相关论文: Gain-Only Neural Operators for PDE Backstepping

We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to…

The Backprop algorithm for learning in neural networks utilizes two mechanisms: first, stochastic gradient descent and second, initialization with small random weights, where the latter is essential to the effectiveness of the former. We…

In this paper we propose a new methodology for decision-making under uncertainty using recent advancements in the areas of nonlinear stochastic optimal control theory, applied mathematics, and machine learning. Grounded on the fundamental…

This brief constructs the adaptive backstepping control scheme for a class of pure-feedback systems with input delay and full state constraints. With the help of Mean Value Theorem, the pure-feedback system is transformed into…

Deep convolutional neural networks (CNNs) for image denoising are usually trained on large datasets. These models achieve the current state of the art, but they have difficulties generalizing when applied to data that deviate from the…

Biological evidence suggests that adaptation of synaptic delays on short to medium timescales plays an important role in learning in the brain. Inspired by biology, we explore the feasibility and power of using synaptic delays to solve…

This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…

Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…

Projected Gradient Ascent (PGA) is the most commonly used optimization scheme in machine learning and operations research areas. Nevertheless, numerous studies and examples have shown that the PGA methods may fail to achieve the tight…

Backpropagation (BP) is the standard algorithm for training the deep neural networks that power modern artificial intelligence including large language models. However, BP is energy inefficient and unlikely to be implemented by the brain.…

Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this…

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While…

Neural operators have emerged as a powerful tool for learning mappings between infinite-dimensional function spaces. However, their approximation properties in Sobolev norms remain poorly quantified, even though these norms control both…

Predictive coding (PC) is a general theory of cortical function. The local, gradient-based learning rules found in one kind of PC model have recently been shown to closely approximate backpropagation. This finding suggests that this…

Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. Deep learning is also considered as a powerful tool with high flexibility to approximate functions. In the present work,…

This paper deals with the tracking control problem for a very simple class of unknown nonlinear systems. In this paper, we presents a design strategy for tracking control of time-varying state constrained nonlinear systems in an adaptive…

We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize only this information to numerically approximate the…

This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…