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Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…

Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…

Due to the computational complexity of 3D medical image segmentation, training with downsampled images is a common remedy for out-of-memory errors in deep learning. Nevertheless, as standard spatial convolution is sensitive to variations in…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an…

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. These models often require solving a system…

Deep learning models have emerged as the cornerstone of medical image segmentation, but their efficacy hinges on the availability of extensive manually labeled datasets and their adaptability to unforeseen categories remains a challenge.…

Neural Ordinary Differential Equations (NODEs) are a novel neural architecture, built around initial value problems with learned dynamics which are solved during inference. Thought to be inherently more robust against adversarial…

Few-shot segmentation (FSS) is proposed to segment unknown class targets with just a few annotated samples. Most current FSS methods follow the paradigm of mining the semantics from the support images to guide the query image segmentation.…

Few-shot learning (FSL) via customization of a deep learning network with limited data has emerged as a promising technique to achieve personalized user experiences on edge devices. However, existing FSL methods primarily assume independent…

Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning…

Conventional training of deep neural networks requires a large number of the annotated image which is a laborious and time-consuming task, particularly for rare objects. Few-shot object detection (FSOD) methods offer a remedy by realizing…

The scarcity of labeled clinical data in oncology makes Few-Shot Learning (FSL) a critical framework for Computer Aided Diagnostics, but we observed that standard Prototypical Networks often struggle with the "prototype instability" caused…

Few-shot segmentation~(FSS) performance has been extensively promoted by introducing episodic training and class-wise prototypes. However, the FSS problem remains challenging due to three limitations: (1) Models are distracted by…

There has recently been increasing attention towards developing foundational neural Partial Differential Equation (PDE) solvers and neural operators through large-scale pretraining. However, unlike vision and language models that make use…

The deep CNNs in image semantic segmentation typically require a large number of densely-annotated images for training and have difficulties in generalizing to unseen object categories. Therefore, few-shot segmentation has been developed to…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

Deep learning has achieved tremendous success in computer vision, while medical image segmentation (MIS) remains a challenge, due to the scarcity of data annotations. Meta-learning techniques for few-shot segmentation (Meta-FSS) have been…