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

arXiv: https://arxiv.org/abs/2001.11086 · HTML: https://mlsanity.com/paper/2001.11086/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2020.

## Built on by (most cited first, 30 of 59)

- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
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- [Physics-constrained Deep Learning for Robust Inverse ECG Modeling](https://mlsanity.com/paper/2107.12780/) (2021)
- [Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers](https://mlsanity.com/paper/2207.11417/) (2022)
- [XLB: A differentiable massively parallel lattice Boltzmann library in Python](https://mlsanity.com/paper/2311.16080/) (2023)
- [Knowledge-augmented Deep Learning and Its Applications: A Survey](https://mlsanity.com/paper/2212.00017/) (2022)
- [Physics-Regulated Deep Reinforcement Learning: Invariant Embeddings](https://mlsanity.com/paper/2305.16614/) (2023)
- [Surrogate Modeling of Fluid Dynamics with a Multigrid Inspired Neural Network Architecture](https://mlsanity.com/paper/2105.03854/) (2021)
- [Heterogeneous Stream-reservoir Graph Networks with Data Assimilation](https://mlsanity.com/paper/2110.04959/) (2021)
- [Origin-Destination Network Generation via Gravity-Guided GAN](https://mlsanity.com/paper/2306.03390/) (2023)
- [FREE: The Foundational Semantic Recognition for Modeling Environmental Ecosystems](https://mlsanity.com/paper/2311.10255/) (2023)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [Task-Adaptive Meta-Learning Framework for Advancing Spatial Generalizability](https://mlsanity.com/paper/2212.06864/) (2022)
- [Physics vs. Learned Priors: Rethinking Camera and Algorithm Design for Task-Specific Imaging](https://mlsanity.com/paper/2204.09871/) (2022)
- [Real-time simulation of viscoelastic tissue behavior with physics-guided deep learning](https://mlsanity.com/paper/2301.04614/) (2023)
- [Time Series Predictions in Unmonitored Sites: A Survey of Machine Learning Techniques in Water Resources](https://mlsanity.com/paper/2308.09766/) (2023)
- [Foundation Models for Environmental Science: A Survey of Emerging Frontiers](https://mlsanity.com/paper/2504.04280/) (2025)
- [Phys-JEPA: Physics-Informed Latent World Models for Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2606.16076/) (2026)
- [Multiphysics discovery with moving boundaries using Ensemble SINDy and Peridynamic Differential Operator](https://mlsanity.com/paper/2303.15631/) (2023)
- [The Deep Arbitrary Polynomial Chaos Neural Network or how Deep Artificial Neural Networks could benefit from Data-Driven Homogeneous Chaos Theory](https://mlsanity.com/paper/2306.14753/) (2023)
- [Physics-Informed Graph Learning](https://mlsanity.com/paper/2202.10679/) (2022)
- [Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems](https://mlsanity.com/paper/2204.12972/) (2022)
- [Adaptive Sampling for Discovery](https://mlsanity.com/paper/2205.14829/) (2022)
- [Point Neuron Learning: A New Physics-Informed Neural Network Architecture](https://mlsanity.com/paper/2408.16969/) (2024)
- [X-MethaneWet: A Cross-scale Global Wetland Methane Emission Benchmark Dataset for Advancing Science Discovery with AI](https://mlsanity.com/paper/2505.18355/) (2025)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Process-Guided Concept Bottleneck Model](https://mlsanity.com/paper/2601.10562/) (2026)
- [Recent Ice Trends in Swiss Mountain Lakes: 20-year Analysis of MODIS Imagery](https://mlsanity.com/paper/2103.12434/) (2021)

## Abstract (arXiv)

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.