Related papers: Implicit Neural Spatial Representations for Time-d…

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…

Implicit Neural Representations (INRs), also known as neural fields, have emerged as a powerful paradigm in deep learning, parameterizing continuous spatial fields using coordinate-based neural networks. In this paper, we propose…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Existing self-supervised learning (SSL) methods primarily learn object-invariant representations but often neglect the spatial structure and relationships among object parts. To address this limitation, we introduce Spatial Prediction (SP),…

The storage of medical images is one of the challenges in the medical imaging field. There are variable works that use implicit neural representation (INR) to compress volumetric medical images. However, there is room to improve the…

In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the…

One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable. Here, we introduce a graph neural network approach to finding efficient PDE…

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the…

Dynamic MRI reconstruction, one of inverse problems, has seen a surge by the use of deep learning techniques. Especially, the practical difficulty of obtaining ground truth data has led to the emergence of unsupervised learning approaches.…

Implicit Neural Representations (INRs) have recently advanced the field of deep learning due to their ability to learn continuous representations of signals without the need for large training datasets. Although INR methods have been…

Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications. Neural PDE solvers offer a promising alternative to classical numerical methods. However, existing approaches typically…

Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image…

Dynamic magnetic resonance imaging (dMRI) captures temporally-resolved anatomy but is often challenged by limited sampling and motion-induced artifacts. Conventional motion-compensated reconstructions typically rely on pre-estimated optical…

This paper proposes a novel neural network framework, denoted as spectral integrated neural networks (SINNs), for resolving three-dimensional forward and inverse dynamic problems. In the SINNs, the spectral integration method is applied to…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the…

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

Encoder-decoder recurrent neural network models (RNN Seq2Seq) have achieved great success in ubiquitous areas of computation and applications. It was shown to be successful in modeling data with both temporal and spatial dependencies for…

The nonlinear Schr\"{o}dinger (NLS) equation possesses an infinite hierarchy of conserved densities and the numerical preservation of some of these quantities is critical for accurate long-time simulations, particularly for multi-soliton…