相关论文: Single-shot prediction of parametric partial diffe…
We present fast, spatially dispersionless and unconditionally stable high-order solvers for Partial Differential Equations (PDEs) with variable coefficients in general smooth domains. Our solvers, which are based on (i) A certain "Fourier…
We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation…
Separating shared and independent features is crucial for multi-phase contrast-enhanced (CE) MRI synthesis. However, existing methods use deep autoencoder generators with low parameter efficiency and lack interpretable training strategies.…
A variational autoencoder (VAE) derived from Tsallis statistics called q-VAE is proposed. In the proposed method, a standard VAE is employed to statistically extract latent space hidden in sampled data, and this latent space helps make…
Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…
Developing neural operators that accurately predict the behavior of systems governed by partial differential equations (PDEs) across unseen parameter regimes is crucial for robust generalization in scientific and engineering applications.…
Latent variable models such as the Variational Auto-Encoder (VAE) have become a go-to tool for analyzing biological data, especially in the field of single-cell genomics. One remaining challenge is the interpretability of latent variables…
Recently, probabilistic predictive coding that directly models the conditional distribution of latent features across successive frames for temporal redundancy removal has yielded promising results. Existing methods using a single-scale…
The variational autoencoder (VAE) is a simple and efficient generative artificial intelligence method for modeling complex probability distributions of various types of data, such as images and texts. However, it suffers some main…
A novel stability-enhanced Gaussian process variational autoencoder (SEGP-VAE) is proposed for indirectly training a low-dimensional linear time invariant (LTI) system, using high-dimensional video data. The mean and covariance function of…
Latent Diffusion Models (LDM), a subclass of diffusion models, mitigate the computational complexity of pixel-space diffusion by operating within a compressed latent space constructed by Variational Autoencoders (VAEs), demonstrating…
The spatial context of single-cell gene expression data is crucial for many downstream analyses, yet often remains inaccessible due to practical and technical limitations, restricting the utility of such datasets. In this paper, we propose…
Deep Learning Reduced Order Models (ROMs) are becoming increasingly popular as surrogate models for parametric partial differential equations (PDEs) due to their ability to handle high-dimensional data, approximate highly nonlinear…
Most visual generative models compress images into a latent space before applying diffusion or autoregressive modelling. Yet, existing approaches such as VAEs and foundation model aligned encoders implicitly constrain the latent space…
Variational autoencoders (VAEs) employ Bayesian inference to interpret sensory inputs, mirroring processes that occur in primate vision across both ventral (Higgins et al., 2021) and dorsal (Vafaii et al., 2023) pathways. Despite their…
Recently, autoencoders (AEs) have gained interest for creating parametric and invertible projections of multidimensional data. Parametric projections make it possible to embed new, unseen samples without recalculating the entire projection,…
Medical image segmentation is crucial for clinical diagnosis and treatment planning. Traditional methods typically produce a single segmentation mask, failing to capture inherent uncertainty. Recent generative models enable the creation of…
Video Variational Autoencoder (VAE) encodes videos into a low-dimensional latent space, becoming a key component of most Latent Video Diffusion Models (LVDMs) to reduce model training costs. However, as the resolution and duration of…
We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…
Vector Quantized-Variational AutoEncoders (VQ-VAE) are generative models based on discrete latent representations of the data, where inputs are mapped to a finite set of learned embeddings.To generate new samples, an autoregressive prior…