Neural Network aided Adaptive Tabulation with Dynamic Load Balancing for Vapor-Liquid Equilibrium Modeling of Transcritical Multiphase Flows

High-fidelity simulation of transcritical multiphase flows is critical for the design of next-generation high-pressure combustors. However, the computational cost and robustness issues associated with real-fluid Vapor-Liquid Equilibrium (VLE) calculations remain a significant bottleneck. Standard iterative flash solvers are computationally expensive and prone to convergence failures near critical points, while traditional tabulation methods suffer from the curse of dimensionality. This study presents a novel computational framework that integrates Artificial Neural Networks (ANN) with In Situ Adaptive Tabulation (ISAT) to accelerate and stabilize VLE modeling within CFD simulations. The ANN model, trained on high-fidelity VLE data and deployed via the ONNX runtime, replaces direct iterative solvers to ensure robustness and memory efficiency. To further enhance performance, an ISAT layer is coupled with the ANN to enable rapid retrieval of repeatedly accessed states and provide error control. Addressing the load imbalance inherent in tabulation-based parallel computing, a Dynamic Load Balancing (DLB) strategy is implemented to redistribute computational workloads across MPI ranks efficiently. The proposed framework is implemented in OpenFOAM and validated using a Mach 5 shock-droplet interaction case relevant to detonation conditions. Results demonstrate that the combined DLB-ISAT-ANN approach achieves substantial speed-ups (up to 2.8x) and excellent parallel scaling, even when coupled with Adaptive Mesh Refinement (AMR), while maintaining high accuracy in predicting complex thermodynamic phase behaviors.