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

The accurate estimation of the state of complex uncertain physical systems requires reconciling theoretical models, with inherent imperfections, with noisy experimental data. In this work, we propose an effective hybrid approach that…

The presence of noise is common in signal processing regardless the signal type. Deep neural networks have shown good performance in noise removal, especially on the image domain. In this work, we consider deep neural networks as a…

Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…

We propose a one-class neural network (OC-NN) model to detect anomalies in complex data sets. OC-NN combines the ability of deep networks to extract a progressively rich representation of data with the one-class objective of creating a…

Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algorithms for approximate solutions are based on constructing…

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…

Transformers have shown significant success in hyperspectral unmixing (HU). However, challenges remain. While multi-scale and long-range spatial correlations are essential in unmixing tasks, current Transformer-based unmixing networks,…

We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous…

This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…

A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under…

Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…

In this paper, we investigate the applications of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate neural…

Training deep neural networks (DNNs) in large-cluster computing environments is increasingly necessary, as networks grow in size and complexity. Local memory and processing limitations require robust data and model parallelism for crossing…

With the accumulation of resources in the era of big data and the rise of pre-trained models in deep learning, optimizing neural networks for various tasks often involves different strategies for fine-tuning pre-trained models versus…

We analyze the regression accuracy of convolutional neural networks assembled from encoders, decoders and skip connections and trained with multifidelity data. Besides requiring significantly less trainable parameters than equivalent fully…

Recently, a deep reinforcement learning method is proposed to solve multiobjective optimization problem. In this method, the multiobjective optimization problem is decomposed to a number of single-objective optimization subproblems and all…

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…

We consider ill-posed inverse problems where the forward operator $T$ is unknown, and instead we have access to training data consisting of functions $f_i$ and their noisy images $Tf_i$. This is a practically relevant and challenging…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…