  Physics-based models of dynamical systems are often used to study engineering
and environmental systems. Despite their extensive use, these models have
several well-known limitations due to simplified representations of the
physical processes being modeled or challenges in selecting appropriate
parameters. While-state-of-the-art machine learning models can sometimes
outperform physics-based models given ample amount of training data, they can
produce results that are physically inconsistent. This paper proposes a
physics-guided recurrent neural network model (PGRNN) that combines RNNs and
physics-based models to leverage their complementary strengths and improves the
modeling of physical processes. Specifically, we show that a PGRNN can improve
prediction accuracy over that of physics-based models, while generating outputs
consistent with physical laws. An important aspect of our PGRNN approach lies
in its ability to incorporate the knowledge encoded in physics-based models.
This allows training the PGRNN model using very few true observed data while
also ensuring high prediction accuracy. Although we present and evaluate this
methodology in the context of modeling the dynamics of temperature in lakes, it
is applicable more widely to a range of scientific and engineering disciplines
where physics-based (also known as mechanistic) models are used, e.g., climate
science, materials science, computational chemistry, and biomedicine.
