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Zipeng Chen

Publications and source records attributed to Zipeng Chen.

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Beyond Action Imitation: Learning a Decision-Aware User Simulator for Online Advertising

Recent advances in LLM-based user simulation have shown promise for offline evaluation of recommendation and advertising systems. However, existing simulators typically infer user preferences from single-domain interaction histories and are primarily optimized to reproduce observable actions such as clicks. Consequently, they capture only a partial view of user preferences, while action-only prediction easily induces model shortcuts and limits both the fidelity and diagnostic value of simulation. To address these challenges, we propose DASH, a decision-aware user simulator that jointly generates thinking traces and predicts behavioral actions from heterogeneous cross-domain histories. DASH first introduces a Context Engineering stage that folds heterogeneous cross-domain histories into decision-relevant context, together with prompt optimization for effective reasoning over the folded context. To train a user simulator, DASH distills thinking trajectories from strong LLMs as SFT data, and further tailors a rubric-based reward model that evaluates thinking traces along form, content, and logic for RL training. Combined with the action reward, these signals jointly improve action prediction and thinking quality. Extensive experiments on real-world Tencent advertising data spanning five heterogeneous content domains demonstrate the effectiveness, efficiency, fidelity, and diagnostic value of DASH.

cs.IR

Non-uniqueness for the hyperdissipative Navier-Stokes equations with arbitrarily small subcritical data

In this paper, we consider the hyperdissipative Navier-Stokes equations with fractional dissipation $(-\Delta)^{\beta}$ with $\beta>1$. We prove that smooth solutions of the hyperdissipative Navier-Stokes equations are non-unique with arbitrarily small initial data in ${B}^{-\beta-\alpha}_{\infty,1}(\mathbb{T}^d)$ for any $\alpha>0$. Moreover, we show the existence of a solution with arbitrarily small initial data in ${B}^{-\beta-\alpha}_{\infty,1}(\mathbb{T}^d)$ ($\alpha>0$) that grows arbitrarily large in $\dot{B}^{-s}_{\infty,\infty}(\mathbb{T}^d)$ for all $s\in\mathbb{R}$ in arbitrarily small time. It is worth pointing out that ${B}^{-\beta-\alpha}_{\infty,1}(\mathbb{T}^d)$ lies in the subcritical regime when $0<\alpha<\beta-1$. To the best of our knowledge, this is the first non-uniqueness result of the Navier-Stokes equations with initial data at the subcritical regularity. To show the sharpness of the above results, we establish the local well-posedness of the hyperdissipative Navier-Stokes equations with initial data in $\dot{B}^{-\beta-\alpha}_{\infty,\infty}(\mathbb{T}^d)$ with $\alpha< 0$.

math.AP

Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data

Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in $BMO^{-1}$. Inspired by their breakthrough work, we develop their schemes for the incompressible magnetohydrodynamic equations and obtain a similar result in 5 dimensional case. More precisely, we construct two distinct global solutions with a initial data, which has nonvanishing velocity and magnetic fields in $BMO^{-1}(\mathbb{T}^5)$.

math.AP

Sharp non-uniqueness for the Boussinesq equation with fractional dissipation

This paper focuses on the $d$-dimensional ($d\geq2$) Boussinesq equation with fractional dissipation $(-\Delta)^{\alpha}$ on the torus. We show that the uniqueness property breaks down within the function space $L^p_tL^\infty_x$ for any $p<\frac{2\alpha}{2\alpha-1}$ when $1\leq\alpha<\frac{d+1}{2}$ and the function space $L^\frac{2\alpha}{2\alpha-1}_tL^q_x$ for any $q<\infty$ when $1<\alpha<\frac{d+1}{2}$. Moreover, the weak solutions we construct are smooth outside a set of singular times with Hausdorff dimension arbitrarily small. This result is sharp, as weak-strong uniqueness holds in the space $L^{\frac{2\alpha}{2\alpha-1}}_TL^\infty_x$.

math.AP

H\"{o}lder continuous weak solutions of the 3D Boussinesq equation with thermal diffusion

In this paper, we show the existence of H\"{o}lder continuous periodic weak solutions of the 3D Boussinesq equation with thermal diffusion, which apprroximate the Onsager's critical spatial regularity and satisfy the prescribed kinetic energy. More precisely, for any smooth $e(t):[0,T]\rightarrow \mathbb{R}_+$ and $\beta\in (0, \frac{1}{3})$, there exist $v\in C^{\beta}([0,T]\times {\mathbb{T} }^3)$ and $ \theta\in C_t^{1,\frac{\beta}{2}}C_x^{2,\beta}([0,T]\times {\mathbb{T} }^3)$ which solve (\ref{e:boussinesq equation}) in the sense of distribution and satisfy \begin{align} e(t)=\int_{{{\mathbb{T} }^3}}|v(t,x)|^2dx, \quad \forall t\in [0,T].\nonumber \end{align}

math.AP