An efficient data-driven approach for predicting steady airfoil flows is proposed based on the Fourier neural operator(FNO),which is a new framework of neural networks.Theoretical reasons and experimental results are ...An efficient data-driven approach for predicting steady airfoil flows is proposed based on the Fourier neural operator(FNO),which is a new framework of neural networks.Theoretical reasons and experimental results are provided to support the necessity and effectiveness of the improvements made to the FNO,which involve using an additional branch neural operator to approximate the contribution of boundary conditions to steady solutions.The proposed approach runs several orders of magnitude faster than the traditional numerical methods.The predictions for flows around airfoils and ellipses demonstrate the superior accuracy and impressive speed of this novel approach.Furthermore,the property of zero-shot super-resolution enables the proposed approach to overcome the limitations of predicting airfoil flows with Cartesian grids,thereby improving the accuracy in the near-wall region.There is no doubt that the unprecedented speed and accuracy in forecasting steady airfoil flows have massive benefits for airfoil design and optimization.展开更多
Traditionally,classical numerical schemes have been employed to solve partial differential equations(PDEs)using computational methods.Recently,neural network-based methods have emerged.Despite these advancements,neura...Traditionally,classical numerical schemes have been employed to solve partial differential equations(PDEs)using computational methods.Recently,neural network-based methods have emerged.Despite these advancements,neural networkbased methods,such as physics-informed neural networks(PINNs)and neural operators,exhibit deficiencies in robustness and generalization.To address these issues,numerous studies have integrated classical numerical frameworks with machine learning techniques,incorporating neural networks into parts of traditional numerical methods.In this study,we focus on hyperbolic conservation laws by replacing traditional numerical fluxes with neural operators.To this end,we developed loss functions inspired by established numerical schemes related to conservation laws and approximated numerical fluxes using Fourier neural operators(FNOs).Our experiments demonstrated that our approach combines the strengths of both traditional numerical schemes and FNOs,outperforming standard FNO methods in several respects.For instance,we demonstrate that our method is robust,has resolution invariance,and is feasible as a data-driven method.In particular,our method can make continuous predictions over time and exhibits superior generalization capabilities with out-of-distribution(OOD)samples,which are challenges that existing neural operator methods encounter.展开更多
In this work,the structure of 4-((2R)-2-(3,4-dibromophenyl)-1-fluorocyclopropyl)-N-(o-tolyl)benzamide(DBFB)has been determined at room temperature using single-crystal X-ray diffraction data.The structure of the compo...In this work,the structure of 4-((2R)-2-(3,4-dibromophenyl)-1-fluorocyclopropyl)-N-(o-tolyl)benzamide(DBFB)has been determined at room temperature using single-crystal X-ray diffraction data.The structure of the compound was solved using 1464 observed reflections with I≥2σ(I).It crystallizes in monoclinic space group P21 with a=20.0820(10),b=10.2770(10),c=4.860(2)?,β=95.9600(10)°,V=997.6(4)?3,Z=2,Dc=1.675 g/m3,F(000)=500,Μr=503.18,μ=4.09 mm-1 and the final R=0.0639.The molecular packing of the title compound exhibits C–H???O and C–H???F hydrogen bonds forming a supramolecular network.Furthermore,conformational analysis has been performed in order to confirm the most stable conformer of the title compound.Geometrical parameters of the keto conformer in the ground state have been obtained using density functional theory(DFT)method with B3LYP/6-31G(d,p)level of theory.In general,a good agreement between the calculated and experimental results was observed.The normal modes of vibration,molecular boundary orbitals(HOMO and LUMO),reactivity descriptors,Mullikan atomic charges and molecular electrostatic potential for the title compound have been evaluated and discussed.展开更多
文摘An efficient data-driven approach for predicting steady airfoil flows is proposed based on the Fourier neural operator(FNO),which is a new framework of neural networks.Theoretical reasons and experimental results are provided to support the necessity and effectiveness of the improvements made to the FNO,which involve using an additional branch neural operator to approximate the contribution of boundary conditions to steady solutions.The proposed approach runs several orders of magnitude faster than the traditional numerical methods.The predictions for flows around airfoils and ellipses demonstrate the superior accuracy and impressive speed of this novel approach.Furthermore,the property of zero-shot super-resolution enables the proposed approach to overcome the limitations of predicting airfoil flows with Cartesian grids,thereby improving the accuracy in the near-wall region.There is no doubt that the unprecedented speed and accuracy in forecasting steady airfoil flows have massive benefits for airfoil design and optimization.
文摘Traditionally,classical numerical schemes have been employed to solve partial differential equations(PDEs)using computational methods.Recently,neural network-based methods have emerged.Despite these advancements,neural networkbased methods,such as physics-informed neural networks(PINNs)and neural operators,exhibit deficiencies in robustness and generalization.To address these issues,numerous studies have integrated classical numerical frameworks with machine learning techniques,incorporating neural networks into parts of traditional numerical methods.In this study,we focus on hyperbolic conservation laws by replacing traditional numerical fluxes with neural operators.To this end,we developed loss functions inspired by established numerical schemes related to conservation laws and approximated numerical fluxes using Fourier neural operators(FNOs).Our experiments demonstrated that our approach combines the strengths of both traditional numerical schemes and FNOs,outperforming standard FNO methods in several respects.For instance,we demonstrate that our method is robust,has resolution invariance,and is feasible as a data-driven method.In particular,our method can make continuous predictions over time and exhibits superior generalization capabilities with out-of-distribution(OOD)samples,which are challenges that existing neural operator methods encounter.
文摘In this work,the structure of 4-((2R)-2-(3,4-dibromophenyl)-1-fluorocyclopropyl)-N-(o-tolyl)benzamide(DBFB)has been determined at room temperature using single-crystal X-ray diffraction data.The structure of the compound was solved using 1464 observed reflections with I≥2σ(I).It crystallizes in monoclinic space group P21 with a=20.0820(10),b=10.2770(10),c=4.860(2)?,β=95.9600(10)°,V=997.6(4)?3,Z=2,Dc=1.675 g/m3,F(000)=500,Μr=503.18,μ=4.09 mm-1 and the final R=0.0639.The molecular packing of the title compound exhibits C–H???O and C–H???F hydrogen bonds forming a supramolecular network.Furthermore,conformational analysis has been performed in order to confirm the most stable conformer of the title compound.Geometrical parameters of the keto conformer in the ground state have been obtained using density functional theory(DFT)method with B3LYP/6-31G(d,p)level of theory.In general,a good agreement between the calculated and experimental results was observed.The normal modes of vibration,molecular boundary orbitals(HOMO and LUMO),reactivity descriptors,Mullikan atomic charges and molecular electrostatic potential for the title compound have been evaluated and discussed.
