Pingwen Zhang
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View article: China’s Wisdom in Addressing the Imperatives of Global Education Modernization in the Digital Age: On Significance of Digital Education Fronts 2025
China’s Wisdom in Addressing the Imperatives of Global Education Modernization in the Digital Age: On Significance of Digital Education Fronts 2025 Open
View article: Construction and Analysis for Adams Explicit Discretization of High-Index Saddle Dynamics
Construction and Analysis for Adams Explicit Discretization of High-Index Saddle Dynamics Open
View article: Designing a minimal Landau model to stabilize desired quasicrystals
Designing a minimal Landau model to stabilize desired quasicrystals Open
Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a given quasicrystal is a challenging problem. To address this…
View article: Digital Intelligence Education at Wuhan University: Practice and Innovation
Digital Intelligence Education at Wuhan University: Practice and Innovation Open
View article: State-Observation Augmented Diffusion Model for Nonlinear Assimilation with Unknown Dynamics
State-Observation Augmented Diffusion Model for Nonlinear Assimilation with Unknown Dynamics Open
View article: Nonlinear Assimilation via Score-based Sequential Langevin Sampling
Nonlinear Assimilation via Score-based Sequential Langevin Sampling Open
This paper presents score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed method decomposes the assimilation process into alternating …
View article: Stability of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules
Stability of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules Open
Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space ca…
View article: Designing a minimal Landau theory to stabilize desired quasicrystals
Designing a minimal Landau theory to stabilize desired quasicrystals Open
Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a given quasicrystal is a challenging problem. To address this…
View article: Nucleation and phase transition of decagonal quasicrystals
Nucleation and phase transition of decagonal quasicrystals Open
In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely the nullspace-preserving saddle search method. Specifically, we focus on nucl…
View article: A diffuse-interface Landau-de Gennes model for free-boundary problems in the theory of nematic liquid crystals
A diffuse-interface Landau-de Gennes model for free-boundary problems in the theory of nematic liquid crystals Open
We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, and a phase field is introduced to model the deformable inter…
View article: State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics
State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics Open
Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical a…
View article: DRM Revisited: A Complete Error Analysis
DRM Revisited: A Complete Error Analysis Open
In this work, we address a foundational question in the theoretical analysis of the Deep Ritz Method (DRM) under the over-parameteriztion regime: Given a target precision level, how can one determine the appropriate number of training samp…
View article: Recovering the Source Term in Elliptic Equation via Deep Learning: Method and Convergence Analysis
Recovering the Source Term in Elliptic Equation via Deep Learning: Method and Convergence Analysis Open
In this paper, we present a deep learning approach to tackle elliptic inverse source problems.Our method combines Tikhonov regularization with physics-informed neural networks, utilizing separate neural networks to approximate the source t…
View article: Improved freezing rain forecast using machine learning
Improved freezing rain forecast using machine learning Open
Freezing rain is one of the most damaging weather phenomena in winter or early spring in many parts of the world, affecting traffic, power lines and agriculture. Thus, reliable and computationally efficient prediction of its occurrence is …
View article: Characteristic Learning for Provable One Step Generation
Characteristic Learning for Provable One Step Generation Open
We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models. Our model is driven by characte…
View article: Understanding high-index saddle dynamics via numerical analysis
Understanding high-index saddle dynamics via numerical analysis Open
High-index saddle dynamics (HiSD) serves as a competitive instrument in searching the any-index saddle points and constructing the solution landscape of complex systems. The Lagrangian multiplier terms in HiSD ensure the Stiefel manifold c…
View article: An Adaptive Method Based on Local Dynamic Mode Decomposition for Parametric Dynamical Systems
An Adaptive Method Based on Local Dynamic Mode Decomposition for Parametric Dynamical Systems Open
Parametric dynamical systems are widely used to model physical systems, but their numerical simulation can be computationally demanding due to nonlinearity, long-time simulation, and multi-query requirements. Model reduction methods aim to…
View article: Semi-implicit method of high-index saddle dynamics and application to construct solution landscape
Semi-implicit method of high-index saddle dynamics and application to construct solution landscape Open
We analyze the semi-implicit scheme of high-index saddle dynamics, which provides a powerful numerical method for finding the any-index saddle points and constructing the solution landscape. Compared with the explicit schemes of saddle dyn…
View article: Accurately recover global quasiperiodic systems by finite points
Accurately recover global quasiperiodic systems by finite points Open
Quasiperiodic systems, related to irrational numbers, are space-filling structures without decay nor translation invariance. How to accurately recover these systems, especially for non-smooth cases, presents a big challenge in numerical co…
View article: Latent assimilation with implicit neural representations for unknown dynamics
Latent assimilation with implicit neural representations for unknown dynamics Open
Data assimilation is crucial in a wide range of applications, but it often faces challenges such as high computational costs due to data dimensionality and incomplete understanding of underlying mechanisms. To address these challenges, thi…
View article: Error estimate for semi-implicit method of sphere-constrained high-index saddle dynamics
Error estimate for semi-implicit method of sphere-constrained high-index saddle dynamics Open
We prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics, which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained system…
View article: Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions
Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions Open
In this paper, we present an improved analysis of the Physics Informed Neural Networks (PINNs) method for solving second-order elliptic equations.By assuming an intrinsic sparse structure in the underlying solution, we provide a convergenc…
View article: On the approximation of quasiperiodic functions with Diophantine frequencies by periodic functions
On the approximation of quasiperiodic functions with Diophantine frequencies by periodic functions Open
We present an analysis of the approximation error for a $d$-dimensional quasiperiodic function $f$ with Diophantine frequencies, approximated by a periodic function with the fundamental domain $[0,L_1)\times [0,L_2)\times \cdots \times[0,L…
View article: Mathematical and Numerical Analysis to Shrinking-Dimer Saddle Dynamics with Local Lipschitz Conditions
Mathematical and Numerical Analysis to Shrinking-Dimer Saddle Dynamics with Local Lipschitz Conditions Open
We present a mathematical and numerical investigation to the shrinkingdimer saddle dynamics for finding any-index saddle points in the solution landscape.Due to the dimer approximation of Hessian in saddle dynamics, the local Lipschitz ass…
View article: Latent Assimilation with Implicit Neural Representations for Unknown Dynamics
Latent Assimilation with Implicit Neural Representations for Unknown Dynamics Open
View article: A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape
A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape Open
We propose a model-free shrinking-dimer saddle dynamics for finding any-index saddle points and constructing the solution landscapes, in which the force in the standard saddle dynamics is replaced by a surrogate model trained by the Gassia…
View article: Numerical Methods and Analysis of Computing Quasiperiodic Systems
Numerical Methods and Analysis of Computing Quasiperiodic Systems Open
Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method…
View article: Contents
Contents Open
COVER IMAGEThe cover image depicts the data trading in new-type power systems: the spiral formed by dots represents renewable energies, the numbers 0 and 1 represent the data in energy systems, and the network formed by the lines and point…
View article: Shaping future low-carbon energy and transportation systems: Digital technologies and applications
Shaping future low-carbon energy and transportation systems: Digital technologies and applications Open
Digitalization and decarbonization are projected to be two major trends in the coming decades. As the already widespread process of digitalization continues to progress, especially in energy and transportation systems, massive data will be…
View article: Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm
Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm Open