We study a new algorithm for solvingparabolic partial differential equations(PDEs)and backward stochastic differential equations(BSDEs)in high dimension,which is based on an analogy between the BSDE and reinforcement ...We study a new algorithm for solvingparabolic partial differential equations(PDEs)and backward stochastic differential equations(BSDEs)in high dimension,which is based on an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function,and the loss function given by the error between the prescribed terminal condition and the solution of the BSDE.The policy function is then approximated by a neural network,as is done in deep reinforcement learning.Numerical results using TensorFlow illustrate the efficiency and accuracy of the studied algorithm for several 100-dimensional nonlinear PDEs from physics and finance such as the Allen–Cahn equation,the Hamilton–Jacobi–Bellman equation,and a nonlinear pricing model for financial derivatives.展开更多
介绍一种模糊自动控制滤波器的原理及其在时域信号处理中的应用.讨论了滤波器的滤波效果与模糊控制参数间的关系.提出了一种利用短时分形维数来修正滤波器的模糊控制参数,从而改善滤波效果的方法.通过对W e ierstrass函数的滤波,表明了...介绍一种模糊自动控制滤波器的原理及其在时域信号处理中的应用.讨论了滤波器的滤波效果与模糊控制参数间的关系.提出了一种利用短时分形维数来修正滤波器的模糊控制参数,从而改善滤波效果的方法.通过对W e ierstrass函数的滤波,表明了这是一种有效的滤波降噪方法,对各种复杂信号的滤波均有非常好的应用前景.展开更多
文摘We study a new algorithm for solvingparabolic partial differential equations(PDEs)and backward stochastic differential equations(BSDEs)in high dimension,which is based on an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function,and the loss function given by the error between the prescribed terminal condition and the solution of the BSDE.The policy function is then approximated by a neural network,as is done in deep reinforcement learning.Numerical results using TensorFlow illustrate the efficiency and accuracy of the studied algorithm for several 100-dimensional nonlinear PDEs from physics and finance such as the Allen–Cahn equation,the Hamilton–Jacobi–Bellman equation,and a nonlinear pricing model for financial derivatives.
文摘介绍一种模糊自动控制滤波器的原理及其在时域信号处理中的应用.讨论了滤波器的滤波效果与模糊控制参数间的关系.提出了一种利用短时分形维数来修正滤波器的模糊控制参数,从而改善滤波效果的方法.通过对W e ierstrass函数的滤波,表明了这是一种有效的滤波降噪方法,对各种复杂信号的滤波均有非常好的应用前景.
