# Paradigm Shift Through the Integration of Physical Methodology and Data Science

arXiv: https://arxiv.org/abs/2110.01408 · HTML: https://mlsanity.com/paper/2110.01408/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 80 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 22 of 22)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles](https://mlsanity.com/paper/1705.05065/) (2017)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [Small Data Challenges in Big Data Era: A Survey of Recent Progress on Unsupervised and Semi-Supervised Methods](https://mlsanity.com/paper/1903.11260/) (2019)
- [Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/2001.11086/) (2020)
- [Towards Bayesian Deep Learning: A Framework and Some Existing Methods](https://mlsanity.com/paper/1608.06884/) (2016)
- [Machine Learning for the Geosciences: Challenges and Opportunities](https://mlsanity.com/paper/1711.04708/) (2017)
- [Data-driven discovery of PDEs in complex datasets](https://mlsanity.com/paper/1808.10788/) (2018)
- [MeshingNet: A New Mesh Generation Method based on Deep Learning](https://mlsanity.com/paper/2004.07016/) (2020)
- [Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows](https://mlsanity.com/paper/1907.09909/) (2019)
- [Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Control](https://mlsanity.com/paper/1902.09742/) (2019)
- [Machine learning initialization to accelerate Stokes profile inversions](https://mlsanity.com/paper/2103.09651/) (2021)
- [Hybrid Scheme of Kinematic Analysis and Lagrangian Koopman Operator Analysis for Short-term Precipitation Forecasting](https://mlsanity.com/paper/2006.02064/) (2020)

## Abstract (arXiv)

Data science methodologies, which have undergone significant developments recently, provide flexible representational performance and fast computational means to address the challenges faced by traditional scientific methodologies while revealing unprecedented challenges such as the interpretability of computations and the demand for extrapolative predictions on the amount of data. Methods that integrate traditional physical and data science methodologies are new methods of mathematical analysis that complement both methodologies and are being studied in various scientific fields. This paper highlights the significance and importance of such integrated methods from the viewpoint of scientific theory. Additionally, a comprehensive survey of specific methods and applications are conducted, and the current state of the art in relevant research fields are summarized.