Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Wan, Xiaoliang"'
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based formulation where
Externí odkaz:
http://arxiv.org/abs/2409.02810
In this paper we consider adaptive deep neural network approximation for stochastic dynamical systems. Based on the Liouville equation associated with the stochastic dynamical systems, a new temporal KRnet (tKRnet) is proposed to approximate the prob
Externí odkaz:
http://arxiv.org/abs/2405.02810
Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning methods to construct simulators for such systems is a promising direc
Externí odkaz:
http://arxiv.org/abs/2402.11283
We introduce an adaptive sampling method for the Deep Ritz method aimed at solving partial differential equations (PDEs). Two deep neural networks are used. One network is employed to approximate the solution of PDEs, while the other one is a deep ge
Externí odkaz:
http://arxiv.org/abs/2310.17185
Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its flexible meshless discretization and its potential for high-dimension
Externí odkaz:
http://arxiv.org/abs/2305.18702
In this paper, we develop an invertible mapping, called B-KRnet, on a bounded domain and apply it to density estimation/approximation for data or the solutions of PDEs such as the Fokker-Planck equation and the Keller-Segel equation. Similar to KRnet
Externí odkaz:
http://arxiv.org/abs/2305.09063
We present a dimension-reduced KRnet map approach (DR-KRnet) for high-dimensional Bayesian inverse problems, which is based on an explicit construction of a map that pushes forward the prior measure to the posterior measure in the latent space. Our a
Externí odkaz:
http://arxiv.org/abs/2303.00573
In this work, we propose adaptive deep learning approaches based on normalizing flows for solving fractional Fokker-Planck equations (FPEs). The solution of a FPE is a probability density function (PDF). Traditional mesh-based methods are ineffective
Externí odkaz:
http://arxiv.org/abs/2210.14402
In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to generate new coll
Externí odkaz:
http://arxiv.org/abs/2112.14038
Autor:
Wan, Xiaoliang, Tang, Kejun
In this work, we have proposed augmented KRnets including both discrete and continuous models. One difficulty in flow-based generative modeling is to maintain the invertibility of the transport map, which is often a trade-off between effectiveness an
Externí odkaz:
http://arxiv.org/abs/2105.12866