Adaptive Mesh Refinement with Dynamic Load Balancing for Scalable Cosmological Simulations: A Hybrid Meta-Heuristic Approach

We propose a novel framework for cosmological simulations that integrates adaptive mesh refinement (AMR) with dynamic load balancing to address the challenges of spatial-temporal complexity in high-performance computing (HPC) environments. The proposed system employs a hybrid meta-heuristic algorithm, combining particle-swarm optimization with gradient-based heuristics, to dynamically redistribute computational workloads while minimizing communication overhead and latency penalties. The AMR component utilizes a wavelet-based error estimator to adaptively adjust mesh resolution, ensuring physical consistency with refinement criteria tied to local density gradients. Furthermore, the framework replaces conventional static domain decomposition with a dynamic task redistribution mechanism, which interacts seamlessly with gravity and hydrodynamics solvers through non-blocking MPI-3.0 interfaces. Implemented on GPU-accelerated HPC clusters, the system extends the AMReX library with custom CUDA kernels and integrates a distributed Rust-based load balancer for low-latency task migration. The co-design of AMR and load balancing eliminates traditional synchronization bottlenecks, achieving a 30--40\% reduction in preliminary benchmarks. This approach significantly enhances scalability and resolution fidelity in large-scale cosmological simulations, offering a robust solution for modern computational astrophysics. The novelty lies in the tight coupling of mesh adaptation and workload optimization, which collectively improve efficiency without compromising accuracy.