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Systematic physics constrained parameter estimation of stochastic differential equations. (English) Zbl 1507.62143

Summary: A systematic Bayesian framework is developed for physics constrained parameter inference of stochastic differential equations (SDE) from partial observations. Physical constraints are derived for stochastic climate models but are applicable for many fluid systems. A condition is derived for global stability of stochastic climate models based on energy conservation. Stochastic climate models are globally stable when a quadratic form, which is related to the cubic nonlinear operator, is negative definite. A new algorithm for the efficient sampling of such negative definite matrices is developed and also for imputing unobserved data which improve the accuracy of the parameter estimates. The performance of this framework is evaluated on two conceptual climate models.

MSC:

62-08 Computational methods for problems pertaining to statistics
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
62F15 Bayesian inference
86A08 Climate science and climate modeling
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