DeepMoD: Deep learning for model discovery in noisy data

By G. Both, Subham Choudhury, P. Sens, R. Kusters. 2019

159 citations recorded by the source corpus.

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their derivatives. A neural network approximates the data and constructs the function library, but it also performs the sparse regression. This construction makes it extremely robust to noise, applicable to small data sets, and, contrary to other deep learning methods, does not require a training set. We benchmark our approach on several physical problems such as the Burgers', Korteweg-de Vries and Keller-Segel equations, and find that it requires as few as $\mathcal{O}(10^2)$ samples and works at noise levels up to $75\%$. Motivated by these results, we apply DeepMoD directly on noisy experimental time-series data from a gel electrophoresis experiment and find that it discovers the advection-diffusion equation describing this system.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Alvaro Sanchez-Gonzalez
2. Peter W. Battaglia
3. Shirley Ho
4. Miles Cranmer
5. Yang Liu
6. Kyle Cranmer
7. Rui Xu
8. David N. Spergel

In Computer Vision and Pattern Recognition

1. Alvaro Sanchez-Gonzalez
2. Yang Liu
3. Peter W. Battaglia
4. Shirley Ho
5. Trond Kvamsdal
6. Omer San
7. Miles Cranmer
8. Adil Rasheed

In Statistical and Nonlinear Physics

1. Alvaro Sanchez-Gonzalez
2. Trond Kvamsdal
3. Peter W. Battaglia
4. Zhao Chen
5. Shirley Ho
6. Omer San
7. Yang Liu
8. David N. Spergel

Citations in the corpus

• Discovering Symbolic Models from Deep Learning with Inductive Biases (2020, background): “We also note several exciting packages for symbolic regression of partial differential equations on gridded data: [35, 36, 37, 38, 39, 40].”
• Deep learning of physical laws from scarce data (2020, background): “Latest studies (42, 43) show the potential of using DNNs and automatic differentiation to obtain PDEs from noisy data; yet, false positive identification occurs due to the use of less rigorous sparse regression along with DNN training.”
• Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, methodology): “[388] where the feed forward neural networks and sparse regression techniques were combined to handle noisy data.”