arXiv subjects

Jiangwei Zhang

Publications and source records attributed to Jiangwei Zhang.

11 recordsLinked to original sources

arXiv2026

Pullback Measure Attractors, Zero-Noise Limits, and Moderate Deviations for 2D Stochastic Primitive Equations with Multiplicative L\'{e}vy Noise

We study the long-term distributional dynamics and small-noise asymptotics of two-dimensional nonautonomous stochastic primitive equations driven by Gaussian and multiplicative L\'evy noise, together with moderate deviations for the purely jump model. For sufficiently small noise, uniform moment bounds and an exponentially weighted terminal estimate yield a pullback absorbing family and tightness, while a lower semicontinuous vertical-moment functional preserves admissibility under weak limits. We prove the existence and uniqueness of a pullback measure attractor in the weak topology of probability measures and establish its upper semicontinuity as both noise components vanish. For the jump-driven equation, we establish a moderate deviation principle in $\mathcal D([0,T];H)\cap L^2(0,T;V)$ with speed $a^2(\epsilon)/\epsilon$. The proof combines continuity of the skeleton map with controlled stochastic convergence based on entropy bounds, truncation, martingale estimates, and direct vertical estimates, avoiding Lipschitz continuity of the vertical derivative of the jump coefficient.

math.PR↗

arXiv2026

Commutator Estimates Uniform in the Screening Parameter and Mean-Field Limits for Yukawa Interactions

We study quantitative mean-field limits for classical particles with Yukawa (screened Coulomb) interactions in every fixed dimension $d\ge2$, uniformly as the screening parameter $\kappa$ tends to zero. Our main result is a first-order commutator estimate in the natural Yukawa modulated energy, with an additive error of order $N^{-2/d}$ for $d\ge3$ and $(1+\log N)/N$ for $d=2$. It requires only a bounded reference density and a Lipschitz transport field, with no uniform lower bound on interparticle distances and no negative power of $\kappa$. The modified Helmholtz operator $-\Delta+\kappa^2$ creates the main new difficulty. Truncating the potential to a constant inside each truncation ball produces a surface charge and a positive volume charge whose total mass is strictly less than one. We keep the reference density unchanged and control this loss of mass through an exact Green function representation and renormalized energy identities. A stress-energy identity with interface terms and averaging over the truncation radii then give the uniform commutator estimate. Combined with the modulated energy dissipation identity and a normalized quadratic transport cost, this estimate yields weak--strong stability, propagation of chaos, and time-integrated control of the mean-square difference between empirical and mean-field forces. We also prove a quantitative Yukawa-to-Coulomb limit. For smooth product data, $N\to\infty$ and $\kappa\downarrow0$ may be taken simultaneously with no relation between their rates; in dimension three, a direct comparison at the particle level also holds for general symmetric initial laws with finite initial error.

math.AP↗

arXiv2026

Quantitative mean-field limits for repulsive Coulomb flows at bounded density and Riesz weak--strong stability

We establish quantitative mean-field convergence and propagation of chaos for repulsive Coulomb gradient flows at the bounded-density regularity of the limiting equation. The argument couples the dissipative modulated-energy identity with the normalized quadratic transport cost of the full $N$-particle law. The remaining negative mean-square force-error term is used through an exact completion of squares after mollification: the non-Lipschitz remainder is absorbed by this negative term, while a sharp first-order commutator estimate is applied to the mollified Lipschitz field. For the Coulomb equation, the sharp $L^\infty$ decay gives the density envelope $m(t)=\|\rho_0\|_{L^\infty}/(1+t\|\rho_0\|_{L^\infty})$. A density-adapted transport weight and mollification scale $m(t)^{-1/d}$ yield an Osgood comparison. Thus, for every $d\ge2$ and $\rho_0\in\mathcal P_2(\mathbb R^d)\cap L^\infty(\mathbb R^d)$, we obtain quantitative comparison with the global bounded-density Coulomb solution on every prescribed finite interval. For tensorized initial data, the normalized squared Wasserstein distance of the full $N$-particle law, the expected modulated energy, and the time-integrated mean-square force error are bounded by $N^{-2\gamma_{T,d}/d}$ for $d\ge3$ and $((1+\log N)/N)^{\gamma_{T,2}}$ for $d=2$, where $\gamma_{T,d}=(1+T\|\rho_0\|_{L^\infty})^{-c_d}$. For $d-2<s<d$, we also prove Riesz weak--strong stability for prescribed reference solutions in $L^\infty(0,T;B^{s-d+2}_{\infty,q})$, with Gronwall, Bihari, and Osgood comparisons according to $q$, together with uniqueness in the stated Besov class. Finally, an outlier construction separates modulated-energy convergence and Kac chaos from normalized Wasserstein convergence of the full $N$-particle law.

