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Application of Physics-Informed Neural Networks for Solving the Inverse Advection-Diffusion Problem to Localize Pollution Sources

Ivan Chuprov, Denis Derkach, Dmitry Efremenko, Aleksei Kychkin

TL;DR

This work addresses locating pollution sources by solving the inverse advection-diffusion problem with Physics-Informed Neural Networks (PINNs). By formulating a dimensionless PDE framework and optimizing PINN architectures (including FO-PINN, SPINN, and sinusoidal input mappings), the authors demonstrate accurate source localization across synthetic and real atmospheric data, validated against FEM solutions. Key contributions include a detailed loss-structure for PINNs, architecture strategies to improve convergence, and guidance on efficient configurations under varying wind and diffusion scenarios. The findings indicate PINNs offer a viable, data-augmented approach for environmental monitoring, with practical impact for rapid source localization under real-world atmospheric variability, while also highlighting computational cost and the need for automated hyperparameter tuning and potential 3D extensions.

Abstract

This paper investigates the application of Physics-Informed Neural Networks (PINNs) for solving the inverse advection-diffusion problem to localize pollution sources. The study focuses on optimizing neural network architectures to accurately model pollutant dispersion dynamics under diverse conditions, including scenarios with weak and strong winds and multiple pollution sources. Various PINN configurations are evaluated, showing the strong dependence of solution accuracy on hyperparameter selection. Recommendations for efficient PINN configurations are provided based on these comparisons. The approach is tested across multiple scenarios and validated using real-world data that accounts for atmospheric variability. The results demonstrate that the proposed methodology achieves high accuracy in source localization, showcasing the stability and potential of PINNs for addressing environmental monitoring and pollution management challenges under complex weather conditions.

Application of Physics-Informed Neural Networks for Solving the Inverse Advection-Diffusion Problem to Localize Pollution Sources

TL;DR

This work addresses locating pollution sources by solving the inverse advection-diffusion problem with Physics-Informed Neural Networks (PINNs). By formulating a dimensionless PDE framework and optimizing PINN architectures (including FO-PINN, SPINN, and sinusoidal input mappings), the authors demonstrate accurate source localization across synthetic and real atmospheric data, validated against FEM solutions. Key contributions include a detailed loss-structure for PINNs, architecture strategies to improve convergence, and guidance on efficient configurations under varying wind and diffusion scenarios. The findings indicate PINNs offer a viable, data-augmented approach for environmental monitoring, with practical impact for rapid source localization under real-world atmospheric variability, while also highlighting computational cost and the need for automated hyperparameter tuning and potential 3D extensions.

Abstract

This paper investigates the application of Physics-Informed Neural Networks (PINNs) for solving the inverse advection-diffusion problem to localize pollution sources. The study focuses on optimizing neural network architectures to accurately model pollutant dispersion dynamics under diverse conditions, including scenarios with weak and strong winds and multiple pollution sources. Various PINN configurations are evaluated, showing the strong dependence of solution accuracy on hyperparameter selection. Recommendations for efficient PINN configurations are provided based on these comparisons. The approach is tested across multiple scenarios and validated using real-world data that accounts for atmospheric variability. The results demonstrate that the proposed methodology achieves high accuracy in source localization, showcasing the stability and potential of PINNs for addressing environmental monitoring and pollution management challenges under complex weather conditions.

Paper Structure

This paper contains 10 sections, 12 equations, 17 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Problem formulation
  4. PINN methodology
  5. Implementation of PINN
  6. Results
  7. Solution of the forward model
  8. Solution of the inverse problem using synthetic data
  9. Solution of the inverse problem using real data
  10. Conclusions

Figures (17)

  • Figure 1: Example of a PINN architecture. The network takes spatial coordinates $(x, y)$ and time $t$ as input and predicts the pollutant concentration $c(x, y, t)$. The loss function combines data consistency, PDE residuals, and boundary conditions.
  • Figure 2: Loss curves of PINN for the advection-diffusion equation
  • Figure 3: Comparison of classical PINN results with FEM results for the advection-diffusion equation, t = 0-4
  • Figure 4: FO-PINN architecture for solving the forward problem of the advection-diffusion equation
  • Figure 5: Loss curves of the improved PINN for the normalized advection-diffusion equation.
  • ...and 12 more figures