arXiv subjects

Yuzhao Wang

Publications and source records attributed to Yuzhao Wang.

At least 19 recordsLinked to original sources

arXiv2026

Phase transition for weakly interacting focusing Gibbs measures with harmonic potential

In this paper, we study the Gibbs measures on Euclidean spaces associated to the focusing nonlinear Schr\"odinger equation with harmonic potential and critical non linearity whose coupling constant tends to 0, a question initially posed by Brydges-Slade (1996) for the $\Phi^4_2$-model on $\mathbb{T}^2$. In dimension one and in the higher dimensional cases (with radial assumption), we establish a critical threshold below which the frequency-truncated measures converge to the base Gaussian measure (possibly with a renormalized $L^2$ cut-off) while, in the supercritical regime, we prove non-convergence of the frequency-truncated measures, even up to a subsequence.

math.PR↗

arXiv2026

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus

We consider the defocusing Wick-ordered cubic fractional nonlinear Schr\"odinger equation on the two-dimensional torus with dispersion relation $\omega(k)=|k|^\alpha$. In the weakly dispersive regime $\frac{29}{15}<\alpha<2$, we construct global dynamics for almost every initial datum with respect to the associated Gibbs measure as the limit of the finite-dimensional truncated flows and prove invariance of the Gibbs measure. The core of the proof is an almost sure local theory based on the method of random averaging operators (arXiv:1910.08492v2). The main new ingredients are fractional lattice counting estimates and localized random tensor bounds, which exploit the geometric structure of the fractional phase in place of the classical number-theoretic tools available for quadratic dispersion.

math.AP↗

arXiv2026

Unconditional Well-posedness for the MMT Equation on the Torus

We consider the initial value problem (IVP) for a two-parameter family of derivative nonlinear Schr\"odinger equations on the torus, known as the Majda-McLaughlin-Tabak (MMT) model arising in weak wave turbulence theory. For positive derivative order, we show that the flow map is not $C^3$ at the origin. Using an enhanced energy method, we prove unconditional local well-posedness in Sobolev spaces. At the energy regularity, conservation of the Hamiltonian and a mass-type quantity yields unconditional global well-posedness.

math.AP↗

arXiv2026

Norm inflation for the cubic hyperbolic NLS on $\mathbb T^2$

We prove norm inflation for the cubic hyperbolic nonlinear Schr\"odinger equation in $H^s(\mathbb T^2)$ for every $s\in(-\infty,0)\cup(0,\frac12]$. The scaling-critical point $s=0$ is excluded by conservation of the $L^2$ norm. The strong ill-posedness below and above the scaling-critical point arises from two completely different mechanisms. Particularly in the scaling-subcritical regime, this dynamical instability stems from the hyperbolic nature. Together with the local well-posedness result in \cite{WangHNLS}, this gives a sharp dichotomy away from the mass space $L^2(\mathbb T^2)$: local well-posedness holds for $s>\frac12$, whereas norm inflation occurs for all $s\le \frac12$ with $s\ne0$.

math.AP↗

arXiv2026

FlexNPU: Transparent NPU Virtualization for Dynamic LLM Prefill-Decode Co-location

Modern AI serving increasingly relies on NPUs for conventional inference and large language model serving. However, current NPU deployments commonly expose physical devices directly to applications, which limits runtime control over scheduling and makes it difficult to adapt execution to phase-level workload behavior. This limitation is particularly evident in LLM serving, where the prefill phase is compute-intensive while the decode phase is often constrained by memory bandwidth and KV-cache accesses. Static prefill-decode (PD) disaggregation reduces phase interference, but can introduce resource imbalance and unnecessary data movement. We present FlexNPU, a transparent user-space virtualization layer for Ascend NPUs. FlexNPU interposes on AscendCL APIs and routes NPU operations through per-device daemons, decoupling unmodified from physical NPU devices without modifying model code, AI frameworks, or NPU drivers. This runtime boundary allows FlexNPU to virtualize NPU objects, control operator dispatch, and support phase-aware scheduling for LLM serving. In particular, FlexNPU enables dynamic PD co-location, which adapts scheduling between prefill and decode according to their complementary resource characteristics. We implement FlexNPU on Huawei Ascend NPUs and evaluate it with typical LLM workloads. Compared with direct NPU passthrough, FlexNPU introduces no measurable inference overhead and slightly improves throughput in some scenarios. On a 384-card Ascend 910C deployment of DeepSeek-R1, FlexNPU improves throughput over static PD disaggregation by 5.15% and 26.33%. On Qwen2.5-7B, compared with static PD co-location, FlexNPU maintains comparable throughput while reducing TTFT by over 92% across tested workloads with nearly unchanged TPOT. These results show that transparent NPU virtualization is a practical substrate for efficient and responsive LLM serving.

