Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles (2001.11086v3)

Abstract: 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.

• The paper introduces a hybrid Physics-Guided RNN that integrates energy conservation principles to improve lake temperature simulation accuracy by over 20%.
• It addresses limitations of traditional physics-based models by reducing extensive parameter tuning and mitigating inherent simulation biases.
• The model demonstrates robust performance with limited observational data, paving the way for broader applications in environmental simulations.

Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles

This paper presents an innovative approach to augmenting physics-based models with machine learning techniques, specifically targeting the simulation of lake temperature profiles. It introduces a Physics-Guided Recurrent Neural Network (PGRNN) that combines the strengths of Recurrent Neural Networks (RNNs) with physics-based models, enhancing both the accuracy and physical consistency of the simulation results.

Core Contributions

The paper focuses on the limitations of traditional physics-based models, such as the General Lake Model (GLM), which, despite their widespread implementation in environmental studies, often exhibit biases due to simplified representations of complex physical processes. Additionally, these models necessitate extensive parameter tuning, which can be computationally expensive and prone to overfitting.

The PGRNN presented modifies standard RNNs by integrating explicit physical laws, such as energy conservation principles, into the neural network's architecture. This integration is achieved by introducing a physics-based penalty during the training phase, allowing the model to ensure physical consistency and improve predictive accuracy. One of the key findings is that the PGRNN improves the prediction accuracy by over 20% compared to traditional physics models, even when trained with limited observational data.

Strong Numerical Results

The paper reports significant improvements in prediction accuracy, with the PGRNN displaying notable advancements over traditional methods like GLM. These improvements manifest prominently when only a fraction of available training data is utilized, underscoring the model’s efficiency in data-scarce environments. For instance, using only 20% of the observational data, PGRNN outperformed a fully parameterized GLM using 100% of the data, highlighting its robustness and adaptability.

Implications and Future Prospects

The implications of this research are profound, suggesting a paradigm shift in modeling scientific phenomena. The success of PGRNN in lake temperature modeling illustrates the potential for extending similar hybrid models to other domains where physics-based models are traditionally relied upon, such as climate science, computational fluid dynamics, and crop modeling.

The paper speculates that future advancements could explore refining PGRNN to incorporate other fundamental physical laws, such as mass conservation, widening the scope of applicability across different scientific and engineering fields. This represents a promising frontier for AI-driven enhancements in traditional physics-based modeling.

Conclusion

In bridging the gap between data-driven machine learning models and physics-based simulations, the PGRNN stands as a testament to the power of integrating scientific knowledge with computational intelligence. Its successful application provides a reference point for developing more comprehensive, physically-consistent models across various scientific disciplines, marking a step forward in the pursuit of accurate and efficient environmental modeling solutions.