Ludovic Chamoin

• Professor
• Professor (Full) at Ecole normale supérieure Paris-Saclay

This work introduces a combined model that integrates a linear state‐space model with a Koopman‐type machine‐learning model to efficiently predict the dynamics of nonlinear, high‐dimensional, and field‐circuit coupled systems, as encountered in areas such as electromagnetic compatibility, power electronics, and electric machines. Using an extended...

This paper presents a new approach to estimate the remaining useful life of a power electronic module where failure is caused by degradation in the wire bonds. The novelty of this work is that estimation is given for each loading cycle as opposed to estimating only the number of cycles to failure. A direct consequence is that one can make predictio...

In this paper, we propose a general deterministic framework to question the relevance, assess the quality, and ultimately choose the features (in terms of model class and discretization mesh) of the employed computational mechanics model when performing parameter identification. The goal is to exploit both modeling and data at best, with optimized...

Prior to any numerical development, the paper objective is to answer first to a fundamental question: what is the mathematical form of the most general data-driven constitutive model for stable materials, taking maximum account of knowledge from physics and materials science? Here we restrict ourselves to elasto-(visco-)plastic materials under the...

This work proposes a guaranteed error estimator for linear transient elastodynamics, accounting for both time and space discretization errors. The key lies in the definition of a novel dynamic constitutive relation error formulation, which is proven to be a strict bound of the discretization error. Moreover, based on the established dynamic constit...

The early stopping strategy consists in stopping the training process of a neural network (NN) on a set $S$ of input data before training error is minimal. The advantage is that the NN then retains good generalization properties, i.e. it gives good predictions on data outside $S$, and a good estimate of the statistical error (``population loss'') i...

This poster serves as a visual explanation of our Markov-chain based approach to estimate the remaining useful life of power electronic modules. This approach allows us to make accurate predictions in spite of the data scarcity, preserving this accuracy for harder tasks such as interpolation and extrapolation. This approach was built to account for...

Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms, such as Kalman filters and their non-linear extensions, are typically used. However, many of these filters use...

Many dynamical systems are subjected to stochastic influences, such as random excitations, noise and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which usually filtering algorithms, e.g. Kalman filters and their non-linear extensions, are used. Many of these filters however use assump...

In this paper, an alternative to solving Bayesian inverse problems for structural health monitoring based on a variational formulation with so-called transport maps is examined. The Bayesian inverse formulation is a widely used tool in structural health monitoring applications. While Markov Chain Monte Carlo (MCMC) methods are often implemented in...

In this work, the space-time MORe DWR ( M odel O rder Re duction with D ual- W eighted R esidual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pres...

This article proposes a new approach to train physics‐augmented neural networks with observable data to represent mechanical constitutive laws. To train the neural network and learn thermodynamics potentials, the proposed method does not rely on strain‐stress or strain‐free energy pairs but needs only partial strain or displacement measurements ins...

This article proposes a consistent and general approach to train physics-augmented neural networks with observable data to enrich and represent nonlinear history-dependent material behaviors in terms of both state equations and evolution laws. In this learning strategy consistent with thermodynamics, the constitutive model is expressed using two po...

Solving large structural problems with multiple complex localized behaviors is extremely challenging. To address this difficulty, both intrusive and non-intrusive Domain Decomposition Methods (DDM) have been developed in the past, where the refined model (local) is solved separately in its own space and time scales. In this work, the Finite Element...

Digital twins efficiency lies in fast and representative solutions of inverse problems to accomodate models with physical observations. The quality of the solution of an inverse problem is conditioned by inherent features of the latter, in particular (i) the richness of available data, (ii) the a priori experimental and modeling knowledge that allo...

Accurate online state and parameter estimation of uncertain non‐linear dynamical systems is a demanding task that has been traditionally handled by adopting non‐linear Kalman Filters or particle filters. However, in case of Kalman filters the system needs to be linearised and for particle filters the computational demand can be high. Recent advance...

This article proposes a new approach to train physics-augmented neural networks with observable data to represent mechanical constitutive laws. To train the neural network, the proposed method does not rely on strain-stress or strain-free energy pairs but needs only partial strain or displacement measurements inside the structure, as well as bounda...

In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted Residual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with...

It has been theoretically explained, through the notion of Neural Tangent Kernel, why the training error of overparameterized networks converges linearly to 0. In this work, we focus on the case of small (or underparameterized) networks. An advantage of small networks is that they are faster to train while retaining sufficient precision to perform...

Despite recent advances in sensing techniques and rapid growth of computational mechanics, it remains a challenge to monitor mechanical structures in real-time and evaluate their sustainability. In the present work, crack propagation is investigated by dynamically connecting experimental information and physics-based models. In order to perform on-...

