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