# Interpretable Machine Learning in Physics: A Review

arXiv: https://arxiv.org/abs/2503.23616 · HTML: https://mlsanity.com/paper/2503.23616/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 163 of its 460 references that are in the map.
- First posted on arXiv 30 Mar 2025.

## Builds on (most cited first, 30 of 163)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Reinforcement Learning with Unsupervised Auxiliary Tasks](https://mlsanity.com/paper/1611.05397/) (2016)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)

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

- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Explainable AI for Jet Tagging: A Comparative Study of GNNExplainer, GNNShap, and GradCAM for Jet Tagging in the Lund Jet Plane](https://mlsanity.com/paper/2604.25885/) (2026)
- [Sparse probes and murky physics: a case study of interpretability challenges in a foundation model for continuum dynamics](https://mlsanity.com/paper/2606.11657/) (2026)
- [Sequence-Model-Guided Measurement Selection for Quantum State Learning](https://mlsanity.com/paper/2507.09891/) (2025)
- [Automated near-term quantum algorithm discovery for molecular ground states](https://mlsanity.com/paper/2603.26359/) (2026)
- [MonoCon: A general framework for learning ultra-compact high-fidelity representations using monotonicity constraints](https://mlsanity.com/paper/2509.22931/) (2025)
- [Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations](https://mlsanity.com/paper/2512.13913/) (2025)
- [Interpretation of Crystal Energy Landscapes with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.04636/) (2026)
- [Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling](https://mlsanity.com/paper/2604.12806/) (2026)
- [The limits of interpretability in multiple linear regression](https://mlsanity.com/paper/2606.16013/) (2026)
- [How Complexity Contributes to Learning Opacity in Machine Learning](https://mlsanity.com/paper/2606.24953/) (2026)
- [Interpreting learning dynamics of autoencoders: Transient scaling and emerging concepts of the Ising model](https://mlsanity.com/paper/2607.10285/) (2026)
- [A survey detection channel overrides the pixels in an astronomical foundation model, and biases tomographic mean redshifts](https://mlsanity.com/paper/2608.23626/) (2026)

## Abstract (arXiv)

Machine learning is increasingly transforming various scientific fields, enabled by advancements in computational power and access to large data sets from experiments and simulations. As artificial intelligence (AI) continues to grow in capability, these algorithms will enable many scientific discoveries beyond human capabilities. Since the primary goal of science is to understand the world around us, fully leveraging machine learning in scientific discovery requires models that are interpretable -- allowing experts to comprehend the concepts underlying machine-learned predictions. Successful interpretations increase trust in black-box methods, help reduce errors, allow for the improvement of the underlying models, enhance human-AI collaboration, and ultimately enable fully automated scientific discoveries that remain understandable to human scientists. This review examines the role of interpretability in machine learning applied to physics. We categorize different aspects of interpretability, discuss machine learning models in terms of both interpretability and performance, and explore the philosophical implications of interpretability in scientific inquiry. Additionally, we highlight recent advances in interpretable machine learning across many subfields of physics. By bridging boundaries between disciplines -- each with its own unique insights and challenges -- we aim to establish interpretable machine learning as a core research focus in science.