## 2 Extension of Dynamic Relational Network for Spatiotemporal Interpolation  
### Dynamic Relational Network Model for Space Weather Forecasting  
Section 2 extends the dynamic relational network that supports sensor faults by replacing unavailable sensors with virtual sensors. The neighbor sensors virtually create the virtual sensors by communication and information processing, given the fact that actual sensors would be unavailable due to technical reasons or problems of electrical circuits [1]. The virtual sensors could compensate for the faulted sensors, since, the observations can be interpolated by virtual sensors. To this direction, such an extension had not been investigated in the framework of the dynamic relational network. A related study [3] on the dynamic relational network had been proposed. The study reported on the dynamic relational network for space weather forecasting involving virtual sensors for prediction. In that study, the proposed model forecasted the high-energy electron flux at GEO (\(\geq\)2 MeV), 24 h ahead, while the proposed model, involving virtual sensors, was successful on the prediction of the high-energy electron flux. This paper proposes the framework for resilient sensor networks based on the dynamic relational network. As an example, we choose a research issue of space weather forecasting for the high-energy electron flux at GEO. The prediction of condition on high-energy electrons at GEO is vital in space weather forecasting. Because, high-energy electrons penetrate into the satellites and charge on the instruments in them. Moreover, high-energy electrons can damage instruments or electrical circuits of the satellites [1; 13]. Given the fact that different kind of satellites are in operation at GEO: such as broadcasting, communication, and meteorological satellites, those constitute an essential infrastructure for the society. A theoretical model for enhancement of high-energy electrons is still under investigation [15]. Some candidate models had been proposed [16; 17]. However, a critical evidence for these candidate models has not yet been obtained by satellite observations. The observation of the enhancement of high-energy electrons is preparing in ERG project [18]. This project is going to observe high-energy particles by in-situ sensing with its satellite in 2016. However, various kinds of models for prediction of high-energy electron flux at GEO have been proposed. The prediction methods are categorized into two categories: Theoretical approach and information-based approach. In the theoretical approach, dynamics on high-energy electrons are forecasted with dynamics and observed data by numerical simulations [17; 19; 20]. However, the models by this approach are complicated, and it requires many resource for computation (e.g., time and memory). In the information-based approach, on the other hand, various kinds of models have been proposed. For instance, the linear prediction filter has been developed [21] for the prediction of the high-energy electron flux. The studies [22; 23; 24; 25] have also investigated prediction models using neural networks. This paper thinks that the proposed model is categorized into the information-based approach. The relations among sensors are profiled by a knowledge-based information processing. However, space weather forecasting is dynamically predicted by the dynamic relational network model. This paper demonstrates simulations on space weather forecasting by the proposed model in Section 3. Basically, in the proposed model, the sensor network for space weather forecasting consists of four real sensors and for a single virtual sensor. One of the real sensors is a high-energy electron flux (\(\geq\)2 MeV) installed on the Geostationary Operational Environmental Satellite 10 (GOES-10) of National Oceanic and Atmospheric Administration. The other real sensors are for the solar wind speed installed on two satellites in a mission of the Solar Terrestrial Relations Observatory (STEREO) [26] and the Advanced Composition Explorer (ACE) [27].