期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 348, 期 -, 页码 683-693出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2017.07.050
关键词
Probabilistic machine learning; Inverse problems; Fractional differential equations; Uncertainty quantification; Functional genomics
资金
- DARPA EQUiPS grant [N66001-15-2-4055]
- MURI/ARO grant [W911NF-15-1-0562]
- AFOSR grant [FA9550-17-1-0013]
This work leverages recent advances in probabilistic machine learning to discover governing equations expressed by parametric linear operators. Such equations involve, but are not limited to, ordinary and partial differential, integro-differential, and fractional order operators. Here, Gaussian process priors are modified according to the particular form of such operators and are employed to infer parameters of the linear equations from scarce and possibly noisy observations. Such observations may come from experiments or blackbox computer simulations, as demonstrated in several synthetic examples and a realistic application in functional genomics. (C) 2017 Elsevier Inc. All rights reserved.
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