Cooperative path planning in complex coastal mountainous environments near the shore is a knowledge-intensive engineering task crucial for demanding multi-UAV operations such as disaster rescue, environmental monitoring, and coastal emergency response. However, the complex coupling constraints in 3D space make it a challenging high-dimensional optimization problem where traditional metaheuristics often suffer from undirected blind exploration and invalid trial and error. To overcome these limitations, we propose the deep neural network-guided phototropic growth algorithm (DNN-PGA), an engineering informatics framework that deeply couples explicit spatial knowledge representation with traditional heuristic search mechanisms. Specifically, we implement a spatial prior generation method to transform unstructured 3D environmental data into structured knowledge distributions. We utilize deep neural networks to extract spatial heatmap priors from multi-channel voxel representations, serving as a formal representation of potential high-quality path regions. Subsequently, the core search operator of PGA is reconstructed by deploying these explicit spatial priors as structural constraints to strictly guide engineering decision-making. Within the DNN-PGA, a neural network-guided initialization mechanism ensures efficient spatial focusing of the initial population. Secondly, a neural control golden-sine strategy was designed to enable dynamic regulation of local exploitation intensity, and a neural limited lens opposition-based learning mechanism was developed to accurately guide individuals out of local optima using learned spatial knowledge. Extensive experiments confirm that the DNN-PGA achieves an average reduction of 29.49% in mean path cost compared with the best-performing competing algorithm across all scenarios under complex operational conditions. Ultimately, the DNN-PGA successfully establishes a highly robust, knowledge-driven practical solution for demanding 3D multi-UAV cooperative path planning tasks in coastal mountainous environments.