Related papers: Neural Operator Feedback for a First-Order PIDE wi…
Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…
In machine learning, asynchronous parallel stochastic gradient descent (APSGD) is broadly used to speed up the training process through multi-workers. Meanwhile, the time delay of stale gradients in asynchronous algorithms is generally…
We propose a deep unfolding-based approach for stabilization of time-delay linear systems. Deep unfolding is an emerging framework for design and improvement of iterative algorithms and attracting significant attentions in signal…
We explore theoretically the navigation of an active particle based on delayed feedback control. The delayed feedback enters in our expression for the particle orientation which, for an active particle, determines (up to noise) the…
We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that…
In this paper, we design a controller for an interconnected system consisting of a linear Stochastic Differential Equation (SDE) actuated through a linear hyperbolic Partial Differential Equation (PDE). Our approach aims to minimize the…
This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action,…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
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…
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…
In this work, we consider the problem of boundary stabilization for a quasilinear 2X2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H^2…
The communication bottleneck has been a critical problem in large-scale distributed deep learning. In this work, we study distributed SGD with random block-wise sparsification as the gradient compressor, which is ring-allreduce compatible…
Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit…
Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown…
This work proposes a new procedure for the stabilization of time-delay systems using Static Output Feedback (SOF) control. A previous convex optimization approach to SOF for Ordinary Differential Equations (ODEs) is extended to time-delay…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…
An adaptive observer is proposed to estimate the synaptic distribution between neurons asymptotically from the measurement of a part of the neuronal activity and a delayed neural field evolution model. The convergence of the observer is…
Feedback control (based on the quantum continuous measurement) of quantum systems inevitably suffers from estimation delays. In this paper we give a delay-dependent stability criterion for a wide class of nonlinear stochastic systems…
Neural PDE simulators often receive only a single observed field at deployment. In this setting, a field-to-future predictor can collapse distinct latent problem states into the same deterministic interface, losing the ambiguity needed for…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…