The operations and maintenance of satellite networks heavily depend on traffic measurements. Due to the large-scale and highly dynamic nature of satellite networks, global measurement encounters significant challenges in terms of complexity and overhead. Estimating global network traffic data from partial traffic measurements is a promising solution. However, the majority of current estimation methods concentrate on low-rank linear decomposition, which is unable to accurately estimate. The reason lies in its inability to capture the intricate nonlinear spatio-temporal relationship found in large-scale, highly dynamic traffic data.

The operations and maintenance of satellite networks heavily depend on traffic measurements.

The operations and maintenance of satellite networks heavily depend on traffic measurements. Due to the large-scale and highly dynamic nature of satellite networks, global measurement encounters significant challenges in terms of complexity and overhead. Estimating global network traffic data from partial traffic measurements is a promising solution. However, the majority of current estimation methods concentrate on low-rank linear decomposition, which is unable to accurately estimate. The reason lies in its inability to capture the intricate nonlinear spatio-temporal relationship found in large-scale, highly dynamic traffic data.

In this paper, we propose SATformer, a novel Transformer-based solution for Boolean satisfiability (SAT) solving. Different from existing learning-based SAT solvers that learn at the problem instance level, SATformer learns the minimum unsatisfiable cores (MUC) of unsatisfiable problem instances, which provide rich information for the causality of such problems. Specifically, we apply a graph neural network (GNN) to obtain the embeddings of the clauses in the conjunctive normal format (CNF). A hierarchical Transformer architecture is applied on the clause embeddings to capture the relationships among clauses, and the self-attention weight is learned to be high when those clauses forming UNSAT cores are attended together, and set to be low otherwise. By doing so, SATformer effectively learns the correlations among clauses for SAT prediction. Experimental results show that SATformer is more powerful than existing end-to-end learning-based SAT solvers.