Related papers: Representing Flow Fields with Divergence-Free Kern…
This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…
In this paper we present a novel method for efficient and effective 3D surface reconstruction in open scenes. Existing Neural Radiance Fields (NeRF) based works typically require extensive training and rendering time due to the adopted…
Sensing the fluid flow around an arbitrary geometry entails extrapolating from the physical quantities perceived at its surface in order to reconstruct the features of the surrounding fluid. This is a challenging inverse problem, yet one…
Echo-planar imaging (EPI) remains the cornerstone of diffusion MRI, but it is prone to severe geometric distortions due to its rapid sampling scheme that renders the sequence highly sensitive to $B_{0}$ field inhomogeneities. While deep…
Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and…
Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the…
We present FractalPINN-Flow, an unsupervised deep learning framework for dense optical flow estimation that learns directly from consecutive grayscale frames without requiring ground truth. The architecture centers on the Fractal…
In this paper we present advanced representation learning study on integrating deep learning techniques and sparse approximation, including diffusion models, for advanced flow field analysis and reconstruction. Key applications include…
Finite Rate of Innovation (FRI) sampling techniques provide efficient frameworks for reconstructing signals with inherent sparsity at rates below Nyquist. However, traditional FRI reconstruction methods rely heavily on pre-defined kernels,…
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…
Learning accurate scene reconstruction without pose priors in neural radiance fields is challenging due to inherent geometric ambiguity. Recent development either relies on correspondence priors for regularization or uses off-the-shelf flow…
We present a novel diffusion-based framework for synthesizing 2D vector fields from sparse, coherent inputs (i.e., streamlines) while maintaining physical plausibility. Our method employs a conditional denoising diffusion probabilistic…
This paper presents the rigorous mathematical construction and foundational properties of the Divergence-Free Radiant Transform (DFRT), a spectral transform specifically designed for divergence-free vector fields, with applications in…
Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit…
Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…
We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier--Stokes equations. Traditional numerical solvers incur significant computational costs to respect…
Implicit Neural Representations (INRs) have emerged as a promising paradigm for video compression. However, existing INR-based frameworks typically suffer from inherent spectral bias, which favors low-frequency components and leads to…
Learning can be seen as approximating an unknown function by interpolating the training data. Kriging offers a solution to this problem based on the prior specification of a kernel. We explore a numerical approximation approach to kernel…
In this work, the fast-convolving reproducing kernel particle method (FC-RKPM) is introduced. This method is hundreds to millions of times faster than the traditional RKPM for 3D meshfree simulations. In this approach, the meshfree…
Flow based generative models have charted an impressive path across multiple visual generation tasks by adhering to a simple principle: learning velocity representations of a linear interpolant. However, we observe that training velocity…