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.

翻译：我们考虑含随机数据算子方程统计矩的计算。研究表明，应用PINNs（称为TPINNs）可在对现有PINNs代码进行最小改动的情况下求解诱导张量算子方程，并能够处理非线性和时间相关算子。我们提出两种架构类型，即vanilla和multi-output TPINNs，并探讨其优势与局限性。通过详尽的数值实验验证了其适用性和性能，同时提出了多种具有前景的新研究方向。