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We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

Neural Ordinary Differential Equations (NODEs) probed the usage of numerical solvers to solve the differential equation characterized by a Neural Network (NN), therefore initiating a new paradigm of deep learning models with infinite depth.…

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

The recent popularity of foundation models and the pre-train-and-adapt paradigm, where a large-scale model is transferred to downstream tasks, is gaining attention for volumetric medical image segmentation. However, current transfer…

Medical image segmentation, particularly for brain tumor analysis, demands precise and computationally efficient models due to the complexity of multimodal MRI datasets and diverse tumor morphologies. This study introduces PSO-UNet, which…

The application of deep learning to medical image segmentation has been hampered due to the lack of abundant pixel-level annotated data. Few-shot Semantic Segmentation (FSS) is a promising strategy for breaking the deadlock. However, a…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…

Object detection in remote sensing images relies on a large amount of labeled data for training. However, the increasing number of new categories and class imbalance make exhaustive annotation impractical. Few-shot object detection (FSOD)…

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…

Transformer has been adopted to image recognition tasks and shown to outperform CNNs and RNNs while it suffers from high training cost and computational complexity. To address these issues, a hybrid approach has become a recent research…

We present a comprehensive evaluation of the robustness and explainability of ResNet-like models in the context of Unintended Radiated Emission (URE) classification and suggest a new approach leveraging Neural Stochastic Differential…

A significant research problem of recent interest is the localization of targets like vessels, surgical needles, and tumors in photoacoustic (PA) images. To achieve accurate localization, a high photoacoustic signal-to-noise ratio (SNR) is…

Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

Background and objective: Employing deep learning models in critical domains such as medical imaging poses challenges associated with the limited availability of training data. We present a strategy for improving the performance and…

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

Despite deep convolutional neural networks achieved impressive progress in medical image computing and analysis, its paradigm of supervised learning demands a large number of annotations for training to avoid overfitting and achieving…

Recent advances in deep learning have greatly facilitated the automated segmentation of ultrasound images, which is essential for nodule morphological analysis. Nevertheless, most existing methods depend on extensive and precise annotations…

Neural ordinary differential equations (NODEs) are geometric deep learning models based on dynamical systems and flows generated by vector fields on manifolds. Despite numerous successful applications, particularly within the flow matching…