mlsanityData to 7 Oct 2026

Integration of knowledge and data in machine learning

arXiv 2202.10337 ↗First posted 15 Feb 2022cs.AI cs.LGcited by 13

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Abstract (arXiv)

Scientific research's mandate is to comprehend and explore the world, as well as to improve it based on experience and knowledge. Knowledge embedding and knowledge discovery are two significant methods of integrating knowledge and data. Through knowledge embedding, the barriers between knowledge and data can be eliminated, and machine learning models with physical common sense can be established. Meanwhile, humans' understanding of the world is always limited, and knowledge discovery takes advantage of machine learning to extract new knowledge from observations. Knowledge discovery can not only assist researchers to better grasp the nature of physics, but it can also support them in conducting knowledge embedding research. A closed loop of knowledge generation and usage are formed by combining knowledge embedding with knowledge discovery, which can improve the robustness and accuracy of models and uncover previously unknown scientific principles. This study summarizes and analyzes extant literature, as well as identifies research gaps and future opportunities.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 25 of its 74 references that are in the map. First posted on arXiv 15 Feb 2022.

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25 of 74 references.

References · 25

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  2. 2014Two-Stream Convolutional Networks for Action Recognition in Videoscited by 1,067
  3. 2014Distributed Representations of Sentences and Documentscited by 677
  4. 2017PDE-Net: Learning PDEs from Datacited by 304
  5. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  6. 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 208
  7. 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 173
  8. 2016Theory-guided Data Science: A New Paradigm for Scientific Discovery from Datacited by 169
  9. 2020Physics-informed learning of governing equations from scarce datacited by 167
  10. 2018Learning Equations for Extrapolation and Controlcited by 151
  11. 2017Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modelingcited by 130
  12. 2015Constrained Convolutional Neural Networks for Weakly Supervised Segmentationcited by 100
13 more
  1. 2018Reinforcement Learning of Theorem Provingcited by 69
  2. 2020DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithmcited by 45
  3. 2021Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)cited by 38
  4. 2019Deep Learning of Subsurface Flow via Theory-guided Neural Networkcited by 32
  5. 2020Theory-guided hard constraint projection (HCP): a knowledge-based data-driven scientific machine learning methodcited by 29
  6. 2022Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learningcited by 24
  7. 2021Robust discovery of partial differential equations in complex situationscited by 21
  8. 2020Deep-learning of Parametric Partial Differential Equations from Sparse and Noisy Datacited by 19
  9. 2020Efficient Uncertainty Quantification for Dynamic Subsurface Flow with Surrogate by Theory-guided Neural Networkcited by 17
  10. 2020Deep-learning based discovery of partial differential equations in integral form from sparse and noisy datacited by 14
  11. 2018Identification of physical processes via combined data-driven and data-assimilation methodscited by 4
  12. 2017Saliency Preservation in Low-Resolution Grayscale Imagescited by 2
  13. 2021Discovering PDEs from Multiple Experimentscited by 2

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Citing papers per year: 2022: 5; 2023: 4; 2024: 4.

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  1. 2023Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospectscited by 97
  2. 2024LLM4ED: Large Language Models for Automatic Equation Discoverycited by 13
  3. 2022Discrete Point-wise Attack Is Not Enough: Generalized Manifold Adversarial Attack for Face Recognitioncited by 11
  4. 2022AutoKE: An automatic knowledge embedding framework for scientific machine learningcited by 6
  5. 2022DISCOVER: Deep identification of symbolically concise open-form PDEs via enhanced reinforcement-learningcited by 3
  6. 2023Depression Detection Using Digital Traces on Social Media: A Knowledge-aware Deep Learning Approachcited by 3
  7. 2024A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systemscited by 3
  8. 2022TgDLF2.0: Theory-guided deep-learning for electrical load forecasting via Transformer and transfer learningcited by 2
  9. 2024Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regressioncited by 2
  10. 2022Knowledge-Injected Federated Learningcited by 1
  11. 2023Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning frameworkcited by 1
  12. 2023Transforming organic chemistry research paradigms: moving from manual efforts to the intersection of automation and artificial intelligencecited by 0
1 more
  1. 2024A Noise-robust Multi-head Attention Mechanism for Formation Resistivity Prediction: Frequency Aware LSTMcited by 0