Data assimilation (DA) combines numerical model simulations with observed data to obtain the best possible description of a dynamical system and its uncertainty. Incorrect modeling assumptions can lead to filter divergence, making model identification an important issue in the field of DA. Variations in dynamic model structures can result in differences in parameter dimensions, complicating the resampling step in PFs. To meet this challenge, the Sequential Hierarchical Bayesian Model (SHBM) is proposed in this paper, which integrates the evolution model along with observation model from the DA scheme, and the hierarchical parameter model. A two-step resampling method are also proposed to estimate the SHBM: the first step uses the resampling scheme in the bootstrap filter to resample new particles based on weights, which may produce some duplicate particles; the second step utilizes the Reversible Jump Markov Chain Monte Carlo (RJMCMC) methods to draw new particles from the target distribution. This approach ensures particle diversity, with the first step aiming at avoiding particle degeneracy, and the second step intends to prevent the sample impoverishment. The performance in the Advection Equation example and Lorenz 96 example demonstrates the effectiveness of the proposed method.

In data assimilation (DA) schemes, the form representing the processes in the evolution models are pre-determined except some parameters to be estimated. In some applications, such as the contaminant solute transport model and the gas reservoir model, the modes in the equations within the evolution model cannot be predetermined from the outset and may change with the time. We propose a framework of sequential DA method named Reversible Jump Ensemble Filter (RJEnF) to identify the governing modes of the evolution model over time. The main idea is to introduce the Reversible Jump Markov Chain Monte Carlo (RJMCMC) method to the DA schemes to fit the situation where the modes of the evolution model are unknown and the dimension of the parameters is changing. Our framework allows us to identify the modes in the evolution model and their changes, as well as estimate the parameters and states of the dynamic system. Numerical experiments are conducted and the results show that our framework can effectively identify the underlying evolution models and increase the predictive accuracy of DA methods.

Long-distance quantum communication and networking require quantum memory nodes with efficient optical interfaces and long memory times. We report the realization of an integrated two-qubit network node based on silicon-vacancy centers (SiVs) in diamond nanophotonic cavities. Our qubit register consists of the SiV electron spin acting as a communication qubit and the strongly coupled silicon-29 nuclear spin acting as a memory qubit with a quantum memory time exceeding 2 seconds. By using a highly strained SiV, we realize electron-photon entangling gates at temperatures up to 1.5 kelvin and nucleus-photon entangling gates up to 4.3 kelvin. We also demonstrate efficient error detection in nuclear spin–photon gates by using the electron spin as a flag qubit, making this platform a promising candidate for scalable quantum repeaters.

Simulations are often used to investigate the flow structures and system dynamics of complex natural phenomena and systems, which are significantly harder to obtain from experiments or theoretical analyses. Surrogate models are employed to mimic the results of simulations by reducing computational costs. In order to reduce the amount of computational time consumed, a novel framework for building efficient surrogate models is proposed in this work. The novelty lies in that the new framework runs simulations using the different simulation time spans for different inputs and builds a comprehensive surrogate model through the fusion of non-homogeneous spatio-temporal data by integrating the temporal and spatial correlations in parametric space. This differs from the existing works in the literature, which only consider the situation of spatio-temporal data with a consistent time span during simulations under different inputs. Some simulation studies and real data analysis concerning the pollution of the river in the Sichuan Province of China are used to demonstrate the superior performance of the proposed methods.