Bidirectional and Nested Models: Bridging Machine Learning and Numerical Simulation for Engineering Prediction

Despite rapid progress in machine learning across diverse fields, its application in engineering remains challenging due to the high dimensionality of data, complex physical mechanisms, and the strong demand for generalization. To address these challenges, we propose a novel Bidirectional and Nested Model (BNM) that integrates submodels constructed by machine learning and numerical simulation methods. Within the BNM framework, these two types of submodels interact bidirectionally, exchange data dynamically, and undergo joint training. A case study on long-term tunnel settlement prediction demonstrates that BNM provides four major advantages: (1) Powerful information integration, (2) Enhanced physical interpretability and analytical capability, (3) Strong evolutionary potential, and (4) Simplified modeling process. The results highlight the broad applicability of BNM for large-scale engineering problems and generative artificial intelligence. This study introduces a new paradigm for data- and physics-driven modeling in engineering, thereby advancing the development of next-generation intelligent engineering systems.