Interval Reduced Order Surrogate Modelling Framework for Uncertainty Quantification

Surrogate models are widely used in the engineering community to approximate costly and large evaluation processes, such as difficult experiments or expensive simulations. This paper presents a non-intrusive framework for epistemic surrogate modelling, which is based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for interval observations. In physical systems modelling, it is important to consider both aleatoric and epistemic uncertainty by constructing an uncertainty model to be included in the surrogate model. However, existing frameworks have a major limitation in that they can only handle scalar data observations and are not designed for non-deterministic observations like interval data. In many applications, the observed data can be inherently non-scalar due to various factors, such as observation uncertainties, conflicting data, or summarized data. In our proposed framework, we integrate POD for interval data with PCE for interval observations. Firstly, we employ interval POD to obtain an optimally reduced-order basis from the full-order snapshot. Then, we approximate this reduced-order basis using a non-intrusive interval PCE method. Allowing non-scalar data, such as intervals, is advantageous as it takes into account more information in the physical system modelling.

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