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Systematic Physics Constrained Parameter Estimation of Stochastic Differential Equations

A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are applicable for many fluid systems. A condition isderived for global stability of stochastic climate models based on energy conservation. Stochasticclimate models are globally stable when a quadratic form, which is related to the cubic nonlinearoperator, 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 theparameter estimates. The performance of this framework is evaluated on two conceptual climatemodels.