cs.DC↗

arXiv2026

Unraveling Surface Chemistry of irreversible reduction of iron oxides through the Time-Resolved APXPS and Chemometrics

This work presents a study on the application of Time-Resolved Ambient Pressure X-ray Photoelectron Spectroscopy (TR-APXPS) in association with chemometric techniques, specifically Principal Component Analysis (PCA) and Multivariate Curve Resolution with Alternating Least Squares (MCR-ALS), to investigate the surface chemistry and dynamics of Fe2O3 reduction processes. The use of TR-APXPS allows for real-time monitoring of chemical changes at the surface of Iron oxides during reduction, providing valuable insights into the reaction mechanisms and kinetics involved. One key challenge in analyzing TR-APXPS data is the presence of overlapping peaks and complex spectral features, which can make accurate quantification and interpretation difficult. Traditional spectral fitting methods may struggle with these complexities and result in ambiguous or inaccurate results. However, the chemometric approaches are promising tools to overcome these challenges by extracting pure spectral profiles of individual chemical species and their temporal profiles from the complex and overlapping data. The results obtained from the TR-APXPS coupled with PCA and MCR-ALS analysis provide a detailed and precise understanding of the surface chemical changes during the Fe2O3 reduction. This includes identifying and following the formation of various intermediate species and their evolution over time, which permits later to establish correlations between surface chemistry and process conditions. The integration of both chemometric tools in TR-APXPS data analysis not only addresses the challenges associated with complex spectral features, but also contributes to a deeper understanding of the underlying chemical changes and their dynamics. The obtained results have significant implications for process optimization, material synthesis, and tailoring of material properties for specific applications.

physics.chem-ph↗

arXiv2026

On the well-posedness of the initial value problem for the MMT model

This work investigates the initial value problem (IVP) for the two-parameter family of dispersive wave equations known as the Majda-McLaughlin-Tabak (MMT) model, which arises in the weak turbulence theory of random waves. The MMT model can be viewed as a derivative nonlinear Schr\"odinger (dNLS) equation where both the nonlinearity and dispersion involve nonlocal fractional derivatives. The purpose of this study is twofold: first, to establish a sharp well-posedness theory for the MMT model; and second, to identify the critical threshold for the derivative in the nonlinearity relative to the dispersive order required to ensure well-posedness. As a by-product, we establish sharp well-posedness for non-local fractional dNLS equations; notably, our results resolve the regularity endpoint left open in https://www.aimsciences.org/article/doi/10.3934/dcdsb.2022039 .

math.AP↗

arXiv2025

Large deviations principle for the cubic NLS equation with slowly decaying data

In this note, we prove a sharp large derivation principle (LDP) for the cubic nonlinear Schrödinger equation with Gaussian random initial data in Fourier Lebesgue spaces. As a consequence, we improve the exponential decay condition in [M.A. Garrido, R. Grande, K.M. Kurianski, G. Staffilani. Commun. Pure Appl. Math. 76 (2023), 4087--4136] to $\ell^1$ decay.

math.AP↗

arXiv2025

FlipVQA: Scaling Multi-modal Instruction Tuning via Textbook-to-Knowledge Synthesis

Textbooks are among the richest repositories of human-verified reasoning knowledge, yet their complex layouts contain multi-column typesetting, cross-page question answer separation, and interleaved figures, make automated extraction of structured QA and VQA pairs extremely challenging. Existing alternatives either synthesize data from scratch, which lacks authentic problem contexts, or rely on costly expert annotation that cannot scale. We propose $\textbf{FlipVQA-Miner}$, an automated pipeline that resolves long-range logical dependencies and cross-page discontinuities in OCR-parsed documents, recovering coherent question--answer--figure associations even when answers reside in separate companion volumes. A subsequent multi-stage curation pipeline transforms these raw extractions into AI-ready supervision signals. Using FlipVQA-Miner, we construct $\textbf{FlipVQA-83K}$, comprising 83K QA and VQA pairs spanning 11 academic disciplines, at a $\textbf{50$\times$}$ cost saving compared to manual annotation while maintaining high structural fidelity ($F_1 > 0.96$). Models fine-tuned on FlipVQA-83K demonstrate significantly improved reasoning ability and cross-domain generalization, establishing a scalable paradigm for human-knowledge-grounded data curation. Our dataset and the complete data generating and curating methods can be found in https://github.com/OpenDCAI/DataFlow-VQA .

