Related papers: Robust Data-Driven Discovery of Partial Differenti…
In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…
Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
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 discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…
In this paper, we introduce PDE-LEARN, a novel deep learning algorithm that can identify governing partial differential equations (PDEs) directly from noisy, limited measurements of a physical system of interest. PDE-LEARN uses a Rational…
Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…
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…
Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…
We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…
Recent advancements in machine learning have transformed the discovery of physical laws, moving from manual derivation to data-driven methods that simultaneously learn both the structure and parameters of governing equations. This shift…
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…
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…
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…
Data-driven discovery of partial differential equations (PDEs) from observed data in machine learning has been developed by embedding the discovery problem. Recently, the discovery of traditional ODEs dynamics using linear multistep methods…