Related papers: Identification of Partial-Differential-Equations-B…
We investigate methods for learning partial differential equation (PDE) models from spatiotemporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select…
This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…
Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this…
In this work we present a data-driven method for the discovery of parametric partial differential equations (PDEs), thus allowing one to disambiguate between the underlying evolution equations and their parametric dependencies. Group…
We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. Weak-PDE-LEARN uses an adaptive loss function based on weak forms…
Partial Differential Equations (PDEs) model various physical phenomena, such as electromagnetic fields and fluid mechanics. Methods like Sparse Identification of Nonlinear Dynamics (SINDy) and PDE-Net 2.0 have been developed to identify and…
The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…
Identifying Ordinary Differential Equations (ODEs) from measurement data requires both fitting the dynamics and assimilating, either implicitly or explicitly, the measurement data. The Sparse Identification of Nonlinear Dynamics (SINDy)…
In this paper, we propose Stoch-IDENT, a novel framework for identifying stochastic partial differential equations (SPDEs) from observational data. Our method can handle linear and nonlinear high-order SPDEs driven by time-dependent Wiener…
The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…
In this paper, we propose a data-driven framework for model discovery of stochastic differential equations (SDEs) from a single trajectory, without requiring the ergodicity or stationary assumption on the underlying continuous process. By…
We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares…
In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phenomena are prevalent in fluid dynamics and materials science,…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
We study the problem of identifying unknown processes embedded in time-dependent partial differential equation (PDE) using observational data, with an application to advection-diffusion type PDE. We first conduct theoretical analysis and…
The discovery of partial differential equations (PDEs) from experimental data holds great promise for uncovering predictive models of complex physical systems. In this study, we introduce an efficient automatic model discovery framework,…
Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…