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

The infrequent occurrence of overfit in deep neural networks is perplexing. On the one hand, theory predicts that as models get larger they should eventually become too specialized for a specific training set, with ensuing decrease in…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

We present two novel hyperparameter optimization strategies for optimization of deep learning models with a modular architecture constructed of multiple subnetworks. As complex networks with multiple subnetworks become more frequently…

Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be…

Overparameterization is central to the success of deep learning, yet the mechanisms by which it improves optimization remain incompletely understood. We analyze weight-space symmetries in neural networks and show that overparameterization…

A combustion chemistry acceleration scheme is developed based on deep operator networks (DeepONets). The scheme is based on the identification of combustion reaction dynamics through a modified DeepOnet architecture such that the solutions…

Successful deep learning models often involve training neural network architectures that contain more parameters than the number of training samples. Such overparametrized models have been extensively studied in recent years, and the…

In this work, we propose a method to learn the solution operators of PDEs defined on varying domains via MIONet, and theoretically justify this method. We first extend the approximation theory of MIONet to further deal with metric spaces,…

Reliable multiscale models of thrombosis require platelet-scale fidelity at organ-scale cost, a gap that scientific machine learning has the potential to narrow. We train a DeepONet surrogate on platelet dynamics generated with LAMMPS for…

Focused ultrasound (FUS) therapy is a promising tool for optimally targeted treatment of spinal cord injuries (SCI), offering submillimeter precision to enhance blood flow at injury sites while minimizing impact on surrounding tissues.…

Deep neural networks (DNNs) are typically optimized using various forms of mini-batch gradient descent algorithm. A major motivation for mini-batch gradient descent is that with a suitably chosen batch size, available computing resources…

This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…

We present a novel regularization approach to train neural networks that enjoys better generalization and test error than standard stochastic gradient descent. Our approach is based on the principles of cross-validation, where a validation…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these…

We introduce a surrogate-based black-box optimization method, termed Polynomial-model-based optimization (PMBO). The algorithm alternates polynomial approximation with Bayesian optimization steps, using Gaussian processes to model the error…

Learning data representations under uncertainty is an important task that emerges in numerous scientific computing and data analysis applications. However, uncertainty quantification techniques are computationally intensive and become…

We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…

The Li-ion battery is a complex physicochemical system that generally takes applied current as input and terminal voltage as output. The mappings from current to voltage can be described by several kinds of models, such as accurate but…

Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model…