Fanze Kong

collaborators

11 papers

math.AP2026

Local Turnpike Stability for Two-Population Second-Order Mean-Field Game Systems

Mohamed Ghattassi, Fanze Kong, Nader Masmoudi

This paper establishes a local turnpike property for a two-population, second-order mean-field game system with a quadratic Hamiltonian, in which the running cost for each populati…

math.NA2026

Energetic Variational Deep Learning for Solving High-Dimensional Stationary Fokker-Planck Equations

Fanze Kong, Zhouyuan Qin, Shuangquan Xie

This paper develops a deep learning framework for solving high-dimensional stationary Fokker-Planck equations by combining Monte Carlo weak supervision, energy-variational physics…

math.AP2026

Maximal Regularity and Existence for Superquadratic Parabolic Hamilton--Jacobi Equations: The Endpoint case

Fanze Kong, Xiaoyu Zeng

We establish interior maximal $L^{q_{c}}$ -regularity for bounded strong solutions of $u_{t} - Δ u + ∣ D u ∣^{γ} = f$ in $T^{d} \times (0, T)$ , where $d \geq 2$ , $γ > 2$ , and $q_{c} = (d + 2) (γ - 1) / γ$ . T…

math.AP2026

Suppression of Blow-up in Two-dimensional Keller--Segel Systems by Stochastic Couette Flows

Fanze Kong, Krutika Tawri

We study Keller--Segel systems on $T \times R$ subject to a stochastic Couette transport flow. We prove that sufficiently strong mixing suppresses chemotactic fini…

math.AP2026

Endpoint Maximal Regularity for Superquadratic Hamilton-Jacobi Equations and Applications to Ergodic Mean-field Games Systems

Fanze Kong

A celebrated conjecture of P.-L. Lions concerns maximal regularity for viscous Hamilton--Jacobi equations. In this paper, we study the endpoint case. We consider normalized strong…

math.AP2026

Global Finite-Energy Weak Solutions and Sharp Entropy Decay for a Poisson-Nernst-Planck System with Interspecies Drag and Steric Effects

Baoli Hao, Fanze Kong, Kei Fong Lam +1

We derive and analyze a binary Poisson-Nernst-Planck system with steric interactions and interspecies drag through the energetic variational approach. The steric effects are incorp…

math.AP2026

Global Well-posedness of the 2D Stochastic Self-consistent Keller-Segel-Navier-Stokes System with Subcritical Cellular Mass

Fanze Kong, Chen-Chih Lai, Krutika Tawri

We consider a stochastic Keller-Segel-Navier-Stokes system in $R^{2}$ describing the collective motion of cells in an ambient stochastic fluid flow, where the cells are attracted by…

math.FA2026

Mountain-Pass Solutions for Second-Order Ergodic Mean-Field Game Systems

Fanze Kong, Yonghui Tong, Xiaoyu Zeng

We study the existence of mountain-pass solutions to a potential-free mean-field game system in the whole space $R^{n}$ under the mass-supercritical regime, assuming an aggre…

math.AP2025

Stability and slow dynamics of an interior spiky pattern in a one-dimensional spatial Solow model with capital-induced labor migration

Fanze Kong, Jiayi Sun, Shuangquan Xie

One of the most significant findings in the study of spatial Solow-Swan models is the emergence of economic agglomeration, in which economic activities concentrate in specific regi…

cs.LG2025

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts

Fanze Kong, Chen-Chih Lai, Yubin Lu

Conservative-dissipative dynamics are ubiquitous across a variety of complex open systems. We propose a data-driven two-phase method, the Moment-DeepRitz Method, for learning drift…

physics.comp-ph2025

Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures

Fanze Kong, Chen-Chih Lai, Yubin Lu

This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws wit…