In this paper, we address the effective and robust identification of material behavior parameters from full-field measurements obtained by means of the advanced Digital Image Correlation (DIC) experimental technique. The objective is to optimize the identification procedure by defining an appropriate and flexible numerical methodology that automati...

This paper is a review on distributed optic fiber sensing for structural health monitoring applications, with a deeper focus on technologies relying on the Rayleigh backscattering phenomenon. It addresses the basic physical principles which are involved, the implementation and instrumentation of the measurement techniques, as well as recent practic...

The paper deals with the use of model reduction techniques to address parametrized strongly-coupled multi-physics problems. Here, the focus is on the numerical study of power electronic modules that exhibit strongly-coupled thermal and mechanical phenomena when crack propagation occurs in critical module components such as solder joints. In order t...

In this paper, a new data assimilation framework for correcting finite element models from datasets acquired on-the-fly in low-frequency dynamics is presented. An Unscented Kalman filter algorithm is coupled with a modified Constitutive Relation Error (mCRE) observer, leading to a Modified Dual Kalman Filter algorithm (MDKF). Built as a Hermitian d...

A major challenge linked to surface integrity is the ability to detect a crack and stop its expansion. Classical approaches seek to predict critical areas and design the structure accordingly. Nevertheless, this passive methodology usually leads to oversize the structure to maintain its integrity. On the other hand, smart material and structures sh...

This paper presents a robust model updating strategy for correcting finite element models from datasets acquired in low-frequency dynamics. The proposed methodology is based on the minimization of a modified Constitutive Relation Error (mCRE) made of two terms: (i) a Hermitian data-to-model distance written in the frequency domain enriched with (ii...

We present a methodology to perform inverse design of reconfigurable topological insulators for flexural waves in plate-like structures. A genetic algorithm based topology optimization method is developed and a C6v plate unit cell topology that offers two-fold degeneracy in the band structure is designed. Piezoelectric patches, that are connected t...

Asbtract. Despite the availability of massive operation datasets, numerous uncertain parameters linger in offshore wind modeling. We propose an identification procedure based on reliability of information coming from both modeling and measurements. The procedure is constructed from the modified Constitutive Relation Error concept, which considers m...

Dear Colleagues, Given the recent interest in information technology and optimization methods for analyzing structures, this book aims to collect contributions on the topic of machine learning and control systems applied to the field of civil engineering for large and medium-scale structures. This Special Issue considers studies related to data-dri...

A reduced weakly-coupled thermo-mechanical model based on the Proper Generalized Decomposition method was developed for the numerical analysis of power modules. The employed model reduction method enabled to obtain, in a preliminary offline phase, the solution of the thermo-mechanical problem over a large range of design parameters, with much time...

This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems, approximated by a conforming numerical discretization. The review mainly aims at presenting in a unified mann...

A current challenge linked to crack growth issues is the ability to detect a crack and stop its expansion during operations. This problematic is somehow related to the thematic of smart structures and health monitoring that show a growing interest for the last decades. The purpose of this study is to demonstrate the feasibility of a smart material...

We present a methodology to perform inverse analysis on reconfigurable topological insulators for flexural waves in plate-like structures. First the unit cell topology of a phononic plate is designed, which offers two-fold degeneracy in the band structure by topology optimization. In the second step, piezoelectric patches bonded over the substrate...

Merging advanced sensing techniques and simulation tools for future structural health monitoring technologies Project DREAM-ON aims to design smart autonomous mechanics structures, able to perform online control of their health and take anticipated actions during service for increased reliability and performance. Its innovative concept is a synergi...

A Correction to this paper has been published: https://doi.org/10.1007/s00466-021-01990-x

We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the MsFEM framework, the concept of Constitutive Relation Error (CRE) to obtain a guaranteed and fully computable a posteriori error estimate in the energy norm (as well as...

This research work deals with the implementation of so-called Dynamic Data-Driven Application Systems (DDDAS) in structural mechanics activities. It aims at designing a real-time numerical feedback loop between a physical system of interest and its numerical simulator, so that (i) the simulation model is dynamically updated from sequential and in s...

For several years, the explosion of the access to experimental data in industrial systems and the considerable change in computing tools have led to the development of data assimilation methods that aim to be used for system monitoring. From data measured on the physical system and a mathematical model, these methods provide an approximation of the...

The article describes thermal datasets collected in a two-story concrete building of the Sense-City equipment during various controlled climatic scenarios. Using the Sense-City climatic chamber, we reproduced stationary thermal conditions, a typical winter climate of the south of France and Paris 2003 heat wave. Each of the three scenarios has a du...

We present an approach for designing material micro-structures by using isogeometric analysis and parameterized level set method. Design variables, which are level set values associated with control points, are updated from the optimizer and represent the geometry of the unit cell. The computational efficiency is further improved in each iteration...

