Search Results for author: Zhongjian Wang

Found 5 papers, 0 papers with code

Mathematical analysis of singularities in the diffusion model under the submanifold assumption

no code implementations19 Jan 2023 Yubin Lu, Zhongjian Wang, Guillaume Bal

Using small-time approximations of the Green's function of the forward diffusion, we show that the analytical mean drift function in DDPM and the score function in SGM asymptotically blow up in the final stages of the sampling process for singular data distributions such as those concentrated on lower-dimensional manifolds, and is therefore difficult to approximate by a network.

A variational neural network approach for glacier modelling with nonlinear rheology

no code implementations5 Sep 2022 Tiangang Cui, Zhongjian Wang, Zhiwen Zhang

We first formulate the solution of non-Newtonian ice flow model into the minimizer of a variational integral with boundary constraints.

A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems

no code implementations31 Aug 2022 Zhongjian Wang, Jack Xin, Zhiwen Zhang

We study a regularized interacting particle method for computing aggregation patterns and near singular solutions of a Keller-Segal (KS) chemotaxis system in two and three space dimensions, then further develop DeepParticle (DP) method to learn and generate solutions under variations of physical parameters.

DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method

no code implementations2 Nov 2021 Zhongjian Wang, Jack Xin, Zhiwen Zhang

We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM).

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