Related papers: Machine Learning of Partial Differential Equations…
A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…
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…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
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…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
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…
The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in recent years. The stability and precision in identifying PDE…
Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general…
Time-frequency analysis is often used to study non stationary multicomponent signals, which can be viewed as the surperimposition of modes, associated with ridges in the TF plane. To understand such signals, it is essential to identify…
We propose a supervised learning algorithm for machine learning applications. Contrary to the model developing in the classical methods, which treat training, validation, and test as separate steps, in the presented approach, there is a…
This paper presents a novel approach that combines the Deep Ritz Method (DRM) with Fourier feature mapping to solve minimization problems comprised of multi-well, non-convex energy potentials. These problems present computational challenges…
Elder people consequence a variety of problems while living Activities of Daily Living (ADL) for the reason of age, sense, loneliness and cognitive changes. These cause the risk to ADL which leads to several falls. Getting real life fall…
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
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,…
Deep neural networks (DNNs) have achieved remarkable success across diverse domains, but their performance can be severely degraded by noisy or corrupted training data. Conventional noise mitigation methods often rely on explicit…
Deep neural networks have achieved remarkable success in computer vision tasks. Existing neural networks mainly operate in the spatial domain with fixed input sizes. For practical applications, images are usually large and have to be…
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 introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…
Seismic data noise processing is an important part of seismic exploration data processing, and the effect of noise elimination is directly related to the follow-up processing of data. In response to this problem, many authors have proposed…