相关论文: On the influence of over-parameterization in manif…

Deep learning (DL)-based channel state information (CSI) feedback has shown great potential in improving spectrum efficiency in massive MIMO systems. However, DL models optimized for specific environments often experience performance…

We present a novel deep operator network (DeepONet) architecture for operator learning, the ensemble DeepONet, that allows for enriching the trunk network of a single DeepONet with multiple distinct trunk networks. This trunk enrichment…

In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive…

We present a deep layered architecture that generalizes convolutional neural networks (ConvNets). The architecture, called SimNets, is driven by two operators: (i) a similarity function that generalizes inner-product, and (ii) a…

This paper presents a detailed comparison between 3 methods for emulating CPU-intensive reactive transport models (RTMs): Gaussian processes (GPs), polynomial chaos expansion (PCE) and deep neural networks (DNNs). Besides direct emulation…

The success of DNNs is driven by the counter-intuitive ability of over-parameterized networks to generalize, even when they perfectly fit the training data. In practice, test error often continues to decrease with increasing…

We consider the numerical approximation of different ordinary differential equations (ODEs) and partial differential equations (PDEs) with periodic boundary conditions involving a one-dimensional random parameter, comparing the intrusive…

The goal of this work is to investigate the capability of a neural operator (DeepONet) to accurately capture the complex deformation of a platelet's membrane under shear flow. The surrogate model approximated by the neural operator predicts…

While overfitting and, more generally, double descent are ubiquitous in machine learning, increasing the number of parameters of the most widely used tensor network, the matrix product state (MPS), has generally lead to monotonic…

The bias-variance trade-off is a central concept in supervised learning. In classical statistics, increasing the complexity of a model (e.g., number of parameters) reduces bias but also increases variance. Until recently, it was commonly…

In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions…

Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…

Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…

The diffusion of deepfake technologies has sparked serious concerns about its potential misuse across various domains, prompting the urgent need for robust detection methods. Despite advancement, many current approaches prioritize…

Overparameterization and overfitting are common concerns when designing and training deep neural networks, that are often counteracted by pruning and regularization strategies. However, these strategies remain secondary to most learning…

This study presents an enhanced multi-fidelity Deep Operator Network (DeepONet) framework for efficient spatio-temporal flow field prediction when high-fidelity data is scarce. Key innovations include: a merge network replacing traditional…

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…