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Found 12 papers, 5 papers with code
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.
Weak-Form Latent Space Dynamics Identification
With WLaSDI, the local latent space is obtained using weak-form equation learning techniques.
Coarse-Graining Hamiltonian Systems Using WSINDy
In this work we extend this capability to the problem of coarse-graining Hamiltonian dynamics which possess approximate symmetries associated with timescale separation.
Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics
We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs.
Asymptotic consistency of the WSINDy algorithm in the limit of continuum data
Conversely, we also show that in general the WSINDy estimator is only conditionally asymptotically consistent, yielding discovery of spurious terms with probability one if the noise level is above some critical threshold and the nonlinearities exhibit sufficiently fast growth.
Learning diffusion coefficients, kinetic parameters, and the number of underlying states from a multi-state diffusion process: robustness results and application to PDK1/PKC$α$, dynamics
The primary contribution of this work is a study of the robustness of this method to infer parameters of a three-state HMM, and a discussion of the challenges and degeneracies that arise from considering three states.
Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
Motivated by the success of IPS models to describe the spatial movement of organisms, we develop WSINDy for second order IPSs to model the movement of communities of cells.
Online Weak-form Sparse Identification of Partial Differential Equations
This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy).
Learning Mean-Field Equations from Particle Data Using WSINDy
We develop a weak-form sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number $N$ and offering robustness to either intrinsic or extrinsic noise.
Analytical singular value decomposition for a class of stoichiometry matrices
We present the analytical singular value decomposition of the stoichiometry matrix for a spatially discrete reaction-diffusion system on a one dimensional domain.
Weak SINDy For Partial Differential Equations
Furthermore, our Fourier-based implementation reveals a connection between robustness to noise and the spectra of test functions, which we utilize in an \textit{a priori} selection algorithm for test functions.
Weak SINDy: Galerkin-Based Data-Driven Model Selection
We present a weak formulation and discretization of the system discovery problem from noisy measurement data.
Numerical Analysis Numerical Analysis
