Related papers: Deep Learning of Delay-Compensated Backstepping fo…

This paper presents a delay-adaptive boundary control scheme for a $2\times 2$ coupled linear hyperbolic PDE-ODE cascade system with an unknown and arbitrarily long input delay. To construct a nominal delay-compensated control law, assuming…

The uncertainty in human driving behaviors leads to stop-and-go instabilities in freeway traffic. The traffic dynamics are typically modeled by the Aw-Rascle-Zhang (ARZ) Partial Differential Equation (PDE) models, in which the relaxation…

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

In this work, we present the first stability results for approximate predictors in multi-input non-linear systems with distinct actuation delays. We show that if the predictor approximation satisfies a uniform (in time) error bound,…

Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely in its infancy due to the inherent complexity and diversity, such as long…

We establish that stabilization of a class of linear, hyperbolic partial differential equations (PDEs) with a large (nevertheless finite) number of components, can be achieved via employment of a backstepping-based control law, which is…

In this paper, we propose a deep neural network approximation to the evolution operator for time dependent PDE systems over long time period by recursively using one single neural network propagator, in the form of POD-DeepONet with…

Deep-predictive-coding networks (DPCNs) are hierarchical, generative models. They rely on feed-forward and feed-back connections to modulate latent feature representations of stimuli in a dynamic and context-sensitive manner. A crucial…

We present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by general, quasilinear, first-order hyperbolic PDEs. Since for such PDE-ODE cascades the speed of propagation depends on the PDE state…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

We develop a backstepping control design for a class of continuum systems of linear hyperbolic PDEs, described by a coupled system of an ensemble of rightward transporting PDEs and a (finite) system of $m$ leftward transporting PDEs. The…

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive…

This paper introduces a novel approach to PDE boundary control design using neural operators to alleviate stop-and-go instabilities in congested traffic flow. Our framework leverages neural operators to design control strategies for traffic…

Deep operator networks (DeepONets) are trained to predict the linear amplification of instability waves in high-speed boundary layers and to perform data assimilation. In contrast to traditional networks that approximate functions,…

Modern control systems frequently operate under input delays and sampled state measurements. A common delay-compensation strategy is predictor feedback; however, practical implementations require solving an implicit ODE online, resulting in…