Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to different transport models, from diffusion to advection-diffusion-reaction problems. Once a suitable PINN is established to solve the forward problem, the transport parameters are added as trainable parameters. We find that, for the inverse problem to converge to the correct solution, the different components of the loss function (data misfit, initial conditions, boundary conditions and residual of the transport equation) need to be weighted adaptively as a function of the training iteration (epoch). Similarly, gradients of trainable parameters are scaled at each epoch accordingly. Several examples are presented for different test cases to support our PINN architecture and its scalability and robustness.

翻译：物理信息神经网络（PINN）是一种机器学习工具，可用于求解偏微分方程描述模型的正问题与反问题。本文提出一种自适应逆PINN方法，适用于从扩散到对流-扩散-反应等多种输运模型。在建立适用于正问题求解的PINN后，将输运参数添加为可训练参数。研究发现，为使反问题收敛至正确解，损失函数的不同组成部分（数据失配、初始条件、边界条件和输运方程残差）需根据训练迭代次数（周期）进行自适应加权。类似地，可训练参数的梯度也在每个周期相应缩放。本文通过多个不同测试案例验证所提PINN架构的可扩展性与鲁棒性。