论文标题
具有随机数据的操作员方程的物理信息神经网络
Physics-informed neural networks for operator equations with stochastic data
论文作者
论文摘要
我们考虑使用随机数据将统计矩计算到操作员方程的计算。我们指出的是，PINN的应用（称为TPINNS）允许在现有PINNS代码的最小变化下求解诱导的张量操作员方程，并启用对非线性和时间依赖性操作员的处理。我们提出了两种类型的体系结构，称为香草和多输出tpinn，并研究了它们的收益和局限性。进行详尽的数值实验；证明适用性和性能；提高了各种新的有前途的研究途径。
We consider the computation of statistical moments to operator equations with stochastic data. We remark that application of PINNs -- referred to as TPINNs -- allows to solve the induced tensor operator equations under minimal changes of existing PINNs code, and enabling handling of non-linear and time-dependent operators. We propose two types of architectures, referred to as vanilla and multi-output TPINNs, and investigate their benefits and limitations. Exhaustive numerical experiments are performed; demonstrating applicability and performance; raising a variety of new promising research avenues.
