# Physics-informed learning of governing equations from scarce data

@article{Chen2020PhysicsinformedLO, title={Physics-informed learning of governing equations from scarce data}, author={Zhao Chen and Yang Liu and Hao Sun}, journal={Nature Communications}, year={2020}, volume={12} }

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this…

## 68 Citations

### Physics-informed Spline Learning for Nonlinear Dynamics Discovery

- Computer ScienceIJCAI
- 2021

A novel Physics-informed Spline Learning (PiSL) framework to discover parsimonious governing equations for nonlinear dynamics, based on sparsely sampled noisy data, and the synergy between splines and discovered underlying physics leads to the robust capacity of dealing with high-level data scarcity and noise.

### Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations

- Computer Science
- 2021

A novel physics-guided learning method is proposed, which can not only encode observation knowledge such as initial and boundary conditions but also incorporate the basic physical principles and laws to guide the model optimization.

### Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning

- Computer ScienceICLR
- 2022

This work proposes a novel physics-encoded discrete learning framework for discovering spatiotemporal PDEs from scarce and noisy data and introduces a novel deep convolutional-recurrent network that can encode prior physics knowledge while remaining flexible on representation capability.

### Embedding Physics to Learn Spatiotemporal Dynamics from Sparse Data

- Computer Science, PhysicsArXiv
- 2021

A novel deep learning architecture is proposed that forcibly embedded known physics knowledge in a residual-recurrent Π-block network, to facilitate the learning of the spatiotemporal dynamics in a data-driven manner.

### Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion

- Computer ScienceArXiv
- 2022

A physics-informed information criterion (PIC) is proposed to measure the parsimony and precision of the discovered PDE synthetically, and shows that the discovered macroscale PDE is precise and parsimonious, and satisfies underlying symmetries, which facilitates understanding and simulation of the physical process.

### PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2022

### PDE-LEARN: Using Deep Learning to Discover Partial Differential Equations from Noisy, Limited Data

- Computer ScienceArXiv
- 2022

A novel PDE-discovery algorithm that can identify governing partial diﬀerential equations (PDEs) directly from noisy, limited measurements of a physical system of interest and can simultaneously learn from several data sets, allowing it to incorporate results from multiple experiments.

### Discovering sparse interpretable dynamics from partial observations

- Computer ScienceCommunications Physics
- 2022

An artificial intelligence framework that can learn the correct equations of motion for nonlinear systems from incomplete data is introduced, and opens up the door to applying interpretable machine learning techniques on a wide range of applications in the field of nonlinear dynamics.

### Physics-informed Deep Super-resolution for Spatiotemporal Data

- Computer ScienceArXiv
- 2022

This work proposes a novel and eﬁcient spatiotemporal super-resolution framework via physics-informed learning, inspired by the independence between temporal and spatial derivatives in partial diﬀerential equations (PDEs).

### Discovering Governing Equations by Machine Learning implemented with Invariance

- Computer ScienceArXiv
- 2022

Comparing the results with PDE-NET in numerical experiments of Burgers equation and Sine-Gordon equation, it shows that the method presented in this study has better accuracy, parsimony, and interpretability.

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