Structural variants (SVs) are increasingly recognized as important contributors to oncogenesis through their effects on 3D genome folding. Recent advances in whole-genome sequencing have enabled large-scale profiling of SVs across diverse tumors, yet experimental characterization of their individual impact on genome folding remains infeasible. Here, we leveraged a convolutional neural network, Akita, to predict disruptions in genome folding caused by somatic SVs identified in 61 tumor types from the Children\'s Brain Tumor Network dataset. Our analysis reveals significant variability in SV-induced disruptions across tumor types, with the most disruptive SVs coming from lymphomas and sarcomas, metastatic tumors, and germline cell tumors. Dimensionality reduction of disruption scores identified five recurrently disrupted regions enriched for high-impact SVs across multiple tumors. Some of these regions are highly disrupted despite not being highly mutated, and harbor tumor-associated genes and transcriptional regulators. To further interpret the functional relevance of high-scoring SVs, we integrated epigenetic data and developed a modified Activity-by-Contact scoring approach to prioritize SVs with disrupted genome contacts at active enhancers. This method highlighted highly disruptive SVs near key oncogenes, as well as novel candidate loci potentially implicated in tumorigenesis. These findings highlight the utility of machine learning for identifying novel SVs, loci, and genetic mechanisms contributing to pediatric cancers. This framework provides a foundation for future studies linking SV-driven regulatory changes to cancer pathogenesis.