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

Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…

We present here the details of a backstepping transformation aiming at reformulating the dynamics of a nonlinear systems subject to unknown long input delay in a form which is suitable for Lyapunov stability analysis. The control law…

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein,…

Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure to train a single neural network on data from multiple…

Neurological studies show that injured neurons can regain their functionality with therapeutics such as Chondroitinase ABC (ChABC). These therapeutics promote axon elongation by manipulating the injured neuron and its intercellular space to…

Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations. Despite their promising…

In this paper, we present a deep surrogate model for learning the Green's function associated with the reaction-diffusion operator in rectangular domain. The U-Net architecture is utilized to effectively capture the mapping from source to…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…

Neural operators provide a framework for learning solution operators of partial differential equations (PDEs), enabling efficient surrogate modeling for complex systems. While universal approximation results are now well understood,…

Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant computational…

In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…

This paper deals with the backstepping design of observer-based compensators for parabolic ODE-PDE-ODE systems. The latter consist of n coupled parabolic PDEs with distinct diffusion coefficients and spatially-varying coefficients, that are…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

This paper presents a safe delay-adaptive control for a strict-feedback nonlinear ODE with a delayed actuator, whose dynamic is also a strict-feedback nonlinear ODE and the delay length is unknown. By formulating the delay as a transport…

Deep learning has become an increasingly popular and powerful methodology for modern pattern recognition systems. However, many deep neural networks have millions or billions of parameters, making them untenable for real-world applications…

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

This paper considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with…

Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large…