An economic prediction of the finer resolution level wavelet coefficients in electronic structure calculations

Abstract

In wavelet based electronic structure calculations, introducing a new, finer resolution level is usually an expensive task, this is why often a two-level approximation is used with very fine starting resolution level. This process results in large matrices to calculate with and a large number of coefficients to be stored. In our previous work we have developed an adaptively refined solution scheme that determines the indices, where the refined basis functions are to be included, and later a method for predicting the next, finer resolution coefficients in a very economic way. In the present contribution, we would like to determine whether the method can be applied for predicting not only the first, but also the other, higher resolution level coefficients. Also the energy expectation values of the predicted wave functions are studied, as well as the scaling behaviour of the coefficients in the fine resolution limit.

Sports Economic Operation Index Prediction Model Based on Deep Learning and Ensemble Learning

“…It widely exists in the three major industries of the national economy, including the primary leisure industry, the secondary leisure industry, and the secondary leisure industry. The tertiary industry, of which the tertiary leisure industry is the main industry of the leisure industry, is mainly composed of tourism, culture, sports, and other leisure industries [ 2 ]. The transformation of the economic growth mode, especially the consumption-driven economic growth mode, has promoted the rapid development of the leisure industry.…”

Evaluation Index System of Economic and Social Development Pilot Area Based on Spatial Network Structure Analysis

“…Literature [ 12 ] believes that development should include economic, political, and cultural development and believes that as long as poverty, unemployment, and inequality are reduced, it belongs to development. Literature [ 13 ] proposed that development is a multidimensional process that includes the combination of the entire economy, society, culture, technology, ecology, and other elements and internal reorganization, including changes in economic aggregates, economic income growth, social systems, social structures, and even people's beliefs, habits, and other related content that cannot be regarded as a simple process.…”

From Prescriptive to Predictive: an Interdisciplinary Perspective on the Future of Computational Chemistry

“…Advances in real-space numerical electronic structure methods for DFT have been reported recently. [113][114][115][116][117][118][119][120][121][122] Many real-space methods are wavelet based, 123 take sparsity into account, 124 provide controls for numerical errors, 125,126 are robust and efficient, 127 allow for basis set truncation errors below chemical accuracy and with predetermined numerical accuracy, Fig. 4 (d), 128 and they are easily adapted to massively parallel simulations.…”