Neural Network Variational Monte Carlo Energy Determination

The patent performs preliminary iteration rounds to establish the linear relationship between energy errors and energy variances before the final energy determination. By pre-characterizing the error-variance relationship through multiple iteration rounds with different initial guesses, the method prepares extrapolation parameters in advance, allowing the final energy calculation to be obtained quickly through simple extrapolation rather than requiring extensive additional computations.

The patent replaces the traditional mechanical iterative convergence process with a mathematical extrapolation approach. Instead of continuing iterations until energy variance converges to zero (which is computationally expensive), the method substitutes this with linear extrapolation based on the established error-variance relationship, achieving the same goal of obtaining accurate energy values with significantly reduced computational effort.

The patent performs a sufficient number of iteration rounds to establish the linear relationship between energy errors and energy variances, but stops before complete convergence is achieved. This partial action is sufficient to characterize the error-variance relationship, and the remaining accuracy is obtained through extrapolation, avoiding the excessive computational cost of achieving full convergence while still maintaining high accuracy.

Multiple iteration rounds are performed preliminarily to map the energy error-variance relationship. This preliminary characterization allows the final accurate energy value to be obtained through extrapolation to zero variance, rather than requiring the computationally expensive complete convergence process.

The patent substitutes the time-consuming mechanical process of performing numerous iteration rounds to reduce energy error with a mathematical extrapolation method. By establishing the linear relationship between energy errors and energy variances through limited iterations, the method can extrapolate the energy error at zero variance, achieving high precision without requiring extensive additional iteration time.

The patent creates a linear model (copy) of the energy error-variance relationship based on limited iteration data. This linear model serves as a surrogate that can predict the energy error at zero variance without requiring actual computation at that point, thus obtaining high precision results efficiently through the copied relationship rather than direct computation.