Colloquia

Summary

Stochastic modelling with neural networks requires large datasets to learn the physics-based models described by uncertain parameters. Although such trained networks can predict the model output, their extrapolation capability is rather limited.  Extrapolation can be improved by constraining the network to physical laws defined as a new type of loss function.

In this work, at first, a 3D non-linear finite element model of a simplified, homogeneous, cylindrical battery under radial compression is considered. The elastic material properties are modelled as random and sampled to output reaction forces with finite element simulations. The samples are used to train a neural network classically to build a proxy model of the battery mechanical response. 

Secondly, a similar but linear battery model under axial compression based on a physics-constrained neural network is studied. The model state is approximated by a neural network, and further, the strong form of elasticity equations are solved in a weak sense on a set of randomly distributed points in its computational domain. The solution is obtained by generating new types of loss functions based on the primal and mixed formulations. In another approach, the neural network used to approximate the battery deformation is additively decomposed into boundary and physics-based parts, both of which are modelled by separate neural networks. As a result of comparing the different formulations, a 2D version of the decomposed model based on an analytical boundary function and a physics-based neural network is considered. The battery model is trained with a non-linear optimiser and compared to a finite element solution of an identical problem.

The results indicate that the weak formulation of the finite element solution can predict stress concentrations better than the strong formulation of the physically constrained network approach. However, the neural network approach is more general and can be used for different types of loading and boundary conditions.