinguishing an explained quantity, measured quantitatively, the possible changes [...]

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• Accurate solution of linear operator approximations using green's functions by a multi-level neural network approach

  Z. Aldirany, C. Bilodeau, R. Cottereau, M. Laforest

  WCCM2024.

  
  

  Abstract

  Lately, the approximation of operators for partial differential equations using deep learning has been extensively investigated. However, these deep learning approaches have limitations in terms of accuracy. In this work, we present a multi-level approach to accurately approximate linear operators using physics-informed Green operator networks. This method allows for the iterative reduction of the approximation errors through a sequence of operators, each targeting errors of increasing complexity at progressively smaller scales. Numerical examples for the one-dimensional Poisson problem will be presented to demonstrate the effectivenessof the proposed multi-level approach.

  Abstract
  Lately, the approximation of operators for partial differential equations using deep learning has been extensively investigated. However, these deep learning approaches have [...]

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• Symbolic regression via neural networks

  J. Moehlis, N. Boddupalli, T. Matchen

  WCCM2024.

  
  

  Abstract

  Mathematical models allow researchers to understand, analyze, and predict the behavior of systems of physical, biological, and technological interest, and are required for many techniques from dynamical systems and control theory to be used. Unfortunately, it is often impossible to derive mathematical models from first principles, and in such cases system identification is a powerful tool which can be used to deduce models from observed data. Many existing system identification techniques require pre-specification of a dictionary of possible terms in a mathematical model, limiting their ability to give models with the nonlinearities which can arise for biological and other complex systems. We present a methodology which overcomes this limitation by dynamically generating the terms in a model with the necessary complexity and nonlinearity to accurately describe a system’s dynamics. This uses a multilayered, operation-based symbolic regression approach, with the capacity to learn combinations and compositions of operations by training artificial neural networks. Our approach provides a powerful alternative to genetic programming strategies for symbolic regression, and can exploit many of the attractive features of artificial neural networks such as a straightforward learning strategy.

  Abstract
  Mathematical models allow researchers to understand, analyze, and predict the behavior of systems of physical, biological, and technological interest, and are required for [...]

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• Structural optimization through generative adversarial networks

  L. Pereira, L. Driemeier

  WCCM2024.

  
  

  Abstract

  The finite element method (FEM) is a well known approach to solve partial differential equations. It has important applications in structural engineering, such as in topology optimization (TO). TO involves, at each iteration, the solution of structural problems via FEM, which can add up to a high computational cost. Therefore, a line of research to accelerate TO emerged over the years focusing on machine learning (ML) approaches. Particularly, Artificial Neural Networks (ANNs) have been proposed to significantly speed-up the process by eliminating the iterative algorithm, which is intrinsic to TO. Since ANN is a supervised ML method, first a dataset is generated, containing finite element analysis (FEA) inputs, volume fraction, postprocessing, and final topologies. Then, with the Wasserstein Generative Adversarial Networks (WGANs) is trained on this dataset to map fields of physical quantities, such as the von Mises stress, to the final optimized structure. The final designs obtained via ML are quantitatively analyzed according to the metrics.

  Abstract
  The finite element method (FEM) is a well known approach to solve partial differential equations. It has important applications in structural engineering, such as in topology [...]

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• Data-driven modeling of complex mechanical components for integration in system-level simulations

  S. Vanpaemel, N. Kutz, S. Brunton

  WCCM2024.

  
  

  Abstract

  This contribution presents a data-driven approach featuring a physics-inspired neural network structure for modeling complex components in mecha(tro)nic systems. In the present approach, gated recurrent units (GRUs) are employed to approximate the ordinary differential equations (ODEs) describing the system’s states over time, followed by a deep feedforward neural network (FFNN) mapping these states to a target variable. The networks are shown to predict a latent space capable of modeling the underlying dynamics, without the need for measuring the full state vector and only relying on input-output measurements. Subsequently it is shown that a nonlinear coordinate transformation exists between the latent space of the network and the states obtained from the reference ODE integration (simulation). To have a verification of the network’s performance, it is applied to simulation-based data of an academic example for which the states and equations are known beforehand. Furthermore, the methodology is also applied to real measurement data from an INSTRON testing system capturing shock damper and bushing dynamic behaviour. Lastly, it is demonstrated that an ODE expression can be extracted from the trained network. This feature allows seamless integration of these networks into variable time-step, system-level simulation software.

