How Neural Networks Can Reveal the Source of Atmospheric Pollution?

Physics-informed neural networks, or PINNs, are changing how we tackle complex problems. In environmental science, pinpointing an emission source is crucial, yet data are often sparse and noisy. This research introduces a method that merges PINNs with an adaptive algorithm based on neural tangent kernels to invert atmospheric dispersion problems. In practice, the network simultaneously reconstructs pollutant concentrations and estimates the source location along with velocity and diffusion parameters that may change across space and time. The key is using the advection‑diffusion equation as a constraint: every possible solution must obey the physical law, allowing the network to extract maximum information from limited measurements. Numerical tests in 2D and 3D show the approach remains stable even with added noise, proving its robustness and accuracy. This ability to “read” the atmosphere with few sensors opens new avenues for environmental monitoring, making source identification faster and more reliable, from industrial stacks to accidental gas leaks.

Physics‑Informed Neural Networks (PINNs) embed partial differential equations (PDEs) directly into the network loss function. Here, the PDE is the advection‑diffusion equation: \(\frac{\partial C}{\partial t}+\nabla\cdot(\mathbf{v}C)=\nabla\cdot(D\nabla C)+S\), with \(C\) concentration, \(\mathbf{v}\) velocity field, \(D\) diffusion coefficient and \(S\) source term. The network simultaneously learns \(C(\mathbf{x},t)\), \(\mathbf{v}(\mathbf{x},t)\), \(D(\mathbf{x},t)\) and \(S(\mathbf{x},t)\) by minimizing a loss composed of data terms (measurements of \(C\)) and PDE residual terms. Adaptive weighting, guided by the neural tangent kernel (NTK), assigns higher importance to regions with larger residuals, improving convergence in highly ill‑posed problems. The formulation also allows Bayesian regularization to handle data uncertainty and dropout techniques to estimate prediction variance. Results show that, compared to traditional iterative inversion methods, adaptive PINNs drastically cut the number of iterations needed and retain accuracy even with up to 10% measurement noise. This approach is especially promising for sparse sensor networks, where data density is low but rapid decision‑making is critical.