相关论文: Integral Quadratic Constraints with Infinite-Dimen…
Partial differential equations (PDEs) with uncertain or random inputs have been considered in many studies of uncertainty quantification. In forward uncertainty quantification, one is interested in analyzing the stochastic response of the…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we construct high order operator splitting schemes using the…
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…
Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable…
Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…
The discovery of partial differential equations (PDEs) from datasets has attracted increased attention. However, the discovery of governing equations from sparse data with high noise is still very challenging due to the difficulty of…
This paper proposes a novel fault detection and isolation (FDI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the proposed…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
This paper studies the input-to-state stability (ISS) properties based on the method of Lyapunov functionals for a class of semi-linear parabolic partial differential equations (PDEs) with respect to boundary disturbances. In order to avoid…
In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a…
Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical…
Data-driven discovery of partial differential equations (PDEs) has emerged as a promising approach for deriving governing physics when domain knowledge about observed data is limited. Despite recent progress, the identification of governing…
We develop a foundational framework for inverse problems governed by evolutionary partial differential equations (PDEs) on the Wasserstein space of probability measures. While the forward problems for such transport-type PDEs have been…
Quadratization for partial differential equations (PDEs) is a process that transforms a nonquadratic PDE into a quadratic form by introducing auxiliary variables. This symbolic transformation has been used in diverse fields to simplify the…
We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…
A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in $\mathbb{R}^n$ is given in terms of an infinite-dimensional dynamical system. The dynamical system is on the space of boundary data for…
In this paper, we study the Integrated Communication and Control (ICAC) problem. Specifically, we investigate how messages can be transmitted from the controller/encoder to the observer/decoder through the control signal in Multiple-Input…