  Abstract
  This contribution presents a data-driven approach featuring a physics-inspired neural network structure for modeling complex components in mecha(tro)nic systems. In the present [...]

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• Data-efficient one-step mechanical design of composites using generative AI

  M. Masrouri, Z. Qin

  WCCM2024.

  
  

  Abstract

  The distribution of material phases is crucial to determine the composite's mechanical properties. While the entire structure-mechanics relationship of highly ordered material distributions can be studied with a finite number of cases, this relationship is challenging to reveal for complex irregular distributions, preventing the design of such material structures from meeting specific mechanical requirements. The noticeable developments of artificial intelligence algorithms in material design enable the discovery of hidden structure-mechanics correlations, which is essential for designing composites of complex structures. It is intriguing how these tools can assist composite design. Here, we focus on the rapid generation of complex irregular composite structures and the stress distribution in loading. We find that generative AI, enabled through fine-tuned Low-Rank Adaptation models, can be trained with a few inputs to generate synthetic composite structures and the corresponding von Mises stress distribution. The results show that this technique is convenient in generating massive composite designs with useful mechanical information that dictates stiffness, fracture, and robustness of the material with one model, and such must be done by several different experimental or simulation tests. This research offers valuable insights for improving composite design to expand the design space and automatic screening of composite designs for improved mechanical functions.

  Abstract
  The distribution of material phases is crucial to determine the composite's mechanical properties. While the entire structure-mechanics relationship of highly ordered material [...]

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• A dynamic weighted loss function for enhancing the performance of neural networks

  C. Mang, A. Tahmasebi Moradi, D. Danan, M. Yagoubi

  WCCM2024.

  
  

  Abstract

  In machine learning process, hyper parameters are chosen in a way to decrease the prediction error and improve the convergence. However, the optimized hyper parameters have a limit in terms of enhancing the performance of the neural networks. In this work, the datasets used for the numerical experiments arise from the resolution of partial differential equations (PDE) defined on a spatial domain. We propose a DYNAmic WEIghted Loss (DYNAWEIL) function-based approach for neural networks that are used to learn these PDE’s solutions. This a two-step process: first we train for a few numbers of epochs in a classical way then the dynamic weighted loss function replaces the classical loss function by leveraging the information from past training error histories. To validate this method, we carry out numerical experiments with different neural networks on datasets arising on two different physics: Goldstein equation [1] and radiative transfer equation [2]. Thus, in order to demonstrate the relevance of this approach, we provide a comparison among a neural network model using a classical loss function, with and without hyper parameters optimization, and a dynamic weighted loss function for both versions.

  Abstract
  In machine learning process, hyper parameters are chosen in a way to decrease the prediction error and improve the convergence. However, the optimized hyper parameters have [...]

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• Prediction of unsteady heat transfer of temperature field on a circuit board using sub-voxels input data structure

  T. Tsukiji, Y. Wada, Y. Iwata, M. Irikiin

  WCCM2024.

  
  

  Abstract

  In this study, we propose a sub-voxel learning method based on a Neural Operator and predict the thermal temperature field on a circuit board in unsteady heat conduction. CAE analysis reduces the cost of experiments using prototypes in the design phase. However, the computational cost is high because the number of trials increases due to changes in analysis conditions. Predictions made by machine learning are less accurate than those made by CAE analysis, but they can significantly reduce computational costs. In general, machine learning is difficult to extrapolate. Thus, the concept of a Neural Operator has attracted attention as one machine learning method incorporating physical laws. In this study, we propose a sub-voxel learning method based on the Neural Operator, inspired by the forward Euler method, and predict the thermal temperature field on a circuit board during unsteady heat conduction. The input data is the analysis data of the current cycle step, and the output data is the data of the next cycle step. Dummy temperatures were set according to the heat generation of each IC in the input data of the 0th cycle step, and pseudo-difference values were generated to extract features. The prediction accuracy of the next cycle step was compared with and without dummy temperatures

  Abstract
  In this study, we propose a sub-voxel learning method based on a Neural Operator and predict the thermal temperature field on a circuit board in unsteady heat conduction. [...]

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