Discovering governing equations from data by sparse identification of nonlinear dynamical systems

# Discovering governing equations from data by sparse identification of nonlinear dynamical systems > OpenAlex Metadata Hub · https://openalex.org/W2239232218 ## Bibliographic - **DOI:** 10.1073/pnas.1517384113 - **Year:** 2016 - **Citations:** 4583 - **Open Access:** Yes (bronze) - **License:** — - **Source:** https://www.pnas.org/content/pnas/113/15/3932.full.pdf ## Authors - Steven L. Brunton - Joshua L. Proctor - J. Nathan Kutz ## Abstract Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. ## Keywords Identification (biology), Nonlinear system, Dynamical systems theory, Applied mathematics, Nonlinear dynamical systems, System identification, Computer science, Mathematics, Physics, Data mining ## Concepts - Identification (biology) - Nonlinear system - Dynamical systems theory - Applied mathematics - Nonlinear dynamical systems - System identification - Computer science - Mathematics - Physics - Data mining - Measure (data warehouse) - Quantum mechanics - Botany - Biology --- *Metadata only — full text not imported unless Open Access license permits.*

Bài “Discovering governing equations from data by sparse identification of nonlinear dynamical systems” được TradingBase chuyển thành Knowledge Product cho trader — không phải trang đọc abstract OpenAlex. Tóm lược học thuật (đã diễn giải): Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that bala… Phần Trading Insights bên dưới nối nghiên cứu với Forex, vàng, USD, lãi suất và risk regime — để bạn đưa vào journal và playbook. Metadata DOI/OA chỉ là rail tham chiếu; nội dung chính là summary, takeaways và ứng dụng thị trường do Content Factory sinh.