Hybrid Physics and Data Framework Delivers Real-Time Forecasts of Atmospheric Pollutants

Forecasting where atmospheric pollutants will travel, accumulate, or dissipate is one of the most consequential problems in air quality management, and a new open-access study proposes a way to do it in near real time. Researchers Amine Ammar and Francisco Chinesta have developed a hybrid framework that splits the governing equation of pollutant evolution into three parts—advection, diffusion, and everything else—and solves each one with a purpose-built technique. Their proof of concept, applied to a Singapore-centred domain using Copernicus data for the whole of 2024, achieves predictions in less than one second per iteration, a pace compatible with operational forecasting.

The work, published in Advanced Modeling and Simulation in Engineering Sciences, departs from the classical Gaussian, Lagrangian, and Eulerian frameworks that have long dominated atmospheric dispersion modelling. Those approaches rely on advection–diffusion equations driven by meteorological forcing, and while they remain the foundation of detailed assessments, the authors argue that purely physics-based formulations struggle to capture every mechanism at play. At the same time, purely data-driven forecasts have known weaknesses, including smoothing and bias growth with lead time. The new method tries to get the best of both worlds by keeping the physics explicit where it is well understood and letting machine learning handle what the equations leave out.

The decomposition is the conceptual heart of the paper. The governing equation is written with three contributions: an advection operator capturing transport by wind direction and intensity, a diffusion operator that in this framework broadly includes any non-advective mechanism, and a so-called gap term representing everything originating outside the system—in this study, temperature, pressure, and water vapour. Each mechanism is identified in sequence, step by step, with an error quantified after every pass so the residual uncertainty is tracked explicitly rather than hidden inside a black box.

For advection, the authors use a backward, or semi-Lagrangian, scheme: to compute the pollutant field at the next time step, they trace each grid point’s trajectory backwards through the known velocity field and interpolate the previous field at the departure point. In geographic coordinates this displacement is computed on the sphere using the Earth’s radius, with the departure point generally falling between grid nodes and handled by interpolation. The authors note that the semi-Lagrangian approach is more permissive than Eulerian schemes regarding stability, though boundary handling and conservative interpolation may be needed to limit mass loss.

Diffusion is handled entirely by learning rather than by prescribing a diffusion coefficient. After the advective step, the error between the advected field and the real field is computed, and Dynamic Mode Decomposition—a data-driven technique that extracts spatio-temporal patterns from sequences of system snapshots without requiring knowledge of the governing equations—is used to identify a linear operator linking that error to the previous field. The matrix is obtained by solving a least-squares problem, effectively inferring diffusion and associated effects such as boundary conditions directly from data. This, the authors say, eliminates the need to impose predefined physical assumptions about how diffusion behaves.

The third component, the gap, is estimated by multilinear regression applied to Proper Orthogonal Decomposition coordinates of the external variables. Rather than regressing directly on the full grid, which would ignore spatial continuity and produce noisy predictions, the error fields and the temperature, pressure, and water vapour fields are compressed into reduced latent-space coordinates. A deliberately simple regression then maps the reduced external variables to the reduced gap. The authors chose multilinear regression precisely because they know from the outset that some data are missing—a more complex model would overfit and fail to generalize—so the goal is to capture the general trend while accepting a residual error.

The validation domain is centred on Singapore, bounded by longitudes 90 to 115 degrees east and latitudes 9 degrees south to 14 degrees north, giving a grid of 34 by 31 points, or 1,045 grid points. The data come from the Copernicus Atmosphere Data Store at a spatial resolution of 0.75 degrees and a temporal resolution of three hours, covering the entire year 2024 for a total of 2,928 snapshots. The chemical species selected for the target field was paraffin. Predictions start from time step 1,501, using a sliding training window of 1,500 time steps—a number chosen to exceed the number of spatial points and ensure over-determination during the decomposition-based learning.

The learning process involves three passes over the training window: the first computes the advected field and its error and solves for the diffusion operator; the second computes the advection–diffusion field, its residual gap, and the regression on the POD coefficients; the third computes the total predicted field and its residual error. Despite the apparent complexity, each pass requires less than one second of CPU time—very reasonable, the authors note, compared with the three-hour forecast horizon. The error norms plotted across the three passes decrease monotonically, which the authors take as confirmation of the method’s robustness, though they acknowledge that gap prediction could be improved by treating additional physical mechanisms.

An ablation study addresses whether the extra complexity pays off. The three-step procedure was compared against a purely data-driven baseline that removes the advection and diffusion layers and predicts the next field in a single pass, using the same data stream, normalization, sliding-window protocol, and dimensionality reduction. Over the same evaluation window, the direct baseline’s error remained consistently larger—by more than one order of magnitude—than the error of the operator-aware scheme, supporting the conclusion that the hybrid decomposition is decisive for accuracy and robustness.

The authors are careful about the limits of the proof of concept. Restricting the gap to three external variables is acknowledged as insufficient to capture all sources of epistemic uncertainty; chemical reactions generating or dissipating the pollutant were ignored, which explains part of the residual error. Future work will expand the set of physical variables, incorporate chemical interactions, and explore more advanced machine learning techniques for gap prediction while guarding against overfitting. Even so, the study demonstrates a feasible template for operational air quality forecasting systems capable of handling multiple chemical constituents under complex meteorological conditions—one that runs fast enough, in principle, to keep pace with the atmosphere itself.

Subject of Research: A hybrid physics and machine learning framework for real-time forecasting of atmospheric pollutant dispersion

Article Title: Hybrid physics: data framework for real-time forecasting of atmospheric pollutants

Article References: Ammar, A., & Chinesta, F. (2026). Hybrid physics: data framework for real-time forecasting of atmospheric pollutants. Advanced Modeling and Simulation in Engineering Sciences, 13(1), Article 8. https://doi.org/10.1186/s40323-026-00331-y

Image Credits: AI Generated

DOI: 10.1186/s40323-026-00331-y

Keywords: air quality, atmospheric pollutants, hybrid modelling, semi-Lagrangian advection, Dynamic Mode Decomposition, Proper Orthogonal Decomposition, machine learning, Copernicus, Singapore, forecasting, data assimilation, reduced-order modelling