Zobrazeno 1 - 10
of 256
pro vyhledávání: '"Liao, Wenjing"'
Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep neural netwo
Externí odkaz:
http://arxiv.org/abs/2406.05320
Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data,
Externí odkaz:
http://arxiv.org/abs/2401.10490
Diffusion generative models have achieved remarkable success in generating images with a fixed resolution. However, existing models have limited ability to generalize to different resolutions when training data at those resolutions are not available.
Externí odkaz:
http://arxiv.org/abs/2401.06144
Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of data lying ex
Externí odkaz:
http://arxiv.org/abs/2306.14859
We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from a single trajectory of noisy observations. Identifying unknown differential equations from noisy observations
Externí odkaz:
http://arxiv.org/abs/2304.05543
Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which en
Externí odkaz:
http://arxiv.org/abs/2303.09863
Generative networks have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that generative networks can generate high-dimensional complex data from a low-dimensional easy-to-sample distributio
Externí odkaz:
http://arxiv.org/abs/2302.13183
Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these me
Externí odkaz:
http://arxiv.org/abs/2212.00700
Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the
Externí odkaz:
http://arxiv.org/abs/2211.03134
Aggregation equations are broadly used to model population dynamics with nonlocal interactions, characterized by a potential in the equation. This paper considers the inverse problem of identifying the potential from a single noisy spatial-temporal p
Externí odkaz:
http://arxiv.org/abs/2207.03358