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Quantifying local and global mass balance errors in physics-informed neural networks

Journal Article · · Scientific Reports
 [1];  [2];  [3];  [4]
  1. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Univ. of Mississippi, University, MS (United States)
  2. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
  3. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States). Environmental Molecular Sciences Laboratory (EMSL)
  4. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.

Research Organization:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Biological and Environmental Research (BER)
Grant/Contract Number:
AC05-76RL01830
OSTI ID:
2426324
Alternate ID(s):
OSTI ID: 2440194
Report Number(s):
PNNL-SA--198826
Journal Information:
Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 14; ISSN 2045-2322
Publisher:
Nature Publishing GroupCopyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (17)

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54 ENVIRONMENTAL SCIENCES
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mass balance errors
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partial differential equations
physics-informed neural networks
porous media flow