一类确定表面热流的热传导反问题的正则化方法

考虑确定表面热流ux(0,t)的如下半无限长杆热传导方程反问题uxx=ut,0≤x,0相似文献   

基本解方法求解一个三维线弹性力学反问题

将用于求解椭圆型偏微分方程边值问题的基本解方法应用于求解一个三维线弹性反问题,即Navier方程组的Cauchy问题.基本解方法离散方程所得的线性方程组是高度病态的,常见的求解方法如最小二乘法等无法得到合理的解.文中应用Tikhonov正则化和截断奇异值分解这两种正则化方法求解线性方程组,所需正则化参数则根据L-曲线确定,克服了问题的病态性.数值算例表明,本文方法能有效地求解三维线弹性力学反问题,而且这两种正则化方法所得到的结果精度相当.     

双调和方程柯西问题的修正的Tikhonov正则化方法

本文研究了双调和方程柯西问题,这类是不适定的,即问题的解(如果存在)不连续依赖于测量数据.首先在精确解的先验假设下给出问题的条件稳定性结果.接着利用修正的Tikhonov正则化方法求解此不适定问题.在先验和后验正则化参数选取规则下,给出正则解和精确解之间的误差估计式.最后给出几个数值例子验证此正则化方法求解此类反问题的有效性.     

Continuous Viewpoint Planning in Conjunction with Dynamic Exploration for Active Object Recognition

Active object recognition (AOR) aims at collecting additional information to improve recognition performance by purposefully adjusting the viewpoint of an agent. How to determine the next best viewpoint of the agent, i.e., viewpoint planning (VP), is a research focus. Most existing VP methods perform viewpoint exploration in the discrete viewpoint space, which have to sample viewpoint space and may bring in significant quantization error. To address this challenge, a continuous VP approach for AOR based on reinforcement learning is proposed. Specifically, we use two separate neural networks to model the VP policy as a parameterized Gaussian distribution and resort the proximal policy optimization framework to learn the policy. Furthermore, an adaptive entropy regularization based dynamic exploration scheme is presented to automatically adjust the viewpoint exploration ability in the learning process. To the end, experimental results on the public dataset GERMS well demonstrate the superiority of our proposed VP method.     

Least Wasserstein distance between disjoint shapes with perimeter regularization

We prove the existence of global minimizers to the double minimization problem where $P(E)$ denotes the perimeter of the set E, $W_p$ is the p-Wasserstein distance between Borel probability measures, and $\lambda >0$ is arbitrary. The result holds in all space dimensions, for all $p\in [1,\infty )$, and for all positive λ. This answers a question of Buttazzo, Carlier, and Laborde.     

An inverse problem of identifying the time-dependent potential in a fourth-order pseudo-parabolic equation from additional condition

The aim of this work is to identify numerically, for the first time, the time-dependent potential coefficient in a fourth-order pseudo-parabolic equation with nonlocal initial data, nonlocal boundary conditions, and the boundary data as overdetermination condition. This problem emerges significantly in the modeling of various phenomena in physics and engineering. From literature we already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, we apply the quintic B-spline (QB-spline) collocation method for discretizing the pseudo-parabolic problem and the Tikhonov regularization for finding a stable and accurate solution. The resulting nonlinear minimization problem is solved using the MATLAB subroutine lsqnonlin. Moreover, the von Neumann stability analysis is also discussed.