With the development of gravity gradient full tensor measurement technique,three-dimensional( 3D) inversion based on gravity gradient tensor can provide more accurate information. But the forward calculation of 3D ful...With the development of gravity gradient full tensor measurement technique,three-dimensional( 3D) inversion based on gravity gradient tensor can provide more accurate information. But the forward calculation of 3D full tensor sensitivity matrix is very time-consuming,which restricts its development and application.According to the symmetry of the kernel function,the authors reconstruct the underground source of geological body to avoid repeat computation of the same value,and work out the corresponding relationship between the response of geological body to the observation point and the response of reconstructed geological body to the observation point. According to the relationship,rapid calculation of full tensor gravity sensitivity matrix can be achieved. The model calculation shows that this method can increase the speed of 30-45 times compared with the traditional calculation method. The sensitivity matrix is applied to the multi-component inversion of gravity gradient. The application of this method on the measured data provides the basis for the promotion of the method.展开更多
The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems.Recently,equ...The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems.Recently,equivariant message passing neural networks(MPNNs)that explicitly incorporate symmetry constraints have demonstrated promise for interatomic potential and density functional theory(DFT)Hamiltonian predictions.However,the high-order tensors used to represent node and edge information are coupled through the Clebsch–Gordan tensor product,leading to steep increases in computational complexity and seriously hindering the performance of equivariant MPNNs.Here,we develop high-order tensor machine-learning Hamiltonian(Hot-Ham),an E(3)equivariant MPNN framework that combines two advanced technologies:local coordinate transformation and Gaunt tensor product to efficiently model DFT Hamiltonians.These two innovations significantly reduce the complexity of tensor products from O(L^(6))to O(L^(3))or O(L^(2)log^(2)L)for the max tensor order L,and enhance the performance of MPNNs.Benchmarks on several public datasets demonstrate its state-of-the-art accuracy with relatively few parameters,and applications to multilayer twisted moire systems,heterostructures,and allotropes showcase its generalization ability and high efficiency.Our Hot-Ham method provides a new perspective for developing efficient equivariant neural networks and would be a promising approach for investigating the electronic properties of large-scale materials systems.展开更多
针对射线追踪法(shooting and bouncing ray,SBR)中反射路径计算,提出了采用反射张量表示单次和多次反射作用的方法,并进行了详细推导。对于同一反射路径,射线方向、极化方向的变化可以用同一个张量与原方向的点积表示。通过分析张量的...针对射线追踪法(shooting and bouncing ray,SBR)中反射路径计算,提出了采用反射张量表示单次和多次反射作用的方法,并进行了详细推导。对于同一反射路径,射线方向、极化方向的变化可以用同一个张量与原方向的点积表示。通过分析张量的运算,研究了单站情形不同极化下射线追踪法计算结果。算例表明,反射张量表示方法用于射线追踪法正确、有效,可方便地对各种构型的散射目标进行分析研究。展开更多
基金Support by Project of Geophysical Comprehensive Survey and Information Extraction of Deep Mineral Resources(2016YFC0600505)
文摘With the development of gravity gradient full tensor measurement technique,three-dimensional( 3D) inversion based on gravity gradient tensor can provide more accurate information. But the forward calculation of 3D full tensor sensitivity matrix is very time-consuming,which restricts its development and application.According to the symmetry of the kernel function,the authors reconstruct the underground source of geological body to avoid repeat computation of the same value,and work out the corresponding relationship between the response of geological body to the observation point and the response of reconstructed geological body to the observation point. According to the relationship,rapid calculation of full tensor gravity sensitivity matrix can be achieved. The model calculation shows that this method can increase the speed of 30-45 times compared with the traditional calculation method. The sensitivity matrix is applied to the multi-component inversion of gravity gradient. The application of this method on the measured data provides the basis for the promotion of the method.
基金supported by the National Natural Science Foundation of China(Grant Nos.12125404,T2495231,and 123B2049)the Basic Research Program of Jiangsu(Grant Nos.BK20233001,BK20241253,and BK20253009)+3 种基金the Jiangsu Funding Program for Excellent Postdoctoral Talent(Grant Nos.2024ZB002 and 2024ZB075)the Postdoctoral Fellowship Program of CPSF(Grant No.GZC20240695)the AI&AI for Science program of Nanjing University,the Artificial Intelligence and Quantum physics(AIQ)program of Nanjing Universitythe Fundamental Research Funds for the Central Universities。
文摘The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems.Recently,equivariant message passing neural networks(MPNNs)that explicitly incorporate symmetry constraints have demonstrated promise for interatomic potential and density functional theory(DFT)Hamiltonian predictions.However,the high-order tensors used to represent node and edge information are coupled through the Clebsch–Gordan tensor product,leading to steep increases in computational complexity and seriously hindering the performance of equivariant MPNNs.Here,we develop high-order tensor machine-learning Hamiltonian(Hot-Ham),an E(3)equivariant MPNN framework that combines two advanced technologies:local coordinate transformation and Gaunt tensor product to efficiently model DFT Hamiltonians.These two innovations significantly reduce the complexity of tensor products from O(L^(6))to O(L^(3))or O(L^(2)log^(2)L)for the max tensor order L,and enhance the performance of MPNNs.Benchmarks on several public datasets demonstrate its state-of-the-art accuracy with relatively few parameters,and applications to multilayer twisted moire systems,heterostructures,and allotropes showcase its generalization ability and high efficiency.Our Hot-Ham method provides a new perspective for developing efficient equivariant neural networks and would be a promising approach for investigating the electronic properties of large-scale materials systems.
文摘针对射线追踪法(shooting and bouncing ray,SBR)中反射路径计算,提出了采用反射张量表示单次和多次反射作用的方法,并进行了详细推导。对于同一反射路径,射线方向、极化方向的变化可以用同一个张量与原方向的点积表示。通过分析张量的运算,研究了单站情形不同极化下射线追踪法计算结果。算例表明,反射张量表示方法用于射线追踪法正确、有效,可方便地对各种构型的散射目标进行分析研究。
