Equations of Motion from a Data Series

By James P. Crutchfield, Bruce S. McNamara. 1987

How researchers see this paper

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

Citations in the corpus

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, background): “The literature on data-driven discovery of dynamical systems [2] is vast and encompasses equation-free modeling [3], ar-tiﬁcial neural networks [4, 5, 6, 7], nonlinear regression [8], empirical dynamic modeling [9, 10], modeling emergent behavior [11], automated inference of dynamics [12, 13, 14],…”
Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, background): “There are a host of additional techniques for modeling emergent behavior [4] and the discovery of governing equations from time-series data [5].”
Hidden physics models: Machine learning of nonlinear partial differential equations (2017, background): “The literature on data-driven discovery of dynamical systems [3] is vast and encompasses equation-free modeling [4], artificial neural networks [5], nonlinear regression [6], empirical dynamic modeling [7,8], modeling emergent behavior [9], automated inference of dynamics [10–12], normal form identi”
Efficient Inference of Parsimonious Phenomenological Models of Cellular Dynamics Using S-Systems and Alternating Regression (2014, methodology): “Following the recipe that can be traced to Crutchfield and McNamara [11], one defines a sufficiently general (and, hopefully, complete [12]) set of possible dynamics using pre-defined combinations of basis functions.”
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, result): “Previous Work Combining machine learning techniques with PDE models has a long history in machine learning [13, 28, 8].”
Gradient calculations for dynamic recurrent neural networks: a survey (1995, background): “[70] and Lapedes and Farber [71] have had success with the identi cation of chaotic systems using models without hidden state, and there is no reason to believe that learning the dynamics of chaotic systems is more di cult than learning the dynamics of non-chaotic ones.”
Nonlinear Dynamical System Identification from Uncertain and Indirect Measurements (2004, methodology): “There are several variants of the LS approach [Crutchfield & McNamara, 1987; Cremers & Hübler, 1987; Breeden & Hübler, 1990; Gouesbet, 1991b; Kadtke et al., 1993; Aguirre & Billings, 1995; Hegger et al., 1998], which have been shown to work for small amounts of noise and if the system of Eqs.”
Linear Models With R (2005, background): “…but does not do justice to the theme of the book: how such systems can be studied with time-series analysis, for example, using symbolic dynamics and related time-series approaches, such as those developed by Crutchﬁeld and coworkers (Crutchﬁeld and McNamara 1987; Young and Crutchﬁeld 1993).”
Causal architecture, complexity and self-organization in time series and cellular automata (2001, background): “Simultaneously and independently, “geometry from a time series” evolved into “equations of motion from a data series” (Crutchfield and McNamara 1987; Timmer, Rust, Horbelt and Voss 2000).”
WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS (2020, methodology): “A important achievement in this field was the formulation and subsequent discretization of the system discovery problem in terms of a candidate basis of nonlinear functions evaluated at the given dataset, together with a sparsification measure to avoid overfitting [6].”
EEG dynamics in patients with Alzheimer's disease. (2004, methodology): “…based on raw EEG data and information obtained from NDA (Kadtke, 1995; Kadtke and Kremliovsky , 1996, 1997), mathematical theory and analysis methods for high-dimensional, physiological systems should be further developed and established (Cremers and Hubler, 1981; Crutchfield and McNamara, 1987).”
Data-driven discovery of coordinates and governing equations (2019, background): “Numerous recent approaches leverage machine learning to identify dynamical systems models from data [19–26], with many using neural networks to model time-series data [18, 27–38].”
Between order and chaos (2011, unknown): “The answer is yes 35 .”