# Learning Physical Concepts in Cyber-Physical Systems: A Case Study

arXiv: https://arxiv.org/abs/2111.14151 · HTML: https://mlsanity.com/paper/2111.14151/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 28 Nov 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [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)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [SOM-VAE: Interpretable Discrete Representation Learning on Time Series](https://mlsanity.com/paper/1806.02199/) (2018)
- [Operationally meaningful representations of physical systems in neural networks](https://mlsanity.com/paper/2001.00593/) (2020)

## Abstract (arXiv)

Machine Learning (ML) has achieved great successes in recent decades, both in research and in practice. In Cyber-Physical Systems (CPS), ML can for example be used to optimize systems, to detect anomalies or to identify root causes of system failures. However, existing algorithms suffer from two major drawbacks: (i) They are hard to interpret by human experts. (ii) Transferring results from one systems to another (similar) system is often a challenge. Concept learning, or Representation Learning (RepL), is a solution to both of these drawbacks; mimicking the human solution approach to explain-ability and transfer-ability: By learning general concepts such as physical quantities or system states, the model becomes interpretable by humans. Furthermore concepts on this abstract level can normally be applied to a wide range of different systems. Modern ML methods are already widely used in CPS, but concept learning and transfer learning are hardly used so far. In this paper, we provide an overview of the current state of research regarding methods for learning physical concepts in time series data, which is the primary form of sensor data of CPS. We also analyze the most important methods from the current state of the art using the example of a three-tank system. Based on these concrete implementations1, we discuss the advantages and disadvantages of the methods and show for which purpose and under which conditions they can be used.