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Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a…
Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…
We present a new approach and a novel architecture, termed WSNet, for learning compact and efficient deep neural networks. Existing approaches conventionally learn full model parameters independently and then compress them via ad hoc…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE).…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
This paper develops a novel deep learning approach for solving evolutionary equations, which integrates sequential learning strategies with an enhanced hard constraint strategy featuring trainable parameters, addressing the low…
In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…
Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…
This paper introduces HPNet, a novel deep-learning approach for segmenting a 3D shape represented as a point cloud into primitive patches. The key to deep primitive segmentation is learning a feature representation that can separate points…
We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can…
Much more attention has been paid to unsupervised feature selection nowadays due to the emergence of massive unlabeled data. The distribution of samples and the latent effect of training a learning method using samples in more effective…
We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed…
We study the Evolutionary Deep Neural Network (EDNN) framework for accelerating numerical solvers of time-dependent partial differential equations (PDEs). We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN), which constrains…
This study aims to optimize the few-shot image classification task and improve the model's feature extraction and classification performance by combining self-supervised learning with the deep network model ResNet-101. During the training…
Ensembling a neural network is a widely recognized approach to enhance model performance, estimate uncertainty, and improve robustness in deep supervised learning. However, deep ensembles often come with high computational costs and memory…
Deep learning models are used to minimize the number of polyps that goes unnoticed by the experts and to accurately segment the detected polyps during interventions. Although state-of-the-art models are proposed, it remains a challenge to…
Large-scale deep neural networks (DNN) have been successfully used in a number of tasks from image recognition to natural language processing. They are trained using large training sets on large models, making them computationally and…