In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symm...In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symmetric points,numerical simulations are conducted to one-soliton and two-soliton solutions of a discrete KdV equation,as well as a one-soliton solution of a discrete Toda lattice equation.Compared with the existing discrete deep learning approach,the numerical results reveal that within the specified spatiotemporal domain,the prediction accuracy by SDE-PINN is excellent regardless of the interior or extrapolation prediction,with a significant reduction in training time.The proposed data enhancement technique and symmetric structure development provides a new perspective for the deep learning approach to solve discrete NLEs.The newly proposed SDE-PINN can also be applied to solve continuous nonlinear equations and other discrete NLEs numerically.展开更多
Low ionic conductivity is a major obstacle for polymer solid-state electrolytes.In response to this issue,a design concept of enhanced regional electric potential difference(EREPD)is proposed to modulate the interacti...Low ionic conductivity is a major obstacle for polymer solid-state electrolytes.In response to this issue,a design concept of enhanced regional electric potential difference(EREPD)is proposed to modulate the interaction of nanofillers with other components in the composite polymer solid-state electrolytes(CPSEs).While ensuring the periodic structure of the graphdiyne(GDY)backbone,methoxysubstituted GDY(OGDY)is prepared by an asymmetric substitution strategy,which increases the electric potential differences within each repeating unit of GDY.The staggered distributed electron-rich regions and electron-deficient regions on the two-dimensional plane of OGDY increase the free Li^(+)concentration through Lewis acid-base pair interaction.The adjacent ERRs and EDRs form uniformly distributed EREPDs,creating a continuous potential gradient that synergistically facilitates the efficient migration of Li^(+).Impressively,the OGDY/poly(ethylene oxide)(PEO)exhibits a high ionic conductivity(1.1×10^(-3)S cm^(−1))and ion mobility number(0.71).In addition,the accelerated Li^(+)migration promotes the formation of uniform and dense SEI layers and inhibits the growth of lithium dendrites.As a proof of concept,Li||Li symmetric cell and Li||LiFePO_(4)full cell and pouch cell assembled with OGDY/PEO exhibit good performance,highlighting the effectiveness of our EREPD design strategy for improving CPSEs performance.展开更多
The changes of proteins in the rice (Oryzasativa L.) Tesanai 2 seedling under salt (NaCl,4 g/L), heat shock (42℃, 3h ), and cold(14℃, 3d ) pretreatments were compared toexplore the mechanism of the cross adaptationt...The changes of proteins in the rice (Oryzasativa L.) Tesanai 2 seedling under salt (NaCl,4 g/L), heat shock (42℃, 3h ), and cold(14℃, 3d ) pretreatments were compared toexplore the mechanism of the cross adaptationto different environmental stresses. The chill-ing resistance of rice seedling after 1℃, 150pmol·msPFD(photo flux density) for 2d was enhanced distinctly by salt, heat shock,展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12071042)the Beijing Natural Science Foundation(Grant No.1202004)Promoting the Development of University Classification-Student Innovation and Entrepreneurship Training Programme(Grant No.5112410857)。
文摘In this paper,we propose a symmetric difference data enhancement physics-informed neural network(SDE-PINN)to study soliton solutions for discrete nonlinear lattice equations(NLEs).By considering known and unknown symmetric points,numerical simulations are conducted to one-soliton and two-soliton solutions of a discrete KdV equation,as well as a one-soliton solution of a discrete Toda lattice equation.Compared with the existing discrete deep learning approach,the numerical results reveal that within the specified spatiotemporal domain,the prediction accuracy by SDE-PINN is excellent regardless of the interior or extrapolation prediction,with a significant reduction in training time.The proposed data enhancement technique and symmetric structure development provides a new perspective for the deep learning approach to solve discrete NLEs.The newly proposed SDE-PINN can also be applied to solve continuous nonlinear equations and other discrete NLEs numerically.
基金supported by the National Key Research and Development Project of China(2022YFA1204500,2022YFA1204503,2018YFA0703501)the National Natural Science Foundation of China(22275115,21875274,11704024)+4 种基金the Natural Science Foundation of Shandong Province(ZR2024ZD02)Natural Science Foundation of Hebei Province(B2020201006)Hebei Province Innovation Capability Enhancement Plan Project(22567620H)Young Scholarship Funding of Shandong University.Post-graduate Innovation Fund Project of Open Laboratory Project Fund of Hebei University(HBU2025SS010)Basic Research Project of Shandong University-Xin’an Group Silicon-Based High-End New Materials Institute.
文摘Low ionic conductivity is a major obstacle for polymer solid-state electrolytes.In response to this issue,a design concept of enhanced regional electric potential difference(EREPD)is proposed to modulate the interaction of nanofillers with other components in the composite polymer solid-state electrolytes(CPSEs).While ensuring the periodic structure of the graphdiyne(GDY)backbone,methoxysubstituted GDY(OGDY)is prepared by an asymmetric substitution strategy,which increases the electric potential differences within each repeating unit of GDY.The staggered distributed electron-rich regions and electron-deficient regions on the two-dimensional plane of OGDY increase the free Li^(+)concentration through Lewis acid-base pair interaction.The adjacent ERRs and EDRs form uniformly distributed EREPDs,creating a continuous potential gradient that synergistically facilitates the efficient migration of Li^(+).Impressively,the OGDY/poly(ethylene oxide)(PEO)exhibits a high ionic conductivity(1.1×10^(-3)S cm^(−1))and ion mobility number(0.71).In addition,the accelerated Li^(+)migration promotes the formation of uniform and dense SEI layers and inhibits the growth of lithium dendrites.As a proof of concept,Li||Li symmetric cell and Li||LiFePO_(4)full cell and pouch cell assembled with OGDY/PEO exhibit good performance,highlighting the effectiveness of our EREPD design strategy for improving CPSEs performance.
文摘The changes of proteins in the rice (Oryzasativa L.) Tesanai 2 seedling under salt (NaCl,4 g/L), heat shock (42℃, 3h ), and cold(14℃, 3d ) pretreatments were compared toexplore the mechanism of the cross adaptationto different environmental stresses. The chill-ing resistance of rice seedling after 1℃, 150pmol·msPFD(photo flux density) for 2d was enhanced distinctly by salt, heat shock,
