Related papers: A hybrid Decoder-DeepONet operator regression fram…

Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

Learning under non-smooth objectives remains a fundamental challenge in machine learning, as abrupt changes in conditioning variables can induce highly non-smooth loss landscapes and destabilize optimization. This difficulty is particularly…

The robustness of image recognition algorithms remains a critical challenge, as current models often depend on large quantities of labeled data. In this paper, we propose a hybrid approach that combines the adaptability of neural networks…

Many different deep networks have been used to approximate, accelerate or improve traditional image operators. Among these traditional operators, many contain parameters which need to be tweaked to obtain the satisfactory results, which we…

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…

Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…

We propose a randomized neural network approach called RaNNDy for learning transfer operators and their spectral decompositions from data. The weights of the hidden layers of the neural network are randomly selected and only the output…

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation…

Anomaly detection (AD) is increasingly recognized as a key component for ensuring the resilience of future communication systems. While deep learning has shown state-of-the-art AD performance, its application in critical systems is hindered…

Neural operators have emerged as powerful tools for learning mappings between function spaces, enabling efficient solutions to partial differential equations across varying inputs and domains. Despite the success, existing methods often…

Deep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. We present a method for folding a deep neural network of arbitrary size into a single neuron with…

In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we…

This work presents a novel hybrid approach that integrates Deep Operator Networks (DeepONet) with the Neural Tangent Kernel (NTK) to solve complex inverse problem. The method effectively addresses tasks such as source localization governed…

Deep neural networks (DNNs) have provided brilliant performance across various tasks. However, this success often comes at the cost of unnecessarily large model sizes, high computational demands, and substantial memory footprints.…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…

Compressive imaging aims to recover a latent image from under-sampled measurements, suffering from a serious ill-posed inverse problem. Recently, deep neural networks have been applied to this problem with superior results, owing to the…