Weak SINDy for partial differential equations
Abstract Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system
discovery that has been shown to successfully recover governing dynamical systems from …
discovery that has been shown to successfully recover governing dynamical systems from …
Towards data-driven discovery of governing equations in geosciences
Governing equations are foundations for modelling, predicting, and understanding the Earth
system. The Earth system is undergoing rapid change, and the conventional approaches for …
system. The Earth system is undergoing rapid change, and the conventional approaches for …
Data-driven deep learning of partial differential equations in modal space
K Wu, D **u - Journal of Computational Physics, 2020 - Elsevier
We present a framework for recovering/approximating unknown time-dependent partial
differential equation (PDE) using its solution data. Instead of identifying the terms in the …
differential equation (PDE) using its solution data. Instead of identifying the terms in the …
Weak SINDy: Galerkin-based data-driven model selection
We present a novel weak formulation and discretization for discovering governing equations
from noisy measurement data. This method of learning differential equations from data fits …
from noisy measurement data. This method of learning differential equations from data fits …
Data-driven prediction of general Hamiltonian dynamics via learning exactly-symplectic maps
R Chen, M Tao - International Conference on Machine …, 2021 - proceedings.mlr.press
We consider the learning and prediction of nonlinear time series generated by a latent
symplectic map. A special case is (not necessarily separable) Hamiltonian systems, whose …
symplectic map. A special case is (not necessarily separable) Hamiltonian systems, whose …
Deep neural network modeling of unknown partial differential equations in nodal space
We present a numerical framework for deep neural network (DNN) modeling of unknown
time-dependent partial differential equation (PDE) using their trajectory data. Unlike the …
time-dependent partial differential equation (PDE) using their trajectory data. Unlike the …
Learning interaction kernels in heterogeneous systems of agents from multiple trajectories
Systems of interacting particles, or agents, have wide applications in many disciplines,
including Physics, Chemistry, Biology and Economics. These systems are governed by …
including Physics, Chemistry, Biology and Economics. These systems are governed by …
Partial differential equations discovery with EPDE framework: Application for real and synthetic data
Data-driven methods provide model creation tools for systems where the application of
conventional analytical methods is restrained. The proposed method involves the data …
conventional analytical methods is restrained. The proposed method involves the data …
On generalized residual network for deep learning of unknown dynamical systems
We present a general numerical approach for learning unknown dynamical systems using
deep neural networks (DNNs). Our method is built upon recent studies that identified …
deep neural networks (DNNs). Our method is built upon recent studies that identified …
A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
Numerical solvers of partial differential equations (PDEs) have been widely employed for
simulating physical systems. However, the computational cost remains a major bottleneck in …
simulating physical systems. However, the computational cost remains a major bottleneck in …