Rafi Muhanna

Naijia Xiao, Francesco Fedele, Rafi Muhanna

We present an interval-based approach for parameter identification in structural static inverse problems. The proposed inverse formulation exploits the Interval Finite Element Method (IFEM) combined with adjoint-based optimization. The inversion consists of a two-step algorithm: first, an estimate of the parameters is obtained by means of a deterministic iterative solver. Then, the algorithm switches to the interval extension of the previous solver, using the deterministic estimate of the parameters as an initial guess. The iterations are terminated based on a new containment-stopping criterion, which is intrinsic to intervals. Various numerical examples show that the proposed method provides guaranteed interval enclosures of the parameters.

David Betancourt, Rafi Muhanna

Deep neural networks (DNNs) are becoming more prevalent in important safety-critical applications, where reliability in the prediction is paramount. Despite their exceptional prediction capabilities, current DNNs do not have an implicit mechanism to quantify and propagate significant input data uncertainty -- which is common in safety-critical applications. In many cases, this uncertainty is epistemic and can arise from multiple sources, such as lack of knowledge about the data generating process, imprecision, ignorance, and poor understanding of physics phenomena. Recent approaches have focused on quantifying parameter uncertainty, but approaches to end-to-end training of DNNs with epistemic input data uncertainty are more limited and largely problem-specific. In this work, we present a DNN optimized with gradient-based methods capable to quantify input and parameter uncertainty by means of interval analysis, which we call Deep Interval Neural Network (DINN). We perform experiments on an air pollution dataset with sensor uncertainty and show that the DINN can produce accurate bounded estimates from uncertain input data.