Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static...Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.展开更多
A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure ass...A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.展开更多
In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled...In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.展开更多
We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independen...We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [20, 28] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.展开更多
Single-phase power converters are widely used in electric distribution systems under 10 kilowatts,where the second-order power imbalance between the AC side and DC side is an inherent issue.The pulsating power is deco...Single-phase power converters are widely used in electric distribution systems under 10 kilowatts,where the second-order power imbalance between the AC side and DC side is an inherent issue.The pulsating power is decoupled from the desired constant DC power,through an auxiliary circuit using energy storage components.This paper provides a comprehensive overview of the evolution of single-phase converter topologies underlining power decoupling techniques.Passive power decoupling techniques were commonly used in single-phase power converters before active power decoupling techniques were developed.Since then,active power decoupling topologies have generally evolved based on three streams of concepts:1)current-reference active power decoupling;2)DC voltage-reference active power decoupling;and 3)AC voltage-reference active power decoupling.The benefits and drawbacks of each topology have been presented and compared with its predecessor,revealing underlying logic in the evolution of the topologies.In addition,a general comparison has also been made in terms of decoupling capacitance/inductance,additional cost,efficiency and complexity of control,providing a benchmark for future power decoupling topologies.展开更多
In this work,we aim to develop an effective fully discrete Spectral-Galerkin numerical scheme for the multi-vesicular phase-field model of lipid vesicles with adhesion potential.The essence of the scheme is to introdu...In this work,we aim to develop an effective fully discrete Spectral-Galerkin numerical scheme for the multi-vesicular phase-field model of lipid vesicles with adhesion potential.The essence of the scheme is to introduce several additional auxiliary variables and design some corresponding auxiliary ODEs to reformulate the system into an equivalent form so that the explicit discretization for the nonlinear terms can also achieve unconditional energy stability.Moreover,the scheme has a full decoupling structure and can avoid calculating variable-coefficient systems.The advantage of this scheme is its high efficiency and ease of implementation,that is,only by solving two independent linear biharmonic equations with constant coefficients for each phase-field variable,the scheme can achieve the second-order accuracy in time,spectral accuracy in space,and unconditional energy stability.We strictly prove that the fully discrete energy stability that the scheme holds and give a detailed step-by-step implementation process.Further,numerical experiments are carried out in 2D and 3D to verify the convergence rate,energy stability,and effectiveness of the developed algorithm.展开更多
基金Project supported by the Basic Science Research Program through the National Research Foundation(NRF)of Korea funded by the Ministry of Science and ICT(No.RS-2024-00337001)。
文摘Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.
文摘A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.
基金Supported by the National Natural Science Foundation of China(Grant No.12261017)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022ZCZX077)。
文摘In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.
基金The authors would like to thank the referees for their valuable comments, which improved much of the quality of the paper. This work is partially support- ed by the National Natural Science Foundations of China under grant numbers 91130003,11171189 and 11571206 by Natural Science Foundation of Shandong Province under grant number ZR2011AZ002+1 种基金 by the U.S. Department of Energy, Office of Science, Office of Ad- vanced Scientific Computing Research, Applied Mathematics program under contract number ERKJE45 and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT-Battelle, LLC, for the U.S. Department of Energy under Contract DE-AC05-00OR22725.
文摘We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [20, 28] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.
文摘Single-phase power converters are widely used in electric distribution systems under 10 kilowatts,where the second-order power imbalance between the AC side and DC side is an inherent issue.The pulsating power is decoupled from the desired constant DC power,through an auxiliary circuit using energy storage components.This paper provides a comprehensive overview of the evolution of single-phase converter topologies underlining power decoupling techniques.Passive power decoupling techniques were commonly used in single-phase power converters before active power decoupling techniques were developed.Since then,active power decoupling topologies have generally evolved based on three streams of concepts:1)current-reference active power decoupling;2)DC voltage-reference active power decoupling;and 3)AC voltage-reference active power decoupling.The benefits and drawbacks of each topology have been presented and compared with its predecessor,revealing underlying logic in the evolution of the topologies.In addition,a general comparison has also been made in terms of decoupling capacitance/inductance,additional cost,efficiency and complexity of control,providing a benchmark for future power decoupling topologies.
基金supported by National Natural Science Foundation of China(11771375)Shandong Provincial Natural Science Foundation(ZR2021ZD03,ZR2021MA010)supported by National Science Foundation with grant number DMS-2012490.
文摘In this work,we aim to develop an effective fully discrete Spectral-Galerkin numerical scheme for the multi-vesicular phase-field model of lipid vesicles with adhesion potential.The essence of the scheme is to introduce several additional auxiliary variables and design some corresponding auxiliary ODEs to reformulate the system into an equivalent form so that the explicit discretization for the nonlinear terms can also achieve unconditional energy stability.Moreover,the scheme has a full decoupling structure and can avoid calculating variable-coefficient systems.The advantage of this scheme is its high efficiency and ease of implementation,that is,only by solving two independent linear biharmonic equations with constant coefficients for each phase-field variable,the scheme can achieve the second-order accuracy in time,spectral accuracy in space,and unconditional energy stability.We strictly prove that the fully discrete energy stability that the scheme holds and give a detailed step-by-step implementation process.Further,numerical experiments are carried out in 2D and 3D to verify the convergence rate,energy stability,and effectiveness of the developed algorithm.
