PINT: Physics-Informed Neural Time Series Models with Applications to Long-term Inference on WeatherBench 2m-Temperature Data

This paper introduces PINT (Physics-Informed Neural Time Series Models), a novel framework designed to integrate physical constraints into neural time series models, thereby enhancing their ability to capture complex dynamics in real-world datasets. To demonstrate its practical utility, we apply PINT to the ERA5 WeatherBench dataset, a widely-used benchmark for climate prediction, focusing on long-term forecasting of 2m-temperature data.PINT leverages the Simple Harmonic Oscillator Equation as a physics-informed prior, incorporating its periodic dynamics into three popular neural architectures: RNN, LSTM, and GRU. The choice of the Simple Harmonic Oscillator Equation is motivated by its well-known analytical solutions (sine and cosine functions), which not only represent periodic dynamics but also enable rigorous evaluation of the performance improvements achieved through the incorporation of physics-informed constraints. By benchmarking against a linear regression baseline derived from the exact solutions of this equation, we quantify the added value of embedding physical principles in data-driven models.Unlike traditional time series approaches that often rely on future observations for inference or training, PINT is designed for practical forecasting scenarios. Using only the first 90 days of observed data, the framework iteratively predicts the next two years, addressing challenges associated with limited or missing real-time updates.Extensive experiments on the WeatherBench dataset showcase PINT’s ability to generalize to unseen data, accurately capture periodic trends, and align with underlying physical principles. This study highlights the potential of physics-informed neural time series models to bridge the gap between data-driven machine learning and the interpretability required for climate applications.