math.AP↗

arXiv2026

Agentic evolution of physically constrained foundation models

Artificial intelligence increasingly drives automated scientific discovery, yet contemporary generalist agents lack physical grounding, frequently hallucinating hardware-incompatible designs. Here, we present a physically grounded, multi-agent discovery engine that autonomously architects hardware-compliant computing systems. Anchored by an Evolutionary Knowledge Graph structuring past scientific innovations, the framework extracts an "algorithmic Chain-of-Thought" to transform blind stochastic search into directed structural evolution. Applied to the extreme testbed of foundation model deployment, the engine evolved two hardware-aware compression methodologies surpassing human-engineered heuristics: Q-Enhance mitigates long-context accuracy loss in dense models, and MoE-Salient-AQ outperforms state-of-the-art manual sparse Mixture-of-Experts designs by 3.7% at sub-3-bit regimes. Utilizing a bandwidth-efficient Sensitivity Profile, we successfully deployed a massive 235-billion-parameter model onto a constrained dual-A100 server, reducing memory requirements by 75% with a marginal 0.64% accuracy degradation. By transforming unconstrained combinatorial search into knowledge-driven autonomy, this establishes a scalable hardware-software co-design paradigm for machine-driven discovery within strict physical boundaries.

cs.AI↗

arXiv2026

Long-time dynamics of stochastic 2D hydrodynamic-type evolution equations driven by multiplicative L\'{e}vy noise

This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the stochastic 2D Navier-Stokes equations, magnetohydrodynamic equations, the magnetic B\'{e}rnard problem, as well as various stochastic shell models of turbulence. Under the assumption that the nonlinear noise coefficients satisfy local Lipschitz and linear growth conditions, we first establish global well-posedness using a truncation technique. Then, by introducing a mean random dynamical system, we prove the existence and uniqueness of weak pullback mean random attractors for the system. Furthermore, when the external force is time-independent, we study the existence of invariant measures for the corresponding autonomous system, as well as the double limiting behavior of invariant measures with respect to the intensities of Gaussian and L\'{e}vy noise. Finally, under additional assumptions on the bilinear nonlinear term (e.g., as in the Navier-Stokes equations), we examine the existence and uniqueness of pullback measure attractors, along with the asymptotically autonomous stability of such attractors as the time parameter tends to negative infinity. It is worth noting that the results of this paper are new even for the single stochastic 2D Navier-Stokes equations.

math.PR↗

arXiv2026

Well-posedness, mean attractors and invariant measures of stochastic discrete long-wave-short-wave resonance equations driven by locally Lipschitz nonlinear noise

This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: $(1)$ the equations contain locally Lipschitz nonlinear coupling terms $u_mv_m$ and $(B(|u(t)|^2))_m$ for $m\in \mathbb{Z}$; $(2)$ the nonlinear coefficients of noises satisfy local Lipschitz conditions; and $(3)$ the system couples real and complex equations and is infinite-dimensional. These inherent structural properties prevent the analysis from being carried out in a standard Bochner product space of the same order and make it difficult to directly verify the tightness of the distribution family of solutions. To address these challenges, we adopt a higher-order Bochner product space $L^4(\Omega,\ell_c^2)\times L^2(\Omega,\ell^2)$ as the phase space and employ the technique of uniform tail-end estimates. The main results include: establishing the global well-posedness of the nonautonomous stochastic discrete long-wave-short-wave resonance equations driven by nonlinear noise in $L^4(\Omega,\ell_c^2)\times L^2(\Omega,\ell^2)$; based on this, defining the mean random dynamical system and proving the existence and uniqueness of weak $\mathscr{D}$-pullback mean random attractors. When the external forcing terms are independent of time and sample, we investigate the existence of invariant measures for the corresponding autonomous system and examine the limiting behavior of the invariant measure as the noise intensity tends to zero.

