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Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Deep learning based methods hold state-of-the-art results in low-level image processing tasks, but remain difficult to interpret due to their black-box construction. Unrolled optimization networks present an interpretable alternative to…

Learning operators from data is central to scientific machine learning. While DeepONets are widely used for their ability to handle complex domains, they require fixed sensor numbers and locations, lack mechanisms for uncertainty…

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…

The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…

We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions among multiple entities. Our framework covers several popular models in recent network analysis literature,…

As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all…

Forecasting the future behavior of all traffic agents in the vicinity is a key task to achieve safe and reliable autonomous driving systems. It is a challenging problem as agents adjust their behavior depending on their intentions, the…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

Image decomposition aims to analyze an image into elementary components, which is essential for numerous downstream tasks and also by nature provides certain interpretability to the analysis. Deep learning can be powerful for such tasks,…

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

The study of operator learning involves the utilization of neural networks to approximate operators. Traditionally, the focus has been on single-operator learning (SOL). However, recent advances have rapidly expanded this to include the…

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…

We develop a unified operator framework for scalar, multivariate, and functional regression based on integral operators defined with respect to general measures. Within this framework, classical regression models, including…

Performance of deep learning models is strongly governed by architectural capacity, with width and depth as primary controls. However, in physical-science applications, models are often compared at a single fixed size or by separating…

Pansharpening aims to synthesize high-resolution multispectral (HR-MS) images by fusing the spatial textures of panchromatic (PAN) images with the spectral information of low-resolution multispectral (LR-MS) images. While recent deep…

The Deep Operator Network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models…

Physics-informed neural networks and Physics-informed DeepONet excel in solving partial differential equations; however, they often fail to converge for singularly perturbed problems. To address this, we propose two novel frameworks,…

Deep neural networks have become the default choice for many of the machine learning tasks such as classification and regression. Dropout, a method commonly used to improve the convergence of deep neural networks, generates an ensemble of…

We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative…