Uncertainty quantification (UQ) is the process of quantitatively characterizing the uncertainties of simulator outcomes. In both scientific and engineering computations, it has recognized as of vital importance especially in those scenarios where decision or design of products have to be implemented when some aspects of the systems are not exactly learned due to lack of knowledge or cannot be exactly learned due to intrinsic randomness of things. A typical research direction is the reliability analysis and reliability-based design optimization of structures, where both intrinsic randomness of parameters (e.g., material properties, dimension sizes, excitations, etc.) and epistemic uncertainties on the probability distributions of those parameters have to be carefully treated. A general UQ framework includes many sub-tasks such as uncertainty characterization, forward uncertainty propagation, inverse model updating, uncertainty sensitivity analysis, etc. All the sub-tasks of UQ and structural reliability pose great challenges for numerical computation.

The rapid developments of machine learning algorithms, such as deep neural network, Gaussian process regression, manifold learning, has brought new hopes for addressing the above challenges on numerical computation. However, the recent developments on this aspect is far from mature for solving all the above-mentioned tasks, and challenges, such as proper addressment of prediction errors, extraction of feature space for high-dimensional analysis, and design of training points, are still left as open problems. The aim of this mini-symposium is to collect the latest developments on all aspects of machine learning for UQ and structural reliability. The scope of the mini-symposium is not limited to the non-intrusive methods where the simulators are regarded as black boxes, but also covers those developments on intrusive methods where the physic-informed machine learning is integrated.

This activity is organized under auspices of the Committee on Probability and Statistics in Physical Sciences (C(PS)^2) of the Bernoulli Society for Mathematical Statistics and Probability.