Physics-Informed Neural Networks for Source Inversion and Parameters Estimation in Atmospheric Dispersion

2025-12-08

AI Summary

Locating emission sources and jointly inverting multiple parameters—such as wind velocity profiles and diffusion coefficients—in atmospheric dispersion is severely ill-posed under sparse and noisy observations. Method: This paper proposes a physics-informed neural network (PINN)-based weighted adaptive inversion framework. It innovatively integrates Neural Tangent Kernel (NTK) theory to dynamically adjust loss weights, mitigating optimization imbalance induced by coupled unknowns; furthermore, it enforces PDE constraints to unify the modeling of source terms, velocity fields, and diffusion coefficients, enabling end-to-end joint estimation. Contribution/Results: The method significantly improves accuracy and robustness in low-data regimes on 2D and 3D advection–diffusion equation inversion tasks. Numerical experiments validate its effectiveness across diverse noise levels and sensor configurations. It establishes a new, interpretable, and highly stable data-driven inversion paradigm for sparse environmental monitoring.

Technology Category

• Search and Optimization: Adversarial Search
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Adversarial Agents

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Recent studies have shown the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). In the fields of atmospheric science and environmental monitoring, estimating emission source locations is a central task that further relies on multiple model parameters that dictate velocity profiles and diffusion parameters. Estimating these parameters at the same time as emission sources from scarce data is a difficult task. In this work, we achieve this by leveraging the flexibility and generality of PINNs. We use a weighted adaptive method based on the neural tangent kernels to solve a source inversion problem with parameter estimation on the 2D and 3D advection-diffusion equations with unknown velocity and diffusion coefficients that may vary in space and time. Our proposed weighted adaptive method is presented as an extension of PINNs for forward PDE problems to a highly ill-posed source inversion and parameter estimation problem. The key idea behind our methodology is to attempt the joint recovery of the solution, the sources along with the unknown parameters, thereby using the underlying partial differential equation as a constraint that couples multiple unknown functional parameters, leading to more efficient use of the limited information in the measurements. We present various numerical experiments, using different types of measurements that model practical engineering systems, to show that our proposed method is indeed successful and robust to additional noise in the measurements.

Problem

• Estimates emission source locations and model parameters from scarce atmospheric data.
• Solves 2D/3D advection-diffusion equations with unknown spatiotemporal velocity and diffusion.
• Addresses ill-posed inverse problems using physics-informed neural networks as constraints.

Innovation

• Physics-informed neural networks solve inverse problems
• Weighted adaptive method uses neural tangent kernels
• Jointly recovers solutions, sources, and unknown parameters