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. This scheme can overcome the curse of dimensionality and covers 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:我们考虑用随机数据计算操作员方程式的统计时间。我们指出,应用PINN(称为TIPNNs)可以在现有PINNs代码的最小修改下解决导导导高压操作员方程式。这个办法可以克服维度的诅咒,覆盖非线性和时间依赖操作员。我们建议了两类结构,即香草和多输出的TPNns,并调查其好处和局限性。进行了Exhausive数字实验;展示了适用性和性;提出了各种有希望的新研究途径。