Machine learning of linear differential equations using Gaussian processes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:348

Article

Raissi, Maziar¹  Perdikaris, Paris²  Karniadakis, George Em¹ 

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] MIT, Dept Mech Engn, Cambridge, MA 02139 USA

关键词: Probabilistic machine learning;    Inverse problems;    Fractional differential equations;    Uncertainty quantification;    Functional genomics;   

DOI  :  10.1016/j.jcp.2017.07.050

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free