Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport

By Qizhi He, David Alonso Barajas-Solano, Guzel Tartakovsky, Alexandre M. Tartakovsky. 2019

360 citations recorded by the source corpus.

Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a physics-informed deep neural networks (DNNs) machine learning method for estimating space-dependent hydraulic conductivity, hydraulic head, and concentration fields from sparse measurements. In this approach, we employ individual DNNs to approximate the unknown parameters (e.g., hydraulic conductivity) and states (e.g., hydraulic head and concentration) of a physical system, and jointly train these DNNs by minimizing the loss function that consists of the governing equations residuals in addition to the error with respect to measurement data. We apply this approach to assimilate conductivity, hydraulic head, and concentration measurements for joint inversion of the conductivity, hydraulic head, and concentration fields in a steady-state advection--dispersion problem. We study the accuracy of the physics-informed DNN approach with respect to data size, number of variables (conductivity and head versus conductivity, head, and concentration), DNNs size, and DNN initialization during training. We demonstrate that the physics-informed DNNs are significantly more accurate than standard data-driven DNNs when the training set consists of sparse data. We also show that the accuracy of parameter estimation increases as additional variables are inverted jointly.

Subfields: Atmospheric Science, Geophysics, Ocean Engineering

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atmospheric Science

1. G. Em Karniadakis
2. Lu Lu
3. Xuhui Meng
4. Yang Liu
5. Zhiping Mao
6. Chengping Rao
7. Maizar Raissi
8. Gianluigi Rozza

In Geophysics

1. Maizar Raissi
2. G. Em Karniadakis
3. Gianluigi Rozza
4. Yang Liu

In Ocean Engineering

1. G. Em Karniadakis
2. Lu Lu

Citations in the corpus

• Physics informed deep learning for computational elastodynamics without labeled data (2020, background): “…problems including modeling fluid flows and Navier-Stokes equations [10, 17–21], solving stochastic PDEs [22], flows transport in porous media [23–25], cardiovascular systems [26–28], design of metamaterials [29– 31], metamodeling of nonlinear structural systems [32, 33], and discovery of…”
• Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture (2020, methodology): “Rather than a single network, we train two separate networks—one for each output variable, α and T —in a manner that resembles past disjoint PINNs [42, 43, 48, 49], where θ α ∈ R D α and θ T ∈ R D T are the parameters for the individual networks.”
• DeepXDE: A Deep Learning Library for Solving Differential Equations (2019, background): “An attractive feature of PINNs is that it can be used to solve inverse problems with minimum change of the code for forward problems [47, 48, 51, 21, 13].”
• Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, methodology): “He et al (2020) propose a two-step training approach in which the loss function is minimized first by the Adam algorithm with a predefined stop condition, then by the L-BFGS-B optimizer.”