Identification of distributed parameter systems: A neural net based approach

By R. González-García, R. Rico-Martínez, Ioannis G. Kevrekidis. 1998

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Citations in the corpus

fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “In this paper, we focus on the identification of the parameters of fractional PDEs whose overall form is known but some coefficients and most importantly the operators themselves are not known.”
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],…”
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”
Modeling of distributed parameter systems for applications—A synthesized review from time–space separation (2010, unknown): “The neural networks are popularly integrated with finite difference method [103], or KL method [104–106] to compensate the structure uncertainty.”
Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks (2018, methodology): “These methods include NARMAX [7], equation-free methods [12], Laplacian spectral analysis [9], and neural networks [11].”
Machine Learning for Fluid Mechanics (2019, background): “Early examples include the use of NNs to learn the solutions of ordinary and partial diﬀerential equations (Dis-sanayake & Phan-Thien 1994; Gonzalez-Garcia et al. 1998; Lagaris et al. 1998).”
Data Driven Governing Equations Approximation Using Deep Neural Networks (2018, methodology): “Earlier efforts include methods using symbolic regression ([5, 43]), equation-free modeling [24], heterogeneous multiscale method (HMM) ([15]), artificial neural networks ([19]), nonlinear regression ([50]), empirical dynamic modeling ([46, 53]), nonlinear Laplacian spectral analysis ([18]), automat”
Data-driven discovery of coordinates and governing equations (2019, background): “One recent area of focus has been the use of NNs for studying dynamical systems, which has a surprisingly rich history [27].”