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Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…
Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black…
This paper proposes a new data-driven method for the reliable prediction of power system post-fault trajectories. The proposed method is based on the fundamentally new concept of Deep Operator Networks (DeepONets). Compared to traditional…
Trajectory tracking control for quadrotors is important for applications ranging from surveying and inspection, to film making. However, designing and tuning classical controllers, such as proportional-integral-derivative (PID) controllers,…
Uncertainty estimation in machine learning is paramount for enhancing the reliability and interpretability of predictive models, especially in high-stakes real-world scenarios. Despite the availability of numerous methods, they often pose a…
Deep neural networks (DNNs) often rely on massive labelled data for training, which is inaccessible in many applications. Data augmentation (DA) tackles data scarcity by creating new labelled data from available ones. Different DA methods…
In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…
We present a new framework of applying deep neural networks (DNN) to devise a universal discrete denoiser. Unlike other approaches that utilize supervised learning for denoising, we do not require any additional training data. In such…
Deep Neural Networks (DNNs) have emerged as the core enabler of many major applications on mobile devices. To achieve high accuracy, DNN models have become increasingly deep with hundreds or even thousands of operator layers, leading to…
Deep convolutional neural networks (DCNN) have recently shown promising results in low-level computer vision problems such as optical flow and disparity estimation, but still, have much room to further improve their performance. In this…
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…
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we…
This paper proposes a deep neural network (DNN)-driven framework to address the longstanding generalization challenge in adaptive filtering (AF). In contrast to traditional AF frameworks that emphasize explicit cost function design, the…
During the forward pass of Deep Neural Networks (DNNs), inputs gradually transformed from low-level features to high-level conceptual labels. While features at different layers could summarize the important factors of the inputs at varying…
Neural operators are capable of capturing nonlinear mappings between infinite-dimensional functional spaces, offering a data-driven approach to modeling complex functional relationships in classical density functional theory (cDFT). In this…
Recent advances in modeling large-scale complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources.…
We present a resilient deep neural network (DNN) framework for decentralized transport and coverage using uncrewed aerial systems (UAS) operating in $\mathbb{R}^n$. The proposed DNN-based mass-transport architecture constructs a layered…
Deep neural networks (DNNs) trained on large-scale datasets have exhibited significant performance in image classification. Many large-scale datasets are collected from websites, however they tend to contain inaccurate labels that are…
A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is…
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…