Related papers: $L_2$-Gain Analysis of Coupled Linear 2D PDEs usin…
This paper presents intersection of Physics informed neural networks (PINNs) and Lie symmetry group to enhance the accuracy and efficiency of solving partial differential equation (PDEs). Various methods have been developed to solve these…
This paper is concerned with incremental stability properties of nonlinear systems. We propose conditions to compute an upper bound on the incremental L2-gain and to assess incremental asymptotic stability of piecewise-affine (PWA) systems.…
It has recently been shown that the evolution of a state, described by a Partial Differential Equation (PDE), can be more conveniently represented as the evolution of the state's highest spatial derivative (the ``fundamental state''), which…
TheL2-gain characterizes a dynamical system's input-output properties, but can be difficult to determine for nonlinear systems. Previous work designed a nonconvex optimization problem to simultaneously search for a continuous piecewise…
Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…
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…
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…
In this paper, we make the first attempt to apply the boundary integrated neural networks (BINNs) for the numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. BINNs combine artificial neural networks with the…
This paper aims to demonstrate the applicability of the L_2-integral transform to Partial Differential Equations (PDEs). Of special interest is section (6), which contains an application of the L_2-transform to a PDE of exponential squared…
A popular approach to designing finite-dimensional boundary controllers for partial differential equations (PDEs) is to decompose the PDE into independent modes and focus on the dominant ones while neglecting highly damped residual modes.…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
Since the introduction of deep learning for solving partial differential equations (PDEs), there has been growing interest in real-time system responses, where the kernel function plays a key role. Physics-informed neural networks (PINNs),…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…
Partial differential equations (PDEs) are widely used for the description of physical and engineering phenomena. Some key parameters involved in PDEs, which represent certain physical properties with important scientific interpretations,…
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…
Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…
In this paper, we consider input-output properties of linear systems consisting of PDEs on a finite domain coupled with ODEs through the boundary conditions of the PDE. This framework can be used to represent e.g. a lumped mass fixed to a…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…