Use of the modified constitutive relation error to learn constitutive relations
Topic(s) : Special Sessions
Co-authors :
Emmanuel BARANGER (FRANCE), Antoine BENADY , Ludovic CHAMOINAbstract :
Simulation tools have taken an important role in composite parts' design and certification process. Near, edges or geometrical singularities, non-linear constitutive models are quite often required. The models are handmade, identified and validated on a set of standard tests. However, for some structures, the constitutive relation is not well known (only elastic properties are well known, for example), while it’s needed for the prognosis of their lifetime. In the context of Dynamic Data Driven Assimilation Systems (DDDAS), one may have to assimilate and correct, on the fly, a non-linear constitutive law. It can be the case to assess the behaviour of wind turbines, for example.
This paper proposes a consistent and general approach to train physics-augmented neural networks with observable data to enrich and represent nonlinear time-dependent material laws in terms of state equations and evolution laws. In this learning strategy consistent with thermodynamics, the constitutive model is expressed using two potentials: the free energy and the dissipation potential, which are represented by input-convex neural networks, thus automatically satisfying the principles of thermodynamics. The neural network is trained thanks to an unsupervised procedure that does not rely on strain-stress pairs but needs only partial strain or displacement measurements inside the structure and potentially uncertain boundary conditions. This method is based on the minimisation of the modified Constitutive Relation Error, and it extends previous works on this error measure for neural networks to the case of history-dependent behaviour, which requires the design of a specific minimisation procedure. This error is the major point of this paper as it allows us to split contributions between the error on the data and the error on the model itself.
Given that neural networks for typical structural health monitoring applications often need to be trained online, a significant emphasis is placed on automatically and adaptively tuning crucial hyperparameters such as learning rate or weighting between losses.
The method is evaluated on anisotropic non-linear elasticity close to damage and elastoplastic and elastoviscoplastic test cases with synthetic optic fiber measurements. It is shown that the method can properly learn hidden behaviour, achieves high robustness to noise levels, and low sensitivity to user-defined hyperparameters.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 101002857).
This paper proposes a consistent and general approach to train physics-augmented neural networks with observable data to enrich and represent nonlinear time-dependent material laws in terms of state equations and evolution laws. In this learning strategy consistent with thermodynamics, the constitutive model is expressed using two potentials: the free energy and the dissipation potential, which are represented by input-convex neural networks, thus automatically satisfying the principles of thermodynamics. The neural network is trained thanks to an unsupervised procedure that does not rely on strain-stress pairs but needs only partial strain or displacement measurements inside the structure and potentially uncertain boundary conditions. This method is based on the minimisation of the modified Constitutive Relation Error, and it extends previous works on this error measure for neural networks to the case of history-dependent behaviour, which requires the design of a specific minimisation procedure. This error is the major point of this paper as it allows us to split contributions between the error on the data and the error on the model itself.
Given that neural networks for typical structural health monitoring applications often need to be trained online, a significant emphasis is placed on automatically and adaptively tuning crucial hyperparameters such as learning rate or weighting between losses.
The method is evaluated on anisotropic non-linear elasticity close to damage and elastoplastic and elastoviscoplastic test cases with synthetic optic fiber measurements. It is shown that the method can properly learn hidden behaviour, achieves high robustness to noise levels, and low sensitivity to user-defined hyperparameters.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 101002857).