Nonlinear Regression Operating on Microstructures Described from Topological Data Analysis for the Real-Time Prediction of Effective Properties

Yun, Minyoung; Argerich, Clara; Duval, Jean‐Louis; Chinesta, Francisco

doi:10.3390/ma13102335

Cited by 12 publications

(14 citation statements)

References 18 publications

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“…At first glance, principal component analysis (PCA) [ 47 , 48 ] appears to be meaningless for our case, because there are no linear dependencies among the inputs that could be easily eliminated. PCA of linearly independent inputs simply translates the original inputs into a smaller number of components by linear combination.…”

Section: Macroscopic Compressionmentioning

confidence: 99%

A Strategy for Dimensionality Reduction and Data Analysis Applied to Microstructure–Property Relationships of Nanoporous Metals

Huber

2021

Materials

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Nanoporous metals, with their complex microstructure, represent an ideal candidate for the development of methods that combine physics, data, and machine learning. The preparation of nanporous metals via dealloying allows for tuning of the microstructure and macroscopic mechanical properties within a large design space, dependent on the chosen dealloying conditions. Specifically, it is possible to define the solid fraction, ligament size, and connectivity density within a large range. These microstructural parameters have a large impact on the macroscopic mechanical behavior. This makes this class of materials an ideal science case for the development of strategies for dimensionality reduction, supporting the analysis and visualization of the underlying structure–property relationships. Efficient finite element beam modeling techniques were used to generate ~200 data sets for macroscopic compression and nanoindentation of open pore nanofoams. A strategy consisting of dimensional analysis, principal component analysis, and machine learning allowed for data mining of the microstructure–property relationships. It turned out that the scaling law of the work hardening rate has the same exponent as the Young’s modulus. Simple linear relationships are derived for the normalized work hardening rate and hardness. The hardness to yield stress ratio is not limited to 1, as commonly assumed for foams, but spreads over a large range of values from 0.5 to 3.

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Section: Macroscopic Compressionmentioning

confidence: 99%

A Strategy for Dimensionality Reduction and Data Analysis Applied to Microstructure–Property Relationships of Nanoporous Metals

Huber

2021

Materials

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“…Ultimately, training, validation and test data sets consisted of 3102, 376 and 376 patterns, respectively. Scaling of inputs and outputs was executed to remain in value ranges of [−1, 1] and [1,5], respectively. The corrected residual stresses are obtained by solving Equation (2) with respect to absolute values σ i ana,j .…”

Section: Data Preparationmentioning

confidence: 99%

“…Likewise, early stopping is implemented to avoid overfitting during training. Normalization of inputs to [−1, 1] and outputs to [1,5] is performed, as for the hybrid model.…”

Section: Setup Of Purely Data-driven Ann As Benchmarkmentioning

confidence: 99%

“…In this domain, the application of machine learning techniques can be a key enabler for accelerated identification, characterization, understanding and optimization of processes, materials and parameters [ 2 ]. For instance, unique material descriptors can be qualified and quantified for material characterization [ 3 , 4 , 5 ]. Optimization and rapid design of novel manufacturing methods and involved materials [ 6 , 7 ] can be achieved, and inaccurate measurement techniques can be corrected [ 8 ].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Modelling by Machine Learning Corrections of Analytical Model Predictions towards High-Fidelity Simulation Solutions

et al. 2021

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Within the fields of materials mechanics, the consideration of physical laws in machine learning predictions besides the use of data can enable low prediction errors and robustness as opposed to predictions only based on data. On the one hand, exclusive utilization of fundamental physical relationships might show significant deviations in their predictions compared to reality, due to simplifications and assumptions. On the other hand, using only data and neglecting well-established physical laws can create the need for unreasonably large data sets that are required to exhibit low bias and are usually expensive to collect. However, fundamental but simplified physics in combination with a corrective model that compensates for possible deviations, e.g., to experimental data, can lead to physics-based predictions with low prediction errors, also despite scarce data. In this article, it is demonstrated that a hybrid model approach consisting of a physics-based model that is corrected via an artificial neural network represents an efficient prediction tool as opposed to a purely data-driven model. In particular, a semi-analytical model serves as an efficient low-fidelity model with noticeable prediction errors outside its calibration domain. An artificial neural network is used to correct the semi-analytical solution towards a desired reference solution provided by high-fidelity finite element simulations, while the efficiency of the semi-analytical model is maintained and the applicability range enhanced. We utilize residual stresses that are induced by laser shock peening as a use-case example. In addition, it is shown that non-unique relationships between model inputs and outputs lead to high prediction errors and the identification of salient input features via dimensionality analysis is highly beneficial to achieve low prediction errors. In a generalization task, predictions are also outside the process parameter space of the training region while remaining in the trained range of corrections. The corrective model predictions show substantially smaller errors than purely data-driven model predictions, which illustrates one of the benefits of the hybrid modelling approach. Ultimately, when the amount of samples in the data set is reduced, the generalization of the physics-related corrective model outperforms the purely data-driven model, which also demonstrates efficient applicability of the proposed hybrid modelling approach to problems where data is scarce.

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“…For that purpose a recently developed technique presented in [20] will be used. This technique has been proven to perform well in the low data limit with accurate regression capabilities in different fields [21]. An extended overview of this technique can be found in Aappendix A.…”

Section: Regression Technique: Code2vectmentioning

confidence: 99%

Empowering Design Based on Hybrid TwinTM: Application to Acoustic Resonators

Martin

Méndez

Sainges

et al. 2020

Designs

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In the framework of civil aviation noise levels are becoming restricted every year, on one hand to provide comfort to the passengers and on the other hand to be compliant with regulations protecting airports surroundings. New technologies are required to reduce noise to cope with this restrictions as well as to guarantee a comfortable flight for passengers. For technological industries it is compulsory to stay competitive and keep improving the technology related to air intake acoustic liners. With an unceasingly growing market, for industries it is key to stay in the vanguard of air inlet technologies, ensuring innovation and establishing a proactive environment for future product generations. One of the main objectives in this framework is the reduction of the development time of these new technologies in all the stages of the process. In this work we focus on the design stage of a new prototype and we propose a hybrid technique enabling faster design and the reduction of development time. When designing new technologies or prototypes there are usually two constraints. On one hand, more innovative prototypes may present unconventional shapes are not accurately represented by conventional physical models. On the other hand, the available data is scarce, thus limiting the use of most innovative techniques based on the state-of-art of Artificial Intelligence. In this paper we propose a solution laying in the hybrid twin paradigm, combining both, data in the low limit and physics to provide a hybrid model able to represent unconventional and innovative acoustic solutions.

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Nonlinear Regression Operating on Microstructures Described from Topological Data Analysis for the Real-Time Prediction of Effective Properties

Cited by 12 publications

References 18 publications

A Strategy for Dimensionality Reduction and Data Analysis Applied to Microstructure–Property Relationships of Nanoporous Metals

A Strategy for Dimensionality Reduction and Data Analysis Applied to Microstructure–Property Relationships of Nanoporous Metals

Hybrid Modelling by Machine Learning Corrections of Analytical Model Predictions towards High-Fidelity Simulation Solutions

Empowering Design Based on Hybrid TwinTM: Application to Acoustic Resonators

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