Abstract
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model regularization (i.e., smoothing) has traditionally been used to minimize these oscillations; unfortunately, it is sometimes impossible to sufficiently remove unwanted artifacts without smoothing away key features of the data set. In this article, we present a method of model regularization that preserves significant features of a data set while minimizing artificial oscillations. Our method varies the strength of a smoothing parameter throughout the domain automatically, removing artifacts in poorly-constrained regions while leaving other regions unchanged. The behavior of our method is validated on a collection of two- and three-dimensional data sets produced by scientific simulations.
This work is supported by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research under Contract DE-AC02-06CH11357, Program Manager Margaret Lentz.
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Notes
- 1.
We consider only “clamped” knot sequences in this paper; thus, the first \(p+1\) knots are always 0 and the last \(p+1\) knots are always 1.
- 2.
Here we assume for simplicity that the degree of the B-spline is the same in each dimension, but the degree can vary in practice if desired.
- 3.
For example, \(\partial ^{(2,0)} f = \partial ^2 f / \partial x_1^2\), and \(\partial ^{(0,2)} f = \partial ^2 f / \partial x_2^2\), while \(\partial ^{(1,1)} f = \partial ^2 f / (\partial x_1 \partial x_2)\).
- 4.
We consider the unnormalized sinc function: \(\mathrm {sinc}(x) = \sin (x)/x\), with \(\mathrm {sinc}(0)=1\).
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© 2022 Raine Yeh and UChicago Argonne, LLC, Operator of Argonne National Laboratory, under exclusive license to Springer Nature Switzerland AG, part of Springer Nature
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Lenz, D., Yeh, R., Mahadevan, V., Grindeanu, I., Peterka, T. (2022). Adaptive Regularization of B-Spline Models for Scientific Data. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13350. Springer, Cham. https://doi.org/10.1007/978-3-031-08751-6_11
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