Model selection for dynamical systems via sparse regression and information criteria

By N. Mangan, J. Nathan Kutz, Steven L. Brunton, Joshua L. Proctor. Proceedings of the Royal Society A, 2017

331 citations recorded by the source corpus.

We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number of candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows feasible computation of Akaike information criteria (AIC) or Bayes information criteria scores for the remaining candidate models. The information criteria hierarchically ranks the most informative models, enabling the automatic and principled selection of the model with the strongest support in relation to the time-series data. Specifically, we show that AIC scores place each candidate model in the strong support, weak support or no support category. The method correctly recovers several canonical dynamical systems, including a susceptible-exposed-infectious-recovered disease model, Burgers’ equation and the Lorenz equations, identifying the correct dynamical system as the only candidate model with strong support.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3fe58a9d54441fe556c403473334d04e4c13aae6

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. G. Em Karniadakis
2. Steven L. Brunton
3. J. Nathan Kutz
4. Liu Yang
5. Xuhui Meng
6. Bingni W. Brunton
7. Maizar Raissi
8. Daniel A. Messenger

In Control and Systems Engineering

1. Steven L. Brunton
2. J. Nathan Kutz
3. Bingni W. Brunton
4. G. Em Karniadakis
5. Daniel A. Messenger
6. David M. Bortz
7. Krithika Manohar
8. Tong Qin

In Statistical and Nonlinear Physics

1. G. Em Karniadakis
2. Steven L. Brunton
3. J. Nathan Kutz
4. Maizar Raissi
5. Bingni W. Brunton
6. Xuhui Meng
7. Dongbin Xiu
8. Paris Perdikaris

Citations in the corpus

• Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, background): “Information criteria [53], [54] has also been leveraged for the sparse identification of non-linear dynamics [42], as in [55], [56], and may also be useful for sensor placement.”
• Universal Differential Equations for Scientific Machine Learning (2020, methodology): “12(7), 2016. [11]Davide Bacciu, Paulo JG Lisboa, JoseD Martn, Ruxandra Stoean, and Alfredo Vellido. Bioinformatics and medicine in the era of deep learning. arXiv preprint arXiv:1802.09791 , 2018. [12]Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physicsinformed neural networks: A deep ”
• Data Driven Governing Equations Approximation Using Deep Neural Networks (2018, methodology): “…conducted to effectively deal with noises in data ([7, 40]), corruptions in data ([48]), partial differential equations [38, 41], etc. Methods have also been developed in conjunction with model selection approach ([28]), Koopman theory ([6]), and Gaussian process regression ([35]), to name a few.”
• Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, unknown): “Discover Governing Equations [30] [227] [37] [167] [168] [216] [123] [200][205] [52] [141] [290] [207] [155] [251]”
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data (2020, background): “The state-of-the-art in data-driven modeling has advanced significantly recently in applications across different fields [1, 2, 3, 4, 5], due to the rapid development of machine learning and explosive growth of available data collected from different sensors (e.g., satellites, cameras, etc.).”
• Data-driven discovery of coordinates and governing equations (2019, unknown): “The selected modes can also be evaluated using information criteria for model selection (42).”
• WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS (2020, methodology): “s. The wide applicability, computational eciency, and interpretability of the SINDy algorithm has spurred an explosion of interest in the problem of identifying nonlinear dynamical systems from data [7,23,9,10, 12,32,19]. In addition to the sparse regression approach adopted in SINDy, some of the pr”