Chetra Mang

Axel TahmasebiMoradi, Vincent Ren, Benjamin Le-Creurer et al.

Aiming to reduce the computational cost of numerical simulations, a convolutional neural network (CNN) and a multi-layer perceptron (MLP) are introduced to build a surrogate model to approximate radiative heat transfer solutions in a 2-D walled domain with participative gases. The originality of this work lays in the adaptation of the inputs of the problem (gas and wall properties) in order to fit with the CNN architecture, more commonly used for image processing. Two precision datasets have been created with the classical solver, ICARUS2D, that uses the discrete transfer radiation method with the statistical narrow bands model. The performance of the CNN architecture is compared to a more classical MLP architecture in terms of speed and accuracy. Thanks to Optuna, all results are obtained using the optimized hyper parameters networks. The results show a significant speedup with industrially acceptable relative errors compared to the classical solver for both architectures. Additionally, the CNN outperforms the MLP in terms of precision and is more robust and stable to changes in hyper-parameters. A performance analysis on the dataset size of the samples have also been carried out to gain a deeper understanding of the model behavior.

Chetra Mang, Axel TahmasebiMoradi, Mouadh Yagoubi

We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold. Moreover, two approaches are developed to reconstruct the inverse projector to project from the lower data component to the original one. Afterward, we provide a detailed strategy to decompose the parametric domain based on the low dimension manifold. Finally, numerical examples of harmonic transport problem are given to illustrate the efficiency and effectiveness of the proposed method comparing to the classical meta-models such as neural networks.

Chetra Mang, Axel TahmasebiMoradi, David Danan et al.

Physical models classically involved Partial Differential equations (PDE) and depending of their underlying complexity and the level of accuracy required, and known to be computationally expensive to numerically solve them. Thus, an idea would be to create a surrogate model relying on data generated by such solver. However, training such a model on an imbalanced data have been shown to be a very difficult task. Indeed, if the distribution of input leads to a poor response manifold representation, the model may not learn well and consequently, it may not predict the outcome with acceptable accuracy. In this work, we present an Adaptive Sampling Algorithm for Data Generation (ASADG) involving a physical model. As the initial input data may not accurately represent the response manifold in higher dimension, this algorithm iteratively adds input data into it. At each step the barycenter of each simplicial complex, that the manifold is discretized into, is added as new input data, if a certain threshold is satisfied. We demonstrate the efficiency of the data sampling algorithm in comparison with LHS method for generating more representative input data. To do so, we focus on the construction of a harmonic transport problem metamodel by generating data through a classical solver. By using such algorithm, it is possible to generate the same number of input data as LHS while providing a better representation of the response manifold.