Related papers: Sparse Identification of Truncation Errors
The present paper proposes new fully discrete schemes for long-time approximations of stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients in a bounded domain $D \subset \R^d, d =1,2,3 $. A novel family…
In this paper we aim to apply an adaptation of the recently developed technique of sparse identification of nonlinear dynamical systems on a Duffing experimental setup with cubic feedback of the output. The Duffing oscillator described by…
We propose a novel framework for discovering Stochastic Partial Differential Equations (SPDEs) from data. The proposed approach combines the concepts of stochastic calculus, variational Bayes theory, and sparse learning. We propose the…
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…
The discovery of underlying surface partial differential equation (PDE) from observational data has significant implications across various fields, bridging the gap between theory and observation, enhancing our understanding of complex…
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…
Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…
Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…
We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
Edge-exchangeable probabilistic network models generate edges as an i.i.d.~sequence from a discrete measure, providing a simple means for statistical inference of latent network properties. The measure is often constructed using the…
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…
We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…