# Physics-Informed Deep Learning to Reduce the Bias in Joint Prediction of Nitrogen Oxides

arXiv: https://arxiv.org/abs/2308.07441 · HTML: https://mlsanity.com/paper/2308.07441/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 66 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Learning Deep Representation for Face Alignment with Auxiliary Attributes](https://mlsanity.com/paper/1408.3967/) (2014)
- [Using Deep Learning to Extend the Range of Air-Pollution Monitoring and Forecasting](https://mlsanity.com/paper/1810.09425/) (2018)
- [Causal inference in the context of an error prone exposure: air pollution and mortality](https://mlsanity.com/paper/1712.00642/) (2017)

## Built on by (most cited first, 5 of 5)

- [AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction](https://mlsanity.com/paper/2402.03784/) (2024)
- [Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems](https://mlsanity.com/paper/2410.19892/) (2024)
- [Breaking the Regional Barrier: Inductive Semantic Topology Learning for Worldwide Air Quality Forecasting](https://mlsanity.com/paper/2601.21899/) (2026)
- [Spatiotemporal Satellite Image Downscaling with Transfer Encoders and Autoregressive Generative Models](https://mlsanity.com/paper/2512.05139/) (2025)
- [NeuroDDAF: Neural Dynamic Diffusion-Advection Fields with Evidential Fusion for Air Quality Forecasting](https://mlsanity.com/paper/2604.01175/) (2026)

## Abstract (arXiv)

Atmospheric nitrogen oxides (NOx) primarily from fuel combustion have recognized acute and chronic health and environmental effects. Machine learning (ML) methods have significantly enhanced our capacity to predict NOx concentrations at ground-level with high spatiotemporal resolution but may suffer from high estimation bias since they lack physical and chemical knowledge about air pollution dynamics. Chemical transport models (CTMs) leverage this knowledge; however, accurate predictions of ground-level concentrations typically necessitate extensive post-calibration. Here, we present a physics-informed deep learning framework that encodes advection-diffusion mechanisms and fluid dynamics constraints to jointly predict NO2 and NOx and reduce ML model bias by 21-42%. Our approach captures fine-scale transport of NO2 and NOx, generates robust spatial extrapolation, and provides explicit uncertainty estimation. The framework fuses knowledge-driven physicochemical principles of CTMs with the predictive power of ML for air quality exposure, health, and policy applications. Our approach offers significant improvements over purely data-driven ML methods and has unprecedented bias reduction in joint NO2 and NOx prediction.