相关论文: Backstepping Control of PDEs on Domains with Graph…

We propose a simple domain adaptation method for neural networks in a supervised setting. Supervised domain adaptation is a way of improving the generalization performance on the target domain by using the source domain dataset, assuming…

A PDE-based control concept is developed to deploy a multi-agent system into desired formation profiles. The dynamic model is based on a coupled linear, time-variant parabolic distributed parameter system. By means of a particular coupling…

In this work, we propose a method to learn the solution operators of PDEs defined on varying domains via MIONet, and theoretically justify this method. We first extend the approximation theory of MIONet to further deal with metric spaces,…

This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…

Pseudospectral time domain (PSTD) methods are widely used in many branches of acoustics for the numerical solution of the wave equation, including biomedical ultrasound and seismology. The use of the Fourier collocation spectral method in…

Since Peng (1993) established a local maximum principle for a general stochastic control problem governed by forward-backward stochastic differential equations (FBSDEs), the corresponding partial differential equation (PDE) characterization…

Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…

The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…

Domain adaptation techniques aim at adapting a classifier learnt on a source domain to work on the target domain. Exploiting the subspaces spanned by features of the source and target domains respectively is one approach that has been…

Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…

Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Proportional-Integral-Differential (PID) control is widely used in industrial control systems. However, up to now there are at least two open problems related with PID control. One is to have a comprehensive understanding of its robustness…

We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…

In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…

Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…

In this paper, we propose a retrofit control method for stable network systems. The proposed approach is a control method that, rather than an entire system model, requires a model of the subsystem of interest for controller design. To…

This paper is concerned with the fault diagnosis problem for general linear heterodirectional hyperbolic ODE-PDE systems. A systematic solution is presented for additive time-varying actuator, process and sensor faults in the presence of…

In this paper, we tackle the problem of domain shift. Most existing methods perform training on multiple source domains using a single model, and the same trained model is used on all unseen target domains. Such solutions are sub-optimal as…

Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…