Search

Compared with the application of Digital Twin (DT) in the industrial field, the application of DT in the field of education is still in its infancy. In this paper, a Digital Twin Campus (DTC) for teaching and learning is proposed. It is argued that DTC possesses two characteristics. First, DTC has a wide variety of employment orientations for students or teachers. Second, teaching-learning resources in DTC system is huge but divisible. These characteristics result in the optional difficulty for teaching-learning objects, i.e., curriculum resources, book information resources, and electronic-article resources. To solve this problem, this paper proposes a Double-layer Collaborative Filtering Algorithm Framework (DCFAF) to recommend teaching-learning objects for digital twin teachers or students in DTC. The recommended objects will be further optimized by simulation and prediction in the virtual space of DTC. DCFAF is designed based on the principle that similar teachers (or students) may prefer similar teaching-learning resources, and for the first time, it is given double-layer property by applying the divisible characteristics of teaching-learning resources. The double-layer property can effectively solve the problem of data sparsity in collaborative filtering algorithms. Finally, the superiority of DCFAF is verified on benchmark data sets including MovieLens100k and MovieLens1M which possess the above two characteristics of DTC. DTC constructed in this way can be expected to carry out simulation, prediction, optimization and feedback continuously with the help of DCFAF, so as to realize deep integration of the teaching-learning process between real campus and virtual campus to some extent.

Traditional methods, including direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles, are the mainstream methods used to solve the volume-temperature flash calculation (called NVT-flash), even though they suffer from drawbacks such as sensitivity to initial value and complexity of derivative calculations. A constrained backtracking search algorithm (CBSA), proposed in 2024, was the first and only metaheuristic algorithm to successfully tackle the NVT-flash problem, which overcomes shortcomings of traditional methods. Considering the advantages of metaheuristic algorithms, a constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (CGPE-QI) is proposed in this paper to deal with the NVT-flash problem. CGPE-QI considers total Helmholtz free energy as the objective function, moles vector, and volume of a single phase as variables. Constraints to solve the NVT-flash problem are addressed by using a direct search method and an exterior point method. Numerical experiments on two-phase equilibrium of pure substance and mixtures are carried out employing CGPE-QI. Experimental results are the same as those obtained by traditional methods, which confirms that CGPE-QI can effectively tackle the NVT-flash problem and possesses energy decay property. In particular, the results demonstrate that CGPE-QI is more competitive than CBSA in terms of convergence speed, stability, and calculation cost. CGPE-QI proposed in this paper is the second metaheuristic algorithm to successfully solve the NVT-flash problem, illustrating that metaheuristic algorithms have great potential in solving phase equilibrium calculation problems. [ABSTRACT FROM AUTHOR]