From the Termination of Brute Force Numerical Accumulation Computing to a Paradigm Shift toward Topological Quantum Relaxation Physical Computing An Empirical Investigation of 10⁸ Level 8D Computing Power Enhance

Abstract: Since Bellman (1961) first proposed the “curse of dimensionality,” Donoho (2000) highlighted the challenges in high-dimensional data analysis, and Bengio et al. (2013) discussed the dimensionality curse in deep learning; meanwhile, recent HPC research (2023) has empirically demonstrated that “the discretization of only a 6-dimensional PDE results in communication overhead exceeding 85%,” indicating that traditional discretization methods face the curse of dimensionality, leading to combinatorial explosion, communication dominance, and slow convergence. In traditional computation, under an 8-dimensional discretization scenario with only 10 variables per dimension, if variables across dimensions are fully coupled, the theoretically most complex computation can reach the order of 10⁻⁶⁴, far exceeding the processing capability of any supercomputer. This study, through physical computation based on the continuous evolution of a topological quantum relaxation field, successfully reduces computational complexity of 8D by 7 orders of magnitude, breaking through the three fundamental HPC barriers, using only 7 GB of available video memory on an RTX 2070S graphics card plus 28 GB of available system memory of DDR3; across 19 test cases of varying difficulty, it achieves an average of 1464 iteration steps and an average runtime of 8.21 minutes, all reaching a convergence accuracy of 10⁻⁶ at the million level. The results empirically demonstrate that, using low-end consumer-grade hardware and ADC-based topological quantum relaxation physical computation, the curse of dimensionality in medium-to-high difficulty mathematical computations under 8D high-dimensional settings can be completely overcome.