Modern machine learning (ML) techniques, in conjunction with simulation-based methods, present remarkable potential for various engineering applications. Within the materials science field, these data-based methods can be used to build efficient structure-property linkages that can be further integrated within multiscale simulations to speed-up communication between hierarchical length scales or guide experiments in a materials discovery setting. A critical shortcoming of state-of-the-art ML techniques however is their lack of reliable uncertainty/error estimates, which severely limits their use for materials or other engineering applications where data is often scarce and uncertainties substantial. This talk will present methods for probabilistic learning of neural networks (NN) that allow consideration of both aleatoric uncertainties, which account for the inherent stochasticity of the data-generating process, and epistemic uncertainties, which arise from consideration of small amounts of data. Integration of accurate UQ schemes within NN pipelines is a challenging task as it involves probabilistic learning in high-dimensionality spaces. Algorithms based on approximate variational inference achieve an appropriate trade-off between accuracy of the uncertainty estimates and accessible computational cost. The performance of such algorithms will be illustrated on an example that pertains to the prediction of homogenized and localized properties of a composite material.
