InverPINN: Diagnosing Source-Strength Bias in Physics-Informed Neural Networks for Sparse Pollution Source Inversion
DOI:
https://doi.org/10.58445/cw3r1209Keywords:
Physics-Informed Neural Networks, Inverse Problems, Source Localization, Air Pollution, Advection-Diffusion, Scientific Machine Learning, PDE-Constrained Optimization, Source-Strength BiasAbstract
Recovering pollution sources from sparse concentration measurements requires both informative observations and reliable inverse methods. This study evaluates physics-informed neural networks (PINNs) for estimating the location and strength of a single stationary Gaussian source in a controlled two-dimensional transient advection-diffusion problem. Experiments use known transport coefficients, 20 fixed sensors, zero added measurement noise, and a 641 × 641 numerical reference assessed through manufactured-solution tests and grid refinement.
Initial PINNs produced negative concentrations and systematically underestimated source strength. Enforcing nonnegative concentration and exact initial and boundary conditions removed physical violations but did not establish reliable source recovery. Conditional source-strength estimation and classical joint inversion showed that accurate recovery was possible under the observation design. We therefore investigated analytical amplitude profiling through a differentiable variable-projection PINN, designated J1, which eliminates source amplitude as an independent optimization parameter by minimizing the sampled PDE residual.
Across 30 new scenarios evaluated under a frozen protocol, J1 achieved median localization error of 0.005574, relative source-strength error of 5.975%, and concentration relative L2 error of 7.423%. However, only 23 of 30 scenarios met the joint recovery criterion, below the preregistered requirement of 27 of 30. J1 therefore failed final confirmation and underestimated source strength in 28 cases. Classical PDE-constrained inversion recovered all 30 sources, with corresponding median errors of 0.001111, 1.218%, and 1.507%.
These findings show that physical admissibility and improved median accuracy do not ensure reliable inverse recovery. Analytical amplitude profiling improved the tested PINN but left substantial source-strength bias and scenario-dependent failures. Conclusions are limited to the tested synthetic source family and observation geometry; real-world pollution-source identification remains unvalidated.
References
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