A goal-oriented inverse technique is proposed for the accurate computation of quantities of interest in thermal building problems. In contrast to the standard inverse methods, only the model parameters sensitive to the chosen quantity of interest are updated. The technique is applied to a real building in the Sense-City equipment. A two-zone therma...

This research work focuses on the so-called non-intrusive model coupling procedure which has been proposed and widely analyzed in structural mechanics during the last decade, and which constitutes a flexible and attractive engineering simulation tool for the analysis of localized phenomena with low implementation effort. In this context, we propose...

The motivation of this research work is to address real-time sequential data assimilation and inference of model parameters within a full Bayesian formulation. For that purpose, we couple two advanced numerical approaches. First, the Transport Map sampling is used as an alternative to classical Markov Chain approaches in order to facilitate the sam...

Optimal hydrophone performance for 1-3 piezoelectric composites is achieved from the design of material properties. The piezocomposite consists of piezoceramic rods immersed in a polymer matrix. We obtain the effective moduli of the piezocomposite by the differential effective medium theory and the results are explicitly dependent on volume fractio...

The motivation of this work is to address real-time sequential inference of parameters with a full Bayesian formulation. The Transport Maps method allows to determine a coupling between a reference density and the posterior density. Here, the contribution is to use the Proper Generalized Decomposition method (PGD) to reduce the evaluation cost of t...

This article introduces a new inverse method for thermal model parameter identification that stands out from standard inverse methods by its formulation. While these latter methods aim at identifying all the model parameters in order to fit the experimental data at best, the proposed goal-oriented inverse method focuses on the prediction of a speci...

The work addresses the optimization of specimen geometry in the context of parameter identification from full-field measurements. For this purpose, we propose to use topology optimization tools in order to maximize the sensitivity of the measured displacement field to sought parameters, under volume fraction constraints and without any a priori inf...

The work introduces new advanced numerical tools for data assimilation in structural mechanics. Considering the general Bayesian inference context, the proposed approach performs real-time and robust sequential updating of selected parameters of a numerical model from noisy measurements, so that accurate predictions on outputs of interest can be ma...

In this paper, we introduce, analyze, and numerically illustrate a goal-oriented version of the Proper Generalized Decomposition method. The objective is to derive a reduced-order formulation such that the accuracy in given quantities of interest is increased when compared to a standard Proper Generalized Decomposition method. Traditional goal-orie...

In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set function for numerical homogenization, sensitivity calculation and optimization of the effective elastic prop...

We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the MsFEM framework, the concept of Constitutive Relation Error (CRE) to obtain a guaranteed and fully computable a posteriori error estimate in the energy norm (as well as...

Purpose The purpose of this paper is to further simplify the use of NURBS in industrial environnements. Although isogeometric analysis (IGA) has been the object of intensive studies over the past decade, its massive deployment in industrial analysis still appears quite marginal. This is partly due to its implementation, which is not straightforward...

The motivation of this work is to address real‐time sequential inference of parameters with a full Bayesian formulation. First, the Proper Generalized Decomposition (PGD) is used to reduce the computational evaluation of the posterior density in the online phase. Second, Transport Map sampling is used to build a deterministic coupling between a ref...

We apply the proper generalized decomposition (PGD) to a static electrothermal model subject to uncertainties. The quadratic electrothermal coupling term is non-standard and requires the introduction of a trilinear form. We use an existing finite integration technique (FIT)-based solver to demonstrate the opportunities of integrating the PGD in exi...

The paper deals with the Isogeometric Analysis (IGA) technology, which has received much attention over the last decade due to its increased flexibility, accuracy, and robustness in many engineering simulations compared to classical Finite Element Analysis (FEA). In this context, we present a verification method, based on duality and the concept of...

The proper generalized decomposition is applied to a static electrothermal model subject to uncertainties. A reduced model that circumvents the curse of dimensionality is obtained. The quadratic electrothermal coupling term is non-standard and requires the introduction of a trilinear form. An existing finite integration technique based solver is us...

The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, st...

The motivation of this work is to propose a general methodology to deal with complex nonlinear mechanical behaviors in the context of identification and model updating problems. We follow here the principle of the modified Constitutive Relation Error that is an energy-based functional suited to the solution of inverse problems, and originally used...

We present a correct-by-design method of state-dependent control synthesis for sampled switching systems. Given a target region R of the state space, our method builds a capture set S and a control that steers any element of S into R. The method works by iterated backward reachability from R. The method is also used to synthesize a recurrence contr...

We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic problems. Using the concept of constitutive relation error, it provides guaranteed and fully computable global/goal-oriented error estimates taking both discretization and PGD...

Keynote Lecture

We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for the global error measured in the energy norm. It is based on dual analysis and the Constitutive Relation Error (...