mlsanityData to 7 Oct 2026

Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems

arXiv 2003.04919 ↗First posted 10 Mar 2020physics.comp-ph cs.LG stat.MLcited by 160

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Abstract (arXiv)

There is a growing consensus that solutions to complex science and engineering problems require novel methodologies that are able to integrate traditional physics-based modeling approaches with state-of-the-art machine learning (ML) techniques. This paper provides a structured overview of such techniques. Application-centric objective areas for which these approaches have been applied are summarized, and then classes of methodologies used to construct physics-guided ML models and hybrid physics-ML frameworks are described. We then provide a taxonomy of these existing techniques, which uncovers knowledge gaps and potential crossovers of methods between disciplines that can serve as ideas for future research.

Key facts. Cited by 160 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Mar 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 30; 2023: 29; 2024: 27; 2025: 25; 2026: 40.

160 papers.

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  1. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 142
  2. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  3. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
  4. 2023Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunitiescited by 60
  5. 2024Explainable Artificial Intelligence: A Survey of Needs, Techniques, Applications, and Future Directioncited by 46
  6. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 37
  7. 2022NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operatorscited by 33
  8. 2021Review of Pedestrian Trajectory Prediction Methods: Comparing Deep Learning and Knowledge-based Approachescited by 30
  9. 2022Physics-informed neural networks for PDE-constrained optimization and controlcited by 19
  10. 2021Physics-enhanced deep surrogates for partial differential equationscited by 18
  11. 2023IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learningcited by 18
  12. 2024Importance-Aware Adaptive Dataset Distillationcited by 18
38 more
  1. 2022Robust Hybrid Learning With Expert Augmentationcited by 17
  2. 2022Trust in AI: Interpretability is not necessary or sufficient, while black-box interaction is necessary and sufficientcited by 13
  3. 2024Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Responsecited by 13
  4. 2024Knowledge-guided Machine Learning: Current Trends and Future Prospectscited by 13
  5. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  6. 2021Physics-constrained Deep Learning for Robust Inverse ECG Modelingcited by 12
  7. 2022Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solverscited by 12
  8. 2024Physics-Enhanced Machine Learning: a position paper for dynamical systems investigationscited by 11
  9. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  10. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  11. 2024Adaptive Process-Guided Learning: An Application in Predicting Lake DO Concentrationscited by 9
  12. 2023Physics-Regulated Deep Reinforcement Learning: Invariant Embeddingscited by 8
  13. 2024Physics-informed Generalizable Wireless Channel Modeling with Segmentation and Deep Learning: Fundamentals, Methodologies, and Challengescited by 8
  14. 2022Predicting waves in fluids with deep neural networkcited by 7
  15. 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
  16. 2022Requirements Engineering for Machine Learning: A Review and Reflectioncited by 7
  17. 2023Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directionscited by 7
  18. 2023Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distributioncited by 7
  19. 2024Randomized Physics-Informed Neural Networks for Bayesian Data Assimilationcited by 7
  20. 2024ExoTST: Exogenous-Aware Temporal Sequence Transformer for Time Series Predictioncited by 7
  21. 2021Enhancing predictive skills in physically-consistent way: Physics Informed Machine Learning for Hydrological Processescited by 6
  22. 2023Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversioncited by 6
  23. 2023Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networkscited by 6
  24. 2023Time Series Predictions in Unmonitored Sites: A Survey of Machine Learning Techniques in Water Resourcescited by 6
  25. 2021Failure-averse Active Learning for Physics-constrained Systemscited by 5
  26. 2022Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networkscited by 5
  27. 2023Augmenting a Physics-Informed Neural Network for the 2D Burgers Equation by Addition of Solution Data Pointscited by 5
  28. 2023Koopman Invertible Autoencoder: Leveraging Forward and Backward Dynamics for Temporal Modelingcited by 5
  29. 2021Making Invisible Visible: Data-Driven Seismic Inversion with Spatio-temporally Constrained Data Augmentationcited by 4
  30. 2022Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equationscited by 4
  31. 2023Eco-PiNN: A Physics-informed Neural Network for Eco-toll Estimationcited by 4
  32. 2023Entity Aware Modelling: A Surveycited by 4
  33. 2023Physics-informed neural networks modeling for systems with moving immersed boundaries: application to an unsteady flow past a plunging foilcited by 4
  34. 2023Reduced Simulations for High-Energy Physics, a Middle Ground for Data-Driven Physics Researchcited by 4
  35. 2026Digital Twin AI: Opportunities and Challenges from Large Language Models to World Modelscited by 4
  36. 2021Hybrid physics-based and data-driven modeling with calibrated uncertainty for lithium-ion battery degradation diagnosis and prognosiscited by 3
  37. 2022ChemTab: A Physics Guided Chemistry Modeling Frameworkcited by 3
  38. 2023Learning Absorption Rates in Glucose-Insulin Dynamics from Meal Covariatescited by 3

50 most cited of 160 All 160 (JSON)