In the field of nonlinear filtering(NLF),it is well-known that the unnormalized conditional density of the states satisfies the Zakai’s equation.The splitting-up algorithm has been first studied in the independent no...In the field of nonlinear filtering(NLF),it is well-known that the unnormalized conditional density of the states satisfies the Zakai’s equation.The splitting-up algorithm has been first studied in the independent noises case by Bensoussan,et al.(1990).In this paper,the authors extend this convergence analysis of the splitting-up algorithm to the correlated noises’case.Given a time discretization,one splits the solution of the Zakai’s equation into two interlacing processes(with possibly computational advantage).These two processes correspond respectively to the prediction and updating.Under certain conditions,the authors show that both processes tend to the solution of the Zakai’s equation,as the time step goes to zero.The authors specify the conditions imposed on the way of splitting-up to guarantee the convergence.The major technical difficulty in the correlated noises’case,compared with the independent case,is to control the gradient of the second process in some sense.To illustrate the potentially computational advantage of the schemes based on the splitting-up ways,the authors experiment on a toy NLF model using the feedback particle filter(FPF)developed based on the splitting-up method and the sampling importance and resampling(SIR)as comparison.The FPF outperforms in both accuracy and efficiency.展开更多
Numerical simulation of oil migration and accumulation is to describe the history of oil migration and accumulation in basin evolution. It is of great value in the exploration of oil resources and their rational evalu...Numerical simulation of oil migration and accumulation is to describe the history of oil migration and accumulation in basin evolution. It is of great value in the exploration of oil resources and their rational evaluation. In this paper, from such actual conditions as the effects of mechanics of fluids in porous media and 3-dimensional geology characteristics, a kind of modified method of second order splitting-up implicit interactive scheme is pur forward. For the famous hydraulic experiment of secondary migration-accumulation, the numerical simulation test has been done, and both the computational and experimental results are basically identical. For the actual problem of Dongying hollow of Shengli Petroleum Oil Field, the numerical simulation test and the actual conditions are basically coincident. Thus the well-known problem has been solved.展开更多
基金financially supported by the National Key R&D Program of China under Grant No.2022YFA1005103National Natural Science Foundation of China under Grant Nos. 12271019, 11871003,12201376, 11961141005the Fundamental Research Funds for the Central Universities under Grant Nos.GK202103002, YWF-22-L-640
文摘In the field of nonlinear filtering(NLF),it is well-known that the unnormalized conditional density of the states satisfies the Zakai’s equation.The splitting-up algorithm has been first studied in the independent noises case by Bensoussan,et al.(1990).In this paper,the authors extend this convergence analysis of the splitting-up algorithm to the correlated noises’case.Given a time discretization,one splits the solution of the Zakai’s equation into two interlacing processes(with possibly computational advantage).These two processes correspond respectively to the prediction and updating.Under certain conditions,the authors show that both processes tend to the solution of the Zakai’s equation,as the time step goes to zero.The authors specify the conditions imposed on the way of splitting-up to guarantee the convergence.The major technical difficulty in the correlated noises’case,compared with the independent case,is to control the gradient of the second process in some sense.To illustrate the potentially computational advantage of the schemes based on the splitting-up ways,the authors experiment on a toy NLF model using the feedback particle filter(FPF)developed based on the splitting-up method and the sampling importance and resampling(SIR)as comparison.The FPF outperforms in both accuracy and efficiency.
文摘Numerical simulation of oil migration and accumulation is to describe the history of oil migration and accumulation in basin evolution. It is of great value in the exploration of oil resources and their rational evaluation. In this paper, from such actual conditions as the effects of mechanics of fluids in porous media and 3-dimensional geology characteristics, a kind of modified method of second order splitting-up implicit interactive scheme is pur forward. For the famous hydraulic experiment of secondary migration-accumulation, the numerical simulation test has been done, and both the computational and experimental results are basically identical. For the actual problem of Dongying hollow of Shengli Petroleum Oil Field, the numerical simulation test and the actual conditions are basically coincident. Thus the well-known problem has been solved.
