mlsanityData to 14 Oct 2026

Achieving Conservation of Energy in Neural Network Emulators for Climate Modeling

arXiv 1906.06622 ↗First posted 15 Jun 2019physics.ao-ph cs.LG physics.comp-phcited by 28

Not on the map. Why?

Abstract (arXiv)

Artificial neural-networks have the potential to emulate cloud processes with higher accuracy than the semi-empirical emulators currently used in climate models. However, neural-network models do not intrinsically conserve energy and mass, which is an obstacle to using them for long-term climate predictions. Here, we propose two methods to enforce linear conservation laws in neural-network emulators of physical models: Constraining (1) the loss function or (2) the architecture of the network itself. Applied to the emulation of explicitly-resolved cloud processes in a prototype multi-scale climate model, we show that architecture constraints can enforce conservation laws to satisfactory numerical precision, while all constraints help the neural-network better generalize to conditions outside of its training set, such as global warming.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Jun 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 7; 2022: 10; 2023: 4; 2024: 3; 2025: 3; 2026: 1.

28 papers.

Sort:

By area:

  1. 2021DC3: A learning method for optimization with hard constraintscited by 184
  2. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 52
  3. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 44
  4. 2021Will Artificial Intelligence supersede Earth System and Climate Models?cited by 37
  5. 2022Hard-Constrained Deep Learning for Climate Downscalingcited by 32
  6. 2023Fourier Neural Operators for Arbitrary Resolution Climate Data Downscalingcited by 26
  7. 2022Differentiable Programming for Earth System Modelingcited by 22
  8. 2021MC-LSTM: Mass-Conserving LSTMcited by 17
  9. 2021Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformerscited by 15
  10. 2024DiffESM: Conditional Emulation of Temperature and Precipitation in Earth System Models with 3D Diffusion Modelscited by 15
  11. 2022Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solverscited by 12
  12. 2022W-Transformers : A Wavelet-based Transformer Framework for Univariate Time Series Forecastingcited by 12
16 more
  1. 2022Knowledge-augmented Deep Learning and Its Applications: A Surveycited by 10
  2. 2023DiffESM: Conditional Emulation of Earth System Models with Diffusion Modelscited by 9
  3. 2021Using Machine Learning at Scale in HPC Simulations with SmartSim: An Application to Ocean Climate Modelingcited by 7
  4. 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
  5. 2025CondensNet: Enabling stable long-term climate simulations via hybrid deep learning models with adaptive physical constraintscited by 6
  6. 2024Calabi-Yau metrics through Grassmannian learning and Donaldson's algorithmcited by 4
  7. 2023Inductive biases in deep learning models for weather predictioncited by 3
  8. 2023Hybrid Modeling Design Patternscited by 2
  9. 2022AutoPINN: When AutoML Meets Physics-Informed Neural Networkscited by 1
  10. 2025Physically consistent model learning for reaction-diffusion systemscited by 1
  11. 2022Physics-Guided Problem Decomposition for Scaling Deep Learning of High-dimensional Eigen-Solvers: The Case of Schr"odinger's Equationcited by 0
  12. 2022Knowledge-based Deep Learning for Modeling Chaotic Systemscited by 0
  13. 2022Emergence of Concepts in DNNs?cited by 0
  14. 2024Downscaling Neural Network for Coastal Simulationscited by 0
  15. 2025Scientifically-Interpretable Reasoning Network (ScIReN): Discovering Hidden Relationships in the Carbon Cycle and Beyondcited by 0
  16. 2026Counterfactual Predictions in Scientific Emulators Without Controlled Experimentscited by 0