  Propositional satisfiability (SAT) is an NP-complete problem that impacts
many research fields, such as planning, verification, and security. Mainstream
modern SAT solvers are based on the Conflict-Driven Clause Learning (CDCL)
algorithm. Recent work aimed to enhance CDCL SAT solvers using Graph Neural
Networks (GNNs). However, so far this approach either has not made solving more
effective, or required substantial GPU resources for frequent online model
inferences. Aiming to make GNN improvements practical, this paper proposes an
approach called NeuroBack, which builds on two insights: (1) predicting phases
(i.e., values) of variables appearing in the majority (or even all) of the
satisfying assignments are essential for CDCL SAT solving, and (2) it is
sufficient to query the neural model only once for the predictions before the
SAT solving starts. Once trained, the offline model inference allows NeuroBack
to execute exclusively on the CPU, removing its reliance on GPU resources. To
train NeuroBack, a new dataset called DataBack containing 120,286 data samples
is created. NeuroBack is implemented as an enhancement to a state-of-the-art
SAT solver called Kissat. As a result, it allowed Kissat to solve up to 5.2%
and 7.4% more problems on two recent SAT competition problem sets, SATCOMP-2022
and SATCOMP-2023, respectively. NeuroBack therefore shows how machine learning
can be harnessed to improve SAT solving in an effective and practical manner.