cs.AI↗

arXiv2025

Hyperbolic $P(Φ)_2$-model on the plane

We study the hyperbolic $Φ^{k+1}_2$-model on the plane. By establishing coming down from infinity for the associated stochastic nonlinear heat equation (SNLH) on the plane, we first construct a $Φ^{k+1}_2$-measure on the plane as a limit of the $Φ^{k+1}_2$-measures on large tori. We then study the canonical stochastic quantization of the $Φ^{k+1}_2$-measure on the plane thus constructed, namely, we study the defocusing stochastic damped nonlinear wave equation forced by an additive space-time white noise (= the hyperbolic $Φ^{k+1}_2$-model) on the plane. In particular, by taking a limit of the invariant Gibbs dynamics on large tori constructed by the first two authors with Gubinelli and Koch (2021), we construct invariant Gibbs dynamics for the hyperbolic $Φ^{k+1}_2$-model on the plane. Our main strategy is to develop further the ideas from a recent work on the hyperbolic $Φ^3_3$-model on the three-dimensional torus by the first two authors and Okamoto (2021), and to study convergence of the so-called enhanced Gibbs measures, for which coming down from infinity for the associated SNLH with positive regularity plays a crucial role. By combining wave and heat analysis together with ideas from optimal transport theory, we then conclude global well-posedness of the hyperbolic $Φ^{k+1}_2$-model on the plane and invariance of the associated Gibbs measure. As a byproduct of our argument, we also obtain invariance of the limiting $Φ^{k+1}_2$-measure on the plane under the dynamics of the parabolic $Φ^{k+1}_2$-model.

math.AP↗

arXiv2025

Well-posedness for the periodic Hyperbolic nonlinear Schrödinger equations

We establish local well-posedness for the hyperbolic nonlinear Schrodinger equation (HNLS) in the critical spaces. Following the approach of Killip and Visan, we derive scale-invariant Strichartz estimates for HNLS on both rational and irrational tori, thereby removing the epsilon-loss of derivative present in the hyperbolic Strichartz estimates of Bourgain and Demeter.

math.AP↗

arXiv2025

Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc

We consider the two-dimensional defocusing nonlinear Schrödinger equation (NLS) on the unit disc in the plane with the Gibbs initial data under radial symmetry. By using a type of random averaging operator ansatz, we build a strong local-in-time solution theory, and thus prove almost sure global well-posedness and invariance of the Gibbs measure via Bourgain's invariant measure argument. This work completes the program initiated by Tzvetkov (2006, 2008) on the construction of invariant Gibbs dynamics (of strong solutions) for NLS on the disc.

math.AP↗

arXiv2025

Optimal divergence rate of the focusing Gibbs measures

We study Gibbs measures on the $d$-dimensional torus with $L^2$-(super)critical focusing interaction potentials. We establish a precise divergence rate of the partition function as we remove regularization, where the optimal constant is given by (i) (the negative of) the minimum value of the Hamiltonian given an $L^2$-constraint in the $L^2$-critical case and (ii) the optimal constant for certain Bernstein's inequality in the mass-supercritical case. In particular, our result in the $L^2$-critical case precisely quantifies the phase transition of the focusing Gibbs measure at the critical $L^2$ threshold, previously studied by Lebowitz, Rose, and Speer (1988) and Sosoe, Tolomeo, and the fourth author (2022).

math.PR↗

arXiv2025

Sharp unconditional well-posedness of the 2-$d$ periodic cubic hyperbolic nonlinear Schrödinger equation

We study semilinear local well-posedness of the two-dimensional periodic cubic hyperbolic nonlinear Schrödinger equation (HNLS) in Fourier-Lebesgue spaces. By employing the Fourier restriction norm method, we first establish sharp semilinear local well-posedness of HNLS in Fourier-Lebesgue spaces (modulo the endpoint case), including almost scaling-critical Fourier-Lebesgue spaces. Then, by adapting the normal form approach, developed by the second author with Guo and Kwon (2013) and by the second and third authors (2021), to the current hyperbolic setting, we establish sharp unconditional uniqueness of HNLS within the semilinear local well-posedness regime. As a key ingredient to both results, we establish sharp counting estimates for the hyperbolic Schrödinger equation. As a byproduct of our analysis, we also obtain sharp unconditional uniqueness of the (usual) two-dimensional periodic cubic nonlinear Schrödinger equation in Fourier--Lebesgue spaces for $p \ge 3$.

