Adaptive Multifidelity Data Assimilation for Nonlinear Subsurface Flow Problems

Sequential data assimilation with multiple nonlinear models and applications to subsurface flow

Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes. Meanwhile, available but limited observations of system state could further complicates one’s prediction choices. Over the years, data assimilation techniques, such...

Data Assimilation Application to the Subsurface Flow and Solute Transport

An Ensemble Multiscale Filter for Large Nonlinear Data Assimilation Problems

Operational data assimilation problems tend to be very large, both in terms of the number of unknowns to be estimated and the number of measurements to be processed. This poses significant computational challenges, especially for ensemble methods, which are critically dependent on the number of replicates used to derive sample covariances and other statistics. Most efforts to deal with the rela...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Nonlinear Ensemble Data Assimilation for the Ocean

Data assimilation in high-resolution atmosphere or ocean models is complicated because of the nonlinearity of these models. Several methods to solve the problem have been presented, all having their own advantages and disadvantages. In this paper so-called particle methods are discussed, based on Sequential Importance Resampling (SIR). Reference is made to related methods, in particular to the ...