Interval deep learning for computational mechanics problems under input uncertainty

Abstract

Solving problems in complex engineering systems often involves employing a cascade of computational models which solve different sub-problems. In computational mechanics in particular, complex systems that use model cascading under uncertainty include important safety-critical applications (e.g., aerospace and nuclear reactor systems). There are two fundamental considerations to solve problems with cascading models. First, the collaborating models involved in solving the problem must share compatible data formats and modeling assumptions. Second, the models must be capable of processing and propagating the uncertainty on the raw measurements and the uncertainty on the predictions from other models. The first consideration is often well-understood and implemented in practice. On the other hand, the second consideration, despite its importance, is less understood and implemented. We argue that in such complex engineering systems it is necessary to employ models capable of processing data uncertainty to obtain reliable predictions for the problem. One main difficulty in uncertainty quantification is that there is often not enough information about the data to make probabilistic assumptions. In fact, sometimes the only information available to the analyst is in the form of upper and lower bounds of the data. In such cases, interval analysis (IA) offers an alternative to quantify the uncertainty. Another difficulty is that we generally do not have direct access to the value of an uncertain mechanical quantity but only to indirect measurements or models that are used to represent it [1]. Indeed, the data uncertainty that flows through the model cascade can arise from measurements or from predictions of other models. To solve these problems, we present a novel interval deep neural network (DINN) that is capable of providing reliable input data to a mechanics model from data containing uncertainty. A numerical experiment is conducted using a dataset of concrete mix measurements with interval uncertainty to predict concrete strength. In general, the DINN can be used to solve multiple problems under uncertainty in science and engineering.