math.PR↗

arXiv2025

Uniform measure attractors of the distribution-dependent 2D stochastic Navier-Stokes equations driven by nonlinear noise

In this paper, we investigate the uniform measure attractors of the distribution-dependent nonautonomous 2D stochastic Navier-Stokes equations driven by nonlinear noise and subject to almost periodic external forcing. Owing to the distribution-dependent structure and the almost periodicity of the external forcing, the resulting solution process becomes an inhomogeneous Markov process, presenting significant analytical challenges. To overcome these difficulties, we propose sufficient conditions on the time-dependent external forcing and distribution-dependent nonlinear terms, and develop novel analytical estimates. As a result, we establish the existence and uniqueness of uniform measure attractors for the system. Notably, the joint continuity of the family of processes is achieved without relying on the Feller property of the distribution law operators.

math.DS↗

arXiv2025

Ergodicity for the fractional Magneto-Hydrodynamic equations driven by a degenerate pure jump noise

This paper is concerned with the ergodicity for stochastic 2D fractional magneto-hydrodynamic equations on the two-dimensional torus driven by a highly degenerate pure jump Lévy noise. We focus on the challenging case where the noise acts in as few as four directions, establishing new results for such high degeneracy. We first employ Malliavin calculus and anticipative stochastic calculus to demonstrate the equi-continuity of the semigroup (or so-called the e-property), and then verify the weak irreducibility of the solution process. Therefore, the uniqueness of invariant measure is proven.

math.PR↗

arXiv2025

Ergodicity for stochastic 2D Boussinesq equations with a highly degenerate pure jump Levy noise

This study aims to analyze the ergodicity for stochastic 2D Boussinesq equations and explore the impact of a highly degenerate pure jump L\'{e}vy noise acting only in the temperature equation, where this noise could appear on only a few Fourier modes. By leveraging the equi-continuity of the semigroup established through Malliavin calculus and an analysis of stochastic calculus, together with the weak irreducibility of the solution process, we prove the existence and uniqueness of the invariant measure. Moreover, we overcome the main challenge of establishing time asymptotic smoothing properties of the Markovian dynamics corresponding to this system by conducting spectral analysis of the Malliavin covariance matrix.

math.PR↗

arXiv2024

On the scalar curvature rigidity for mainifolds with non-positive Yamabe invariant

In this paper, we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant. We prove that if the scalar curvature is not less than the Yamabe invariant in distributional sense, then the manifold must be isometric to an Einstein manifold. This result extends Theorem 1.4 in Jiang, Sheng and the first author (Sci. China Math. 66 (2023) no. 6, 1141-1160), from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant. This result depends highly on an analysis and estimates of geometric evolution equations.

math.AP↗

arXiv2020

PriceAggregator: An Intelligent System for Hotel Price Fetching

This paper describes the hotel price aggregation system - PriceAggregator, deployed at Agoda, a global online travel agency for hotels, vacation rentals, flights and airport transfer. Agoda aggregates non-direct suppliers' hotel rooms to ensure that Agoda's customers always have the widest selection of hotels, room types and packages. As of today, Agoda aggregates millions of hotels. The major challenge is that each supplier only allows Agoda to fetch for the hotel price with a limited amount of Queries Per Second (QPS). Due to the sheer volume of Agoda's user search traffic, this limited amount of QPS is never enough to cover all user searches. Inevitably, many user searches have to be ignored. Hence, booking lost. To overcome the challenge, we built PriceAggregator. PriceAggregator intelligently determines when, how and what to send to the suppliers to fetch for price. In this paper, we not only prove PriceAggregator is optimal theoretically but also demonstrate that PriceAggregator performs well in practice. PriceAggregator has been deployed in Agoda. Extensive online A/B experimentation have shown that PriceAggregator increases Agoda's bookings significantly.

cs.DC↗