This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the mathematical model of inertial memristor-based neural networks(IMNNs) with time delay is propos...This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the mathematical model of inertial memristor-based neural networks(IMNNs) with time delay is proposed, where the coupling matrix satisfies the diffusion condition, which can be symmetric or asymmetric. Secondly, by using differential inclusion method and Halanay inequality, some algebraic self-synchronization criteria are obtained. Then, via constructing effective Lyapunov functional, designing discontinuous control algorithms, some new sufficient conditions are gained to achieve synchronization of networks. Finally, two illustrative simulations are provided to show the validity of the obtained results, which cannot be contained by each other.展开更多
In this paper,we present a discontinuity and cusp capturing physicsinformed neural network(PINN)to solve Stokes equations with a piecewiseconstant viscosity and singular force along an interface.We first reformulate t...In this paper,we present a discontinuity and cusp capturing physicsinformed neural network(PINN)to solve Stokes equations with a piecewiseconstant viscosity and singular force along an interface.We first reformulate the governing equations in each fluid domain separately and replace the singular force effect with the traction balance equation between solutions in two sides along the interface.Since the pressure is discontinuous and the velocity has discontinuous derivatives across the interface,we hereby use a network consisting of two fully-connected sub-networks that approximate the pressure and velocity,respectively.The two sub-networks share the same primary coordinate input arguments but with different augmented feature inputs.These two augmented inputs provide the interface information,so we assume that a level set function is given and its zero level set indicates the position of the interface.The pressure sub-network uses an indicator function as an augmented input to capture the function discontinuity,while the velocity sub-network uses a cusp-enforced level set function to capture the derivative discontinuities via the traction balance equation.We perform a series of numerical experiments to solve two-and three-dimensional Stokes interface problems and perform an accuracy comparison with the augmented immersed interface methods in literature.Our results indicate that even a shallow network with a moderate number of neurons and sufficient training data points can achieve prediction accuracy comparable to that of immersed interface methods.展开更多
Rock-masses are divided into many closed blocks by deterministic and stochastic discontinuities and engineering interfaces in complex rock-mass engineering.Determining the sizes,shapes,and adjacent relations of blocks...Rock-masses are divided into many closed blocks by deterministic and stochastic discontinuities and engineering interfaces in complex rock-mass engineering.Determining the sizes,shapes,and adjacent relations of blocks is important for stability analysis of fractured rock masses.Here we propose an algorithm for identifying spatial blocks based on a hierarchical 3D Rock-mass Structure Model(RSM).First,a model is built composed of deterministic discontinuities,engineering interfaces,and the earth's surface,and the deterministic blocks surrounded by these interfaces are traced.Then,in each deter-ministic block,a network model of stochastic discontinuities is built and the stochastic blocks are traced.Building a unitary wire frame that connects all interfaces seamlessly is the key for our algorithm to identify the above two kinds of blocks.Using this algorithm,geometric models can be built for block theory,discrete element method,and discontinuous deformation analysis.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61573096,61374079 and 61603125)the Chinese Scholarship Council(Grent No.201708410029)+1 种基金the"333 Engineering"Foundation of Jiangsu Province of China(Grant No.BRA2015286)Key Program of Henan Universities(Grant No.17A120001)
文摘This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the mathematical model of inertial memristor-based neural networks(IMNNs) with time delay is proposed, where the coupling matrix satisfies the diffusion condition, which can be symmetric or asymmetric. Secondly, by using differential inclusion method and Halanay inequality, some algebraic self-synchronization criteria are obtained. Then, via constructing effective Lyapunov functional, designing discontinuous control algorithms, some new sufficient conditions are gained to achieve synchronization of networks. Finally, two illustrative simulations are provided to show the validity of the obtained results, which cannot be contained by each other.
基金supports by National Science and Technology Council,Taiwan,under research grants 111-2115-M-390-002 and 110-2115-M-A49-011-MY3,respectively.
文摘In this paper,we present a discontinuity and cusp capturing physicsinformed neural network(PINN)to solve Stokes equations with a piecewiseconstant viscosity and singular force along an interface.We first reformulate the governing equations in each fluid domain separately and replace the singular force effect with the traction balance equation between solutions in two sides along the interface.Since the pressure is discontinuous and the velocity has discontinuous derivatives across the interface,we hereby use a network consisting of two fully-connected sub-networks that approximate the pressure and velocity,respectively.The two sub-networks share the same primary coordinate input arguments but with different augmented feature inputs.These two augmented inputs provide the interface information,so we assume that a level set function is given and its zero level set indicates the position of the interface.The pressure sub-network uses an indicator function as an augmented input to capture the function discontinuity,while the velocity sub-network uses a cusp-enforced level set function to capture the derivative discontinuities via the traction balance equation.We perform a series of numerical experiments to solve two-and three-dimensional Stokes interface problems and perform an accuracy comparison with the augmented immersed interface methods in literature.Our results indicate that even a shallow network with a moderate number of neurons and sufficient training data points can achieve prediction accuracy comparable to that of immersed interface methods.
基金Supported by National Natural Science Foundation of China(Grant Nos.40602037 and 40872183)
文摘Rock-masses are divided into many closed blocks by deterministic and stochastic discontinuities and engineering interfaces in complex rock-mass engineering.Determining the sizes,shapes,and adjacent relations of blocks is important for stability analysis of fractured rock masses.Here we propose an algorithm for identifying spatial blocks based on a hierarchical 3D Rock-mass Structure Model(RSM).First,a model is built composed of deterministic discontinuities,engineering interfaces,and the earth's surface,and the deterministic blocks surrounded by these interfaces are traced.Then,in each deter-ministic block,a network model of stochastic discontinuities is built and the stochastic blocks are traced.Building a unitary wire frame that connects all interfaces seamlessly is the key for our algorithm to identify the above two kinds of blocks.Using this algorithm,geometric models can be built for block theory,discrete element method,and discontinuous deformation analysis.
