# Knowledge-guided Machine Learning: Current Trends and Future Prospects

arXiv: https://arxiv.org/abs/2403.15989 · HTML: https://mlsanity.com/paper/2403.15989/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 74 of its 179 references that are in the map.
- First posted on arXiv 24 Mar 2024.

## Builds on (most cited first, 30 of 74)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Keystroke Dynamics as Part of Lifelogging](https://mlsanity.com/paper/2010.10144/) (2020)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Colorization as a Proxy Task for Visual Understanding](https://mlsanity.com/paper/1703.04044/) (2017)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)

## Built on by (most cited first, 14 of 14)

- [Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems](https://mlsanity.com/paper/2410.19892/) (2024)
- [Adaptive Process-Guided Learning: An Application in Predicting Lake DO Concentrations](https://mlsanity.com/paper/2411.12973/) (2024)
- [Hierarchical Conditioning of Diffusion Models Using Tree-of-Life for Studying Species Evolution](https://mlsanity.com/paper/2408.00160/) (2024)
- [A Language Anchor-Guided Method for Robust Noisy Domain Generalization](https://mlsanity.com/paper/2503.17211/) (2025)
- [A Survey of Foundation Models for Environmental Science](https://mlsanity.com/paper/2503.03142/) (2025)
- [Knowledge Guided Encoder-Decoder Framework: Integrating Multiple Physical Models for Agricultural Ecosystem Modeling](https://mlsanity.com/paper/2505.06266/) (2025)
- [Hierarchically Disentangled Recurrent Network for Factorizing System Dynamics of Multi-scale Systems: An application on Hydrological Systems](https://mlsanity.com/paper/2407.20152/) (2024)
- [What Do You See in Common? Learning Hierarchical Prototypes over Tree-of-Life to Discover Evolutionary Traits](https://mlsanity.com/paper/2409.02335/) (2024)
- [Knowledge-Guided Machine Learning: Illustrating the use of Explainable Boosting Machines to Identify Overshooting Tops in Satellite Imagery](https://mlsanity.com/paper/2507.03183/) (2025)
- [Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation](https://mlsanity.com/paper/2601.17074/) (2026)
- [CHAM-net: A Contrastive Hierarchical Adaptive Meta-network for Robust Global Methane Flux Prediction](https://mlsanity.com/paper/2606.00338/) (2026)
- [Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations](https://mlsanity.com/paper/2608.13234/) (2026)
- [TRACE: Tractable Routing Autoencoder for Clinical ECG](https://mlsanity.com/paper/2609.23460/) (2026)
- [ST-Bench: A Spatial-Temporal Benchmark for Multi-Agent System Generation on Scientific Research Tasks](https://mlsanity.com/paper/2610.07763/) (2026)

## Abstract (arXiv)

This paper presents an overview of scientific modeling and discusses the complementary strengths and weaknesses of ML methods for scientific modeling in comparison to process-based models. It also provides an introduction to the current state of research in the emerging field of scientific knowledge-guided machine learning (KGML) that aims to use both scientific knowledge and data in ML frameworks to achieve better generalizability, scientific consistency, and explainability of results. We discuss different facets of KGML research in terms of the type of scientific knowledge used, the form of knowledge-ML integration explored, and the method for incorporating scientific knowledge in ML. We also discuss some of the common categories of use cases in environmental sciences where KGML methods are being developed, using illustrative examples in each category.