Should physical models be replaced by machine learning?

With rapid advances in artificial intelligence, machine-learning models are increasingly challenging traditional physics-based approaches to forecasting complex systems. This is particularly visible in areas such as weather and climate prediction, where recent AI systems have demonstrated impressive forecasting skill. But does this mean that physical models should eventually be replaced by purely data-driven approaches?

A new paper by Tianlin Yang, Hailiang Du, Louis Aslett and Leonard Smith, recently published in Physica A, explores this question from a probabilistic forecasting perspective. Tianlin is a PhD student in Mathematical Sciences at Durham University, supervised by Hailiang. Rather than treating physics and machine learning as competing alternatives, the study asks whether the strengths of the two approaches can be combined.

The work develops a “physics-corrected” forecasting framework in which an imperfect physical model is retained as part of the forecast system, while a data-driven model learns to correct its systematic errors. Importantly, the correction is formulated probabilistically, so that the method represents not only a best estimate of the future state, but also the associated forecast uncertainty.

Using the Lorenz63 chaotic system as a controlled testbed, the study compares physical, purely data-driven and hybrid forecasting approaches under different levels of model imperfection, observational noise and forecast lead time. This allows the researchers to examine when physical information remains useful, when data-driven methods can provide additional skill, and how uncertainty evolves as forecasts become less predictable.

Across most of the experimental settings considered, the physics-corrected approach outperforms either the standalone physical model or the purely data-driven model. The results also highlight the importance of evaluating forecasts probabilistically rather than relying only on point predictions, particularly in nonlinear systems where forecast distributions can become highly non-Gaussian or multimodal.

The broader message is therefore not simply “physics or AI?”. Instead, the study suggests that combining physical understanding with data-driven learning may provide a more robust, interpretable and uncertainty-aware route to forecasting complex dynamical systems.