# Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations

arXiv: https://arxiv.org/abs/2405.05987 · HTML: https://mlsanity.com/paper/2405.05987/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 8 May 2024.

## Builds on (most cited first, 11 of 11)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach](https://mlsanity.com/paper/2105.04869/) (2021)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [Physics-informed machine learning for Structural Health Monitoring](https://mlsanity.com/paper/2206.15303/) (2022)
- [On generative models as the basis for digital twins](https://mlsanity.com/paper/2203.04384/) (2022)
- [Bayesian system identification for structures considering spatial and temporal correlation](https://mlsanity.com/paper/2305.00867/) (2023)
- [A switching Gaussian process latent force model for the identification of mechanical systems with a discontinuous nonlinearity](https://mlsanity.com/paper/2303.03858/) (2023)

## Built on by (most cited first, 12 of 12)

- [Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models](https://mlsanity.com/paper/2505.10930/) (2025)
- [A Generalizable Physics-Enhanced State Space Model for Long-Term Dynamics Forecasting in Complex Environments](https://mlsanity.com/paper/2507.10792/) (2025)
- [Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder](https://mlsanity.com/paper/2506.13658/) (2025)
- [Adaptive Sensor Steering Strategy Using Deep Reinforcement Learning for Dynamic Data Acquisition in Digital Twins](https://mlsanity.com/paper/2504.10248/) (2025)
- [Variational Rank Reduction Autoencoders for Generative Thermal Design](https://mlsanity.com/paper/2509.08515/) (2025)
- [Controlled oscillation modeling using port-Hamiltonian neural networks](https://mlsanity.com/paper/2602.15704/) (2026)
- [PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty](https://mlsanity.com/paper/2604.26593/) (2026)
- [Digital twin for virtual sensing of ferry quays via a Gaussian Process Latent Force Model](https://mlsanity.com/paper/2506.14925/) (2025)
- [Can Transformers overcome the lack of data in the simulation of history-dependent flows?](https://mlsanity.com/paper/2512.16305/) (2025)
- [In-Context Residual Calibration for Uncertainty Quantification of Energy Time Series over Graphs](https://mlsanity.com/paper/2606.31804/) (2026)
- [From Grey-Box to Green-Box: When can Physics-Informed Machine Learning Reduce Carbon Footprints in Structural Health Monitoring?](https://mlsanity.com/paper/2609.33387/) (2026)
- [Dissipative Lagrangian Neural Networks for the Interpretable Modelling of Passive Mechanical Systems](https://mlsanity.com/paper/2610.15996/) (2026)

## Abstract (arXiv)

This position paper takes a broad look at Physics-Enhanced Machine Learning (PEML) -- also known as Scientific Machine Learning -- with particular focus to those PEML strategies developed to tackle dynamical systems' challenges. The need to go beyond Machine Learning (ML) strategies is driven by: (i) limited volume of informative data, (ii) avoiding accurate-but-wrong predictions; (iii) dealing with uncertainties; (iv) providing Explainable and Interpretable inferences. A general definition of PEML is provided by considering four physics and domain knowledge biases, and three broad groups of PEML approaches are discussed: physics-guided, physics-encoded and physics-informed. The advantages and challenges in developing PEML strategies for guiding high-consequence decision making in engineering applications involving complex dynamical systems, are presented.