在热传导方程的研究中,物理信息神经网络(PINN)的应用已初显成效,其损失函数由多个损失项的加权和组成,这些损失项的加权组合对PINN的有效训练具有关键作用。为此,我们引入了一个基于高斯概率模型的损失项定义,通过噪声参数来描述每个...在热传导方程的研究中,物理信息神经网络(PINN)的应用已初显成效,其损失函数由多个损失项的加权和组成,这些损失项的加权组合对PINN的有效训练具有关键作用。为此,我们引入了一个基于高斯概率模型的损失项定义,通过噪声参数来描述每个损失项的权重,并提出了一种基于极大似然估计原理的自适应损失函数方法,该方法通过不断更新每个训练周期中的噪声参数,实现损失权重的自动分配。采用自适应物理信息神经网络(SalPINN)对一维瞬态热传导方程进行求解,并与传统PINN方法对比,结果显示SalPINN在模拟热传导方程方面表现出更高的精确性和有效性。In the field of research into heat transfer equations, the application of physical information neural network (PINN) has achieved some results. The loss function of PINN consists of a weighted sum of multiple loss terms, and the weighted combination of these loss terms plays an important role in PINN’s effective training. Therefore, we construct a loss term definition based on a Gaussian probability model, where the introduction of noise parameters is used to describe the weight of each loss term. We propose a self-adaptive loss function method based on the maximum likelihood estimation principle to automatically assign loss weights by constantly updating noise parameters in each training cycle. Then, we use self-adaptive loss physical information neural network (SalPINN) to solve the one-dimensional transient heat transfer equation, and compare it with the traditional PINN method, and the results show that SalPINN is more accurate and effective in simulating the heat transfer equation.展开更多
文摘在热传导方程的研究中,物理信息神经网络(PINN)的应用已初显成效,其损失函数由多个损失项的加权和组成,这些损失项的加权组合对PINN的有效训练具有关键作用。为此,我们引入了一个基于高斯概率模型的损失项定义,通过噪声参数来描述每个损失项的权重,并提出了一种基于极大似然估计原理的自适应损失函数方法,该方法通过不断更新每个训练周期中的噪声参数,实现损失权重的自动分配。采用自适应物理信息神经网络(SalPINN)对一维瞬态热传导方程进行求解,并与传统PINN方法对比,结果显示SalPINN在模拟热传导方程方面表现出更高的精确性和有效性。In the field of research into heat transfer equations, the application of physical information neural network (PINN) has achieved some results. The loss function of PINN consists of a weighted sum of multiple loss terms, and the weighted combination of these loss terms plays an important role in PINN’s effective training. Therefore, we construct a loss term definition based on a Gaussian probability model, where the introduction of noise parameters is used to describe the weight of each loss term. We propose a self-adaptive loss function method based on the maximum likelihood estimation principle to automatically assign loss weights by constantly updating noise parameters in each training cycle. Then, we use self-adaptive loss physical information neural network (SalPINN) to solve the one-dimensional transient heat transfer equation, and compare it with the traditional PINN method, and the results show that SalPINN is more accurate and effective in simulating the heat transfer equation.
