SCALABLE PHYSICS-INFORMED NEURAL SOLVERS FOR HIGH-DIMENSIONAL SCIENTIFIC SIMULATIONS IN HETEROGENEOUS COMPUTING ENVIRONMENTS ENHANCED ADAPTIVE SPARSE APPROXIMATION FRAMEWORK INTEGRATING DEEP LEARNING, FINITE ELEMENT METHODS, AND PARALLEL GPU-CPU CO-P

Scientific simulations often struggle to maintain computational efficiency in high-dimensional domains due to the complexity of physical models and the burden on traditional numerical solvers. This paper introduces a hybrid scalable framework combining Physics-Informed Neural Networks (PINNs), adaptive sparse approximation, and Finite Element Methods (FEM) optimized for heterogeneous GPU-CPU co-processing. The proposed architecture enhances scalability and precision across complex domains in climate modeling, material science, and fluid dynamics. By integrating deep learning with FEM and leveraging parallelized processing, this framework significantly reduces execution time and improves convergence rates. Extensive benchmarking highlights the superiority of the hybrid method over standalone approaches.