math.AP↗

arXiv2025

On restricted-type Strichartz estimates and the applications

We establish a rigorous framework for the Zakharov system on waveguide manifolds $\mathbb{R}^m \times \mathbb{T}^n$ ($m,n\geq 1$), which models the nonlinear coupling between optical and acoustic modes in confined geometries such as optical fibers. Our analysis reveals that the sharp \textit{shell-type Strichartz estimate} for $\mathbb{R}^2 \times \mathbb{T}$ is globally valid in time and exhibits no derivative loss via the measure estimate of semi-algebraic sets, unlike the periodic case studied in \cite{MR4665720}. In addition, we demonstrate that such an estimate fails on the product space $\mathbb{R} \times \mathbb{T}^2$ by constructing a counter-example. Moreover, we derive analogues of these shell-type estimates in other dimensions, both in the waveguide and Euclidean settings. As a direct application, we establish, for the first time, a local well-posedness theory for the partially periodic Zakharov system. To summarize, we compare shell-type Strichartz estimates in different settings (the Euclidean, the periodic, and the waveguide). Numerical verification on $\mathbb{R}^2\times\mathbb{T}$ reveals a uniform $L^4$-spacetime bound, while $\mathbb{R}\times\mathbb{T}^2$ exhibits sublinear growth, quantitatively confirming the theoretical dichotomy between geometries with different dimensional confinement. These findings advance the understanding of dispersive effects in hybrid geometries and provide mathematical foundations for efficient waveguide design and signal transmission. Finally, for the Euclidean case, we establish well-posedness theory for supercritical nonlinear Schrödinger equation (NLS) with \textit{strip-type} frequency-restricted initial data, revealing a trade-off between dispersion and confinement, which is of independent mathematical interest. This provides a deterministic analogue to random data theory of NLS.

math.AP↗

arXiv2025

Revisiting Bourgain's probabilistic construction of solutions to the 2-$d$ cubic NLS

In a seminal paper (1996), Bourgain proved invariance of the Gibbs measure for the defocusing cubic nonlinear Schrödinger equation on the two-dimensional torus by constructing local-in-time solutions in a probabilistic manner. In this note, we revisit and streamline his argument, using the random tensor estimate developed by Deng, Nahmod, and Yue (2022).

math.AP↗

arXiv2025

Hyperbolic nonlinear Schr\"odinger equations on $\mathbb{R}\times \mathbb{T}$

In this paper, we consider the hyperbolic nonlinear Schr\"odinger equations (HNLS) on $\mathbb{R}\times\mathbb{T}$. We obtain the sharp local well-posedness up to the critical regularity for cubic nonlinearity and in critical spaces for higher odd nonlinearities. Moreover, when the initial data is small, we prove the global existence and scattering for the solutions to HNLS with higher nonlinearities (except the cubic one) in critical Sobolev spaces. The main ingredient of the proof is the sharp up to the endpoint local/global-in-time Strichartz estimates.

math.AP↗

arXiv2025

MusFlow: Multimodal Music Generation via Conditional Flow Matching

Music generation aims to create music segments that align with human aesthetics based on diverse conditional information. Despite advancements in generating music from specific textual descriptions (e.g., style, genre, instruments), the practical application is still hindered by ordinary users' limited expertise or time to write accurate prompts. To bridge this application gap, this paper introduces MusFlow, a novel multimodal music generation model using Conditional Flow Matching. We employ multiple Multi-Layer Perceptrons (MLPs) to align multimodal conditional information into the audio's CLAP embedding space. Conditional flow matching is trained to reconstruct the compressed Mel-spectrogram in the pretrained VAE latent space guided by aligned feature embedding. MusFlow can generate music from images, story texts, and music captions. To collect data for model training, inspired by multi-agent collaboration, we construct an intelligent data annotation workflow centered around a fine-tuned Qwen2-VL model. Using this workflow, we build a new multimodal music dataset, MMusSet, with each sample containing a quadruple of image, story text, music caption, and music piece. We conduct four sets of experiments: image-to-music, story-to-music, caption-to-music, and multimodal music generation. Experimental results demonstrate that MusFlow can generate high-quality music pieces whether the input conditions are unimodal or multimodal. We hope this work can advance the application of music generation in multimedia field, making music creation more accessible. Our generated samples, code and dataset are available at musflow.github.io.

cs.SD↗