2020/01/29 by Jehanzeb H. Chaudhry, Donald Estep, Chaudhry, Jehanzeb H. +5 · 1 citation
Decision Sciences · Engineering · Physics and Astronomy · #Advanced Control Systems Optimization #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2001.11139
openalex publication_date 2020/01/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Classical a posteriori error analysis for differential equations quantifies\nthe error in a Quantity of Interest (QoI) which is represented as a bounded\nlinear functional of the solution. In this work we consider a posteriori error\nestimates of a quantity of interest that cannot be represented in this fashion,\nnamely the time at which a threshold is crossed for the first time. We derive\ntwo representations for such errors and use an adjoint-based a posteriori\napproach to estimate unknown terms that appear in our representation. The first\nrepresentation is based on linearizations using Taylor's Theorem. The second\nrepresentation is obtained by implementing standard root-finding techniques. We\nprovide several examples which demonstrate the accuracy of the methods. We then\nembed these error estimates within a framework to provide error bounds on a\ncumulative distribution function when parameters of the differential equations\nare uncertain.\n