Tatsuoki Takeda

Neural network CT image reconstruction method for small amount of projection data

Abstract This paper presents a new method for two-dimensional image reconstruction by using a multi-layer neural network. Though a conventionally used object function of such a neural network is composed of a sum of squared errors of the output data, we define an object function composed of a sum of squared residuals of an integral equation. By employing an appropriate numerical line integral for this integral equation, we can construct a neural network which can be used for CT image reconstruction for cases with small amount of projection data. We applied this method to some model problems and obtained satisfactory results. This method is especially useful for analyses of laboratory experiments or field observations where only a small amount of projection data is available in comparison with the well-developed medical applications.

Optimal estimation of parameters of dynamical systems by neural network collocation method

Abstract In this paper we propose a new method to estimate parameters of a dynamical system from observation data on the basis of a neural network collocation method. We construct an object function consisting of squared residuals of dynamical model equations at collocation points and squared deviations of the observations from their corresponding computed values. The neural network is then trained by optimizing the object function. The proposed method is demonstrated by performing several numerical experiments for the optimal estimates of parameters for two different nonlinear systems. Firstly, we consider the weakly and highly nonlinear cases of the Lorenz model and apply the method to estimate the optimum values of parameters for the two cases under various conditions. Then we apply it to estimate the parameters of one-dimensional oscillator with nonlinear damping and restoring terms representing the nonlinear ship roll motion under various conditions. Satisfactory results have been obtained for both the problems.

Application of neural network collocation method to data assimilation

Abstract In this paper we propose a new data assimilation method by using a neural network. In the method we make use of the flexibility of a neural network for constructing an arbitrary mapping function. We train a neural network by optimizing an object function composed of squared residuals of differential equations at collocation points and squared deviations of the observation data from the computed values. The method we propose is, therefore, data assimilation with weak constraints. In this way we can solve an assimilation problem even if the model differential equations do not express the observed phenomena exactly. As an example we applied the new method to a data assimilation problem where the model is the well-known Lorenz model. Though the practically applicable data assimilation method should be able to solve four-dimensional problems (one temporal and three spatial dimensions) and the Lorenz model is one-dimensional, this model is still useful for a benchmark test of the data assimilation methods due to its strong nonlinearity and chaotic nature. We have examined the new method for the above mentioned problem under various conditions and obtained satisfactory results.

Applying a Neural Network Collocation Method to an Incompletely Known Dynamical System via Weak Constraint Data Assimilation

A method based on a neural network collocation method is proposed for approximating incompletely known dynamical systems via weak constraint data assimilation formulation. The aim of the new method is to solve several difficult issues encountered in previous research. For this purpose, the weak constraint property of the neural network collocation method is used. The problem regarding the wider assimilation window is tackled by interconnecting narrower windows with finite overlapping interfaces. The method is examined by considering the Lorenz system as an example where one of the three equations of the system is unknown. The object function of the neural network training is composed of squared residuals of differential equations at collocation points and squared deviations of the observations from their corresponding calculated values. The weakly and highly nonlinear cases of the Lorenz system are considered. The numerical experiments have been carried out with simulated noiseless and noisy observation data under various conditions. The performance of the method for approximating an unknown equation during the assimilation and testing periods is examined for the two cases. Also, the parameters of incomplete dynamical systems are estimated for the two cases. Satisfactory results have been obtained in both cases.

Asymmetric Abel inversion by neural network for reconstruction of plasma density distribution

This paper presents a new method for asymmetric Abel inversion by a neural network. As a typical asymmetric Abel inversion problem, we consider to reconstruct a plasma density distribution in a fusion device from a dataset obtained by interferometric measurement of electromagnetic waves, and propose a new method realized by making use of the excellent feature of a neural network to approximate wide range of mapping functions. In this method, training of the network is carried out by minimizing a squared residual of integral equation along measuring paths, where density contours are also adjusted on the basis of the database of the density contours (the plasma MHD equilibrium). By this method, therefore, we can determine the contour shapes as well as the contour values of the density even in the asymmetric Abel inversion problem. We applied this method to model problems and obtained satisfactory results. This method is applicable to similar problems provided series of contour geometries defined in a one- or a few-dimensional subspace of a multi-dimensional parameter space are given as a numerical database.

Neural network based tomographic approach to detecting the ionospheric anomalies prior to the 2007 Southern Sumatra earthquake

In this paper, neural network based ionospheric tomography was performed to investigate the detailed structure that may be associated with earthquakes. The 2007 Southern Sumatra earthquake (M8.5) is selected because significant decreases in the Total Electron Content (TEC) have been confirmed by GPS data analysis. With respect to the analyzed earthquake, we detected significant decreases at heights of 250–400 km, especially at 300 km. The global tendency is that the decreased region expands to the east with increasing altitude and concentrated in the Southern hemisphere over the epicenter. Furthermore, obtained results are consistent with other satellite observation.

Development and validation of neural network based ionospheric tomography

In order to investigate the dynamics of ionospheric phenomena, perform the 3-D ionospheric tomography is effective. However, it is the ill-posed inverse problem and reconstruction is difficult because of the small number of data. The Residual Minimization Training Neural Network (RMTNN) tomographic approach proposed by Ma et al. [3] has an advantage in reconstruction with sparse data. They have demonstrated few results in quiet conditions of ionosphere in Japan. Therefore, we validate the performance of reconstruction in the case of disturbed period and quite sparse data by the simulation and/or real data in this paper.