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On the Solution of Statistical Inverse Problems using Machine Learning Methods based on Artificial Neural Networks

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Abstract

This work adresses the solution of a statistical inverse problem in computational elastodynamics using machine learning based on artificial neural networks (ANNs). The stochastic computational model (SCM) corresponds to a simplified random elasto-acoustic multilayer model of a biological system that is representative of the axial transmission technique for the ultrasonic characterization of cortical bone properties from experimental velocity measurements. The three-layer biological system consists of a random heterogeneous damaged/weaken elastic solid layer (cortical bone layer) sandwiched between two deterministic homogeneous acoustic fluid layers (soft tissues and marrow bone layers) and excited by an acoustic line source [1]. Such SCM is parameterized by two geometrical parameters, corresponding to the thicknesses of the "healthy" and "damaged" elastic solid parts, a dispersion parameter controlling the level of statistical fluctuations of the random elasticity field, and a spatial correlation length characterizing the spatial correlation structure of the random elasticity field. An innovative ANN-based identification methodology has been recently proposed in [2] and applied to multiscale computational mechanics. In this work, the proposed methodology is extended to linear elastodynamics for the statistical inverse identification of the four aforementioned hyperparameters from fourteen quantities of interest of the SCM, corresponding to the scattered acoustic energy stored at fourteen receivers located in the soft tissues layer. It consists in (i) constructing of a synthetic database generated from the SCM and consisting of network input data (quantities of interest) and target data (hyperparameters), (ii) postprocessing this initial database by conditioning the network input data with respect to the network target data using kernel density estimation methods to improve the ANN performance, (iii) designing an efficient ANN trained using the processed database to identify the optimal hyperparameters corresponding to given expected quantities of interest, (iv) constructing a probabilistic model of the network input random vector to take into account the uncertainties on the input quantities of interest, and (v) designing another ANN trained using the initial and processed input data to identify the probabilistic model of the network input random vector from given observed quantities of interest. REFERENCES [1] C. Desceliers, C. Soize, S. Naili, G. Haiat. Probabilistic model of the human cortical bone with mechanical alterations in ultrasonic range. Mechanical Systems and Signal Processing, 32:170–177, 2012. [2] F. Pled, C. Desceliers, T. Zhang. A robust solution of a statistical inverse problem in multiscale computational mechanics using an artificial neural network. Computer Methods in Applied Mechanics and Engineering, 373:113540, 2021.
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hal-03277972 , version 1 (05-07-2021)

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  • HAL Id : hal-03277972 , version 1

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Florent Pled, C. Desceliers. On the Solution of Statistical Inverse Problems using Machine Learning Methods based on Artificial Neural Networks. 16th U.S. National Congress on Computational Mechanics (USNCCM16), Jul 2021, Chicago, Illinois (virtual), United States. ⟨hal-03277972⟩
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