Bayesian numerical methods for nonlinear partial differential equations

نویسندگان

چکیده

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches applied. However, nonlinear partial (PDEs) pose substantial challenges from inferential perspective, most notably the absence explicit conditioning formula. This paper extends earlier work on linear PDEs a general class initial value problems specified by PDEs, motivated for evaluations right-hand-side, conditions, or boundary conditions PDE have high computational cost. proposed method viewed exact Bayesian under approximate likelihood, is based discretisation operator. Proof-of-concept experimental results demonstrate that meaningful probabilistic uncertainty quantification unknown performed, while controlling number times and are evaluated. A suitable prior model identified using novel theoretical analysis sample path properties Mat\'{e}rn processes, may independent interest.

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ژورنال

عنوان ژورنال: Statistics and Computing

سال: 2021

ISSN: ['0960-3174', '1573-1375']

DOI: https://doi.org/10.1007/s11222-021-10030-w