A Monte Carlo strategy for data-based mathematical modeling
M. R. Banan, K. D. Hjelmstad
We establish the mathematical basis for building the MC-HARP data-processing environment. The MC-HARP strategy determines the functional structure and parameters of a mathematical model simultaneously. A Monte Carlo (MC) strategy combined with the concept of Hierarchical Adaptive Random Partitioning (HARP) and fuzzy subdomains determines the multivariate parallel distributed mapping. The HARP algorithm is based on a divide-and-conquer strategy that partitions the input space into measurable connected subdomains and builds a local approximation for the mapping task. Fuzziness promotes continuity of the mapping constructed by HARP and smooths the mismatching of the local approximations in the neighboring subdomains. The Monte Carlo superposition of a sample of random partitions reduces the localized disturbances among the fuzzy subdomains, controls the global smoothness of the mean average mapping, and improves the generalization of the approximation. We illustrate the procedure by applying it to a two-dimensional surface fitting problem.
Mathematical and Computer Modelling
https://doi.org/10.1016/0895-7177(95)00156-V
10.1016/0895-7177(95)00156-V
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Mathematical Modeling Mathematics 100%
Partitioning Mathematics 99%
Strategy Mathematics 70%
Local Approximation Mathematics 48%
Surface fitting Engineering & Materials Science 35%
Surface Fitting Mathematics 29%
Random Partitions Mathematics 28%
Fuzzy Control Mathematics 27%
Banan, M. R., & Hjelmstad, K. D. (1995). A Monte Carlo strategy for data-based mathematical modeling. Mathematical and Computer Modelling, 22(8), 73-90. https://doi.org/10.1016/0895-7177(95)00156-V
A Monte Carlo strategy for data-based mathematical modeling. / Banan, M. R.; Hjelmstad, K. D.
In: Mathematical and Computer Modelling, Vol. 22, No. 8, 10.1995, p. 73-90.
Banan, MR & Hjelmstad, KD 1995, 'A Monte Carlo strategy for data-based mathematical modeling', Mathematical and Computer Modelling, vol. 22, no. 8, pp. 73-90. https://doi.org/10.1016/0895-7177(95)00156-V
Banan MR, Hjelmstad KD. A Monte Carlo strategy for data-based mathematical modeling. Mathematical and Computer Modelling. 1995 Oct;22(8):73-90. doi: 10.1016/0895-7177(95)00156-V
Banan, M. R. ; Hjelmstad, K. D. / A Monte Carlo strategy for data-based mathematical modeling. In: Mathematical and Computer Modelling. 1995 ; Vol. 22, No. 8. pp. 73-90.
@article{73990f6359f443de81943bf022636948,
title = "A Monte Carlo strategy for data-based mathematical modeling",
abstract = "We establish the mathematical basis for building the MC-HARP data-processing environment. The MC-HARP strategy determines the functional structure and parameters of a mathematical model simultaneously. A Monte Carlo (MC) strategy combined with the concept of Hierarchical Adaptive Random Partitioning (HARP) and fuzzy subdomains determines the multivariate parallel distributed mapping. The HARP algorithm is based on a divide-and-conquer strategy that partitions the input space into measurable connected subdomains and builds a local approximation for the mapping task. Fuzziness promotes continuity of the mapping constructed by HARP and smooths the mismatching of the local approximations in the neighboring subdomains. The Monte Carlo superposition of a sample of random partitions reduces the localized disturbances among the fuzzy subdomains, controls the global smoothness of the mean average mapping, and improves the generalization of the approximation. We illustrate the procedure by applying it to a two-dimensional surface fitting problem.",
author = "Banan, {M. R.} and Hjelmstad, {K. D.}",
doi = "10.1016/0895-7177(95)00156-V",
journal = "Mathematical and Computer Modelling",
T1 - A Monte Carlo strategy for data-based mathematical modeling
AU - Banan, M. R.
AU - Hjelmstad, K. D.
N2 - We establish the mathematical basis for building the MC-HARP data-processing environment. The MC-HARP strategy determines the functional structure and parameters of a mathematical model simultaneously. A Monte Carlo (MC) strategy combined with the concept of Hierarchical Adaptive Random Partitioning (HARP) and fuzzy subdomains determines the multivariate parallel distributed mapping. The HARP algorithm is based on a divide-and-conquer strategy that partitions the input space into measurable connected subdomains and builds a local approximation for the mapping task. Fuzziness promotes continuity of the mapping constructed by HARP and smooths the mismatching of the local approximations in the neighboring subdomains. The Monte Carlo superposition of a sample of random partitions reduces the localized disturbances among the fuzzy subdomains, controls the global smoothness of the mean average mapping, and improves the generalization of the approximation. We illustrate the procedure by applying it to a two-dimensional surface fitting problem.
AB - We establish the mathematical basis for building the MC-HARP data-processing environment. The MC-HARP strategy determines the functional structure and parameters of a mathematical model simultaneously. A Monte Carlo (MC) strategy combined with the concept of Hierarchical Adaptive Random Partitioning (HARP) and fuzzy subdomains determines the multivariate parallel distributed mapping. The HARP algorithm is based on a divide-and-conquer strategy that partitions the input space into measurable connected subdomains and builds a local approximation for the mapping task. Fuzziness promotes continuity of the mapping constructed by HARP and smooths the mismatching of the local approximations in the neighboring subdomains. The Monte Carlo superposition of a sample of random partitions reduces the localized disturbances among the fuzzy subdomains, controls the global smoothness of the mean average mapping, and improves the generalization of the approximation. We illustrate the procedure by applying it to a two-dimensional surface fitting problem.
U2 - 10.1016/0895-7177(95)00156-V
DO - 10.1016/0895-7177(95)00156-V
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling