Learning mappings between functions(operators)defined on complex computational domains is a common theoretical challenge in machine learning.Existing operator learning methods mainly focus on regular computational dom...Learning mappings between functions(operators)defined on complex computational domains is a common theoretical challenge in machine learning.Existing operator learning methods mainly focus on regular computational domains,and have many components that rely on Euclidean structural data.However,many real-life operator learning problems involve complex computational domains such as surfaces and solids,which are non-Euclidean and widely referred to as Riemannian manifolds.Here,we report a new concept,neural operator on Riemannian manifolds(NORM),which generalises neural operator from Euclidean spaces to Riemannian manifolds,and can learn the operators defined on complex geometries while preserving the discretisation-independent model structure.NORM shifts the function-to-function mapping to finite-dimensional mapping in the Laplacian eigenfunctions’subspace of geometry,and holds universal approximation property even with only one fundamental block.The theoretical and experimental analyses prove the significant performance of NORM in operator learning and show its potential for many scientific discoveries and engineering applications.展开更多
Developing high-performance ammonia decomposition catalysts for preparing COx-free hydrogen shows great practical significance.Herein,CeO_(2) is used as a promoter to modulate the metal-support interaction to enhance ...Developing high-performance ammonia decomposition catalysts for preparing COx-free hydrogen shows great practical significance.Herein,CeO_(2) is used as a promoter to modulate the metal-support interaction to enhance the catalytic performance of Ru/Al_(2)O_(3) catalysts.A series of 1Ru/xCe-10AI(x=0.5,1,or 3)catalysts was prepared by a facile colloidal deposition method.We find that the optimized 1 Ru/1Ce-10Al catalyst exhibits excellent activity for the decomposition of ammonia with a very high hydrogen yield of7097 mmolH2/(gRu·min)at 450℃.It is confirmed that Ru species are highly dispersed on the support surface as stable small clusters(~1.3 nm).More importantly,due to the interaction between Ru species and partially reduced CeO_(2-x),the electron density of Ru species is increased,which is beneficial to the high activity of the 1 Ru/xCe-10Al catalysts.This work paves a way to construct high-efficiency ammonia decomposition catalysts modified by CeO_(2).展开更多
基金supported by the National Science Fund for Distinguished Young Scholars (51925505)the General Program of National Natural Science Foundation of China (52275491)+3 种基金the Major Program of the National Natural Science Foundation of China (52090052)the Joint Funds of the National Natural Science Foundation of China (U21B2081)the National Key R&D Program of China (2022YFB3402600)the New Cornerstone Science Foundation through the XPLORER PRIZE
文摘Learning mappings between functions(operators)defined on complex computational domains is a common theoretical challenge in machine learning.Existing operator learning methods mainly focus on regular computational domains,and have many components that rely on Euclidean structural data.However,many real-life operator learning problems involve complex computational domains such as surfaces and solids,which are non-Euclidean and widely referred to as Riemannian manifolds.Here,we report a new concept,neural operator on Riemannian manifolds(NORM),which generalises neural operator from Euclidean spaces to Riemannian manifolds,and can learn the operators defined on complex geometries while preserving the discretisation-independent model structure.NORM shifts the function-to-function mapping to finite-dimensional mapping in the Laplacian eigenfunctions’subspace of geometry,and holds universal approximation property even with only one fundamental block.The theoretical and experimental analyses prove the significant performance of NORM in operator learning and show its potential for many scientific discoveries and engineering applications.
基金Project supported by the National Key Basic Research Program of China(2021YFA1501103)the National Science Fund for Distinguished Young Scholars of China(22225110)+1 种基金the National Natural Science Foundation of China(22075166,22271177)the Taishan Scholar Project of Shandong Province of China,and the Young Scholars Program of Shandong University.
文摘Developing high-performance ammonia decomposition catalysts for preparing COx-free hydrogen shows great practical significance.Herein,CeO_(2) is used as a promoter to modulate the metal-support interaction to enhance the catalytic performance of Ru/Al_(2)O_(3) catalysts.A series of 1Ru/xCe-10AI(x=0.5,1,or 3)catalysts was prepared by a facile colloidal deposition method.We find that the optimized 1 Ru/1Ce-10Al catalyst exhibits excellent activity for the decomposition of ammonia with a very high hydrogen yield of7097 mmolH2/(gRu·min)at 450℃.It is confirmed that Ru species are highly dispersed on the support surface as stable small clusters(~1.3 nm).More importantly,due to the interaction between Ru species and partially reduced CeO_(2-x),the electron density of Ru species is increased,which is beneficial to the high activity of the 1 Ru/xCe-10Al catalysts.This work paves a way to construct high-efficiency ammonia decomposition catalysts modified by CeO_(2).
