Non-isometric Curve to Surface Matching with Incomplete Data for Functional Calibration
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Calibration refers to the process of adjusting features of a computational model that are not observed in the physical process so that the model matches the real process. We propose a framework for calibration when the unobserved features, i.e. calibration parameters, do not assume a single value, but are functionally dependent on other inputs. We demonstrate that this problem is curve to surface matching where the matched curve does not possess the same length as the original curve. Therefore, we perform non-isometric matching of a curve to a surface. Since in practical applications we do not observe a continuous curve but a sample of data points, we use a graph-theoretic approach to solve this matching of incomplete data. We define a graph structure in which the nodes are selected from the incomplete surface and the weights of the edges are decided based on the response values of the curve and surface. We show that the problem of non-isometric incomplete curve to surface matching is a shortest path problem in a directed acyclic graph. We apply the proposed method, graph-theoretic non-isometric matching, to real and synthetic data and demonstrate that the proposed method improves the prediction accuracy in functional calibration.
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