考虑垂直腔面发射激光器(VCSEL)在稳态时载流子数和光子数关系,改进了工作电流与输出光功率强度(L-I)模型的经验公式,利用交替方向乘子法,基于实测数据确定模型的参数.该模型在考虑激光器的偏置电流受激光器温度影响的同时,还考虑了激...考虑垂直腔面发射激光器(VCSEL)在稳态时载流子数和光子数关系,改进了工作电流与输出光功率强度(L-I)模型的经验公式,利用交替方向乘子法,基于实测数据确定模型的参数.该模型在考虑激光器的偏置电流受激光器温度影响的同时,还考虑了激光器内部参数之间的耦合关系.仿真结果显示,改进后的模型所得参数,代入经验L-I模型,在相同算法条件下,和实测数据之间的均方误差值比仅考虑激光器偏置电流受温度影响的L-I模型的参数估计方法降低了约1.61 d B.同时,在较高的温度下工作,改进L-I曲线工作电流的有效区间更大.展开更多
This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated...This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated in [2] added with Savin's method for solving stress concentration of non-circular cavity surfaced with lining in elasticity.Anisotropic media can be used ic simulate the conditions of thegeology.The solving proceeding for this problem can be processed conveniently in the manner similar to that introduced in [2].In this paper.as illustrated in example numerical studies have been done for a square cavity surfaced with lining in anisotropic media.展开更多
This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective function.However,a drawback...This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective function.However,a drawback of this approach is the requirement for manual hyperparameter tuning,making it impractical in the absence of validation data or prior knowledge of the solution.Our investigations of the loss landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to navigate.Our findings demonstrate that high-order PDEs contaminate backpropagated gradients and hinder convergence.To address these challenges,we introduce a novel method that bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated gradients.Consequently,we reduce the dimension of the search space and make learning PDEs with non-smooth solutions feasible.Our method also provides a mechanism to focus on complex regions of the domain.Besides,we present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model’s prediction,with adaptive and independent learning rates inspired by adaptive subgradient methods.We apply our approach to solve various linear and non-linear PDEs.展开更多
文摘考虑垂直腔面发射激光器(VCSEL)在稳态时载流子数和光子数关系,改进了工作电流与输出光功率强度(L-I)模型的经验公式,利用交替方向乘子法,基于实测数据确定模型的参数.该模型在考虑激光器的偏置电流受激光器温度影响的同时,还考虑了激光器内部参数之间的耦合关系.仿真结果显示,改进后的模型所得参数,代入经验L-I模型,在相同算法条件下,和实测数据之间的均方误差值比仅考虑激光器偏置电流受温度影响的L-I模型的参数估计方法降低了约1.61 d B.同时,在较高的温度下工作,改进L-I曲线工作电流的有效区间更大.
文摘This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated in [2] added with Savin's method for solving stress concentration of non-circular cavity surfaced with lining in elasticity.Anisotropic media can be used ic simulate the conditions of thegeology.The solving proceeding for this problem can be processed conveniently in the manner similar to that introduced in [2].In this paper.as illustrated in example numerical studies have been done for a square cavity surfaced with lining in anisotropic media.
文摘This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective function.However,a drawback of this approach is the requirement for manual hyperparameter tuning,making it impractical in the absence of validation data or prior knowledge of the solution.Our investigations of the loss landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to navigate.Our findings demonstrate that high-order PDEs contaminate backpropagated gradients and hinder convergence.To address these challenges,we introduce a novel method that bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated gradients.Consequently,we reduce the dimension of the search space and make learning PDEs with non-smooth solutions feasible.Our method also provides a mechanism to focus on complex regions of the domain.Besides,we present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model’s prediction,with adaptive and independent learning rates inspired by adaptive subgradient methods.We apply our approach to solve various linear and non-linear PDEs.
