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

Z Wang, J Xin, Z Zhang - Journal of Computational Physics, 2022 - Elsevier
We introduce DeepParticle, a method to learn and generate invariant measures of stochastic
dynamical systems with physical parameters based on data computed from an interacting …

A convergent interacting particle method for computing KPP front speeds in random flows

T Zhang, Z Wang, J Xin, Z Zhang - arXiv preprint arXiv:2308.14479, 2023 - arxiv.org
We aim to efficiently compute spreading speeds of reaction-diffusion-advection (RDA) fronts
in divergence free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) …

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

Z Wang, J Xin, Z Zhang - Physica D: Nonlinear Phenomena, 2024 - Elsevier
We study a regularized interacting particle method for computing aggregation patterns and
near singular solutions of a Keller–Segel (KS) chemotaxis system in two and three space …

Lagrangian, game theoretic, and PDE methods for averaging G-equations in turbulent combustion: existence and beyond

J Xin, Y Yu, P Ronney - Bulletin of the American Mathematical Society, 2024 - ams.org
G-equations are popular level set Hamilton–Jacobi nonlinear partial differential equations
(PDEs) of first or second order arising in turbulent combustion. Characterizing the effective …

Residual Diffusivity for Noisy Bernoulli Maps

G Iyer, J Nolen - arXiv preprint arXiv:2409.12410, 2024 - arxiv.org
Consider a discrete time Markov process $ X^\varepsilon $ on $\mathbb R^ d $ that makes a
deterministic jump prescribed by a map $\varphi\colon\mathbb R^ d\to\mathbb R^ d $, and …

An augmented subspace based adaptive proper orthogonal decomposition method for time dependent partial differential equations

X Dai, M Hu, J Xin, A Zhou - Journal of Computational Physics, 2024 - Elsevier
In this paper, we propose an augmented subspace based adaptive proper orthogonal
decomposition (POD) method for solving the time dependent partial differential equations …

Long time asymptotics of mixed-type Kimura diffusions

G Bal, B Chen, Z Wang - arXiv preprint arXiv:2210.10037, 2022 - arxiv.org
This paper concerns the long-time asymptotics of diffusions with degenerate coefficients at
the domain's boundary. Degenerate diffusion operators with mixed linear and quadratic …

Reweighted Interacting Langevin Diffusions: an Accelerated Sampling Methodfor Optimization

J Lyu, Z Chen, W Lyu, J Hao - arXiv preprint arXiv:2301.12640, 2023 - arxiv.org
We proposed a new technique to accelerate sampling methods for solving difficult
optimization problems. Our method investigates the intrinsic connection between posterior …

Partial Differential Equations Arising from Topological Insulators

B Chen - 2024 - knowledge.uchicago.edu
In this thesis, we develop a scattering theory for the asymmetric transport observed at
interfaces separating two-dimensional topological insulators. Starting from the spectral …

[PDF][PDF] A Bibliography of Publications in SIAM Journal on Numerical Analysis: 2010–2019

NHF Beebe - 2024 - ctan.math.utah.edu
A Bibliography of Publications in SIAM Journal on Numerical Analysis: 2010–2019 Page 1
A Bibliography of Publications in SIAM Journal on Numerical Analysis: 2010–2019 Nelson …