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Jia Shen

Publications and source records attributed to Jia Shen.

At least 19 recordsLinked to original sources
arXiv2026

Modified wave operators for nonlinear Schr\"odinger equations in the full subcritical long range regime

We construct modified wave operators for the nonlinear Schr\"odinger equation $i\partial_tu+\frac12\Delta u=|u|^pu$ in the full subcritical long-range case $0<p<2/d$, with small, nonvanishing, analytic final data $W(x)$ with bounded logarithmic gradients. Previous results established large-time asymptotics for selected classes of Cauchy data. Moreover, the exact asymptotic expansion for $p<1/d$ remained unknown. When $1/d<p<2/d$, our result gives the approximation $$\frac{1}{(it)^{\frac{d}{2}}} e^{\frac{i|x|^2}{2t}} W\left(\frac{x}{t}\right) \exp\left[ -i\frac{t^{1-\frac{dp}{2}}-1}{1-\frac{dp}{2}} \left|W\left(\frac{x}{t}\right)\right|^p \right]$$ The wave operator is constructed by an iteration in the analytic spaces with decreasing radius. When $p\le 1/d$, we construct the profile from a finite truncation of a Fuchsian equation coupled with a transport equation. This profile still leaves a long-range triangular coupling whose terminal integral does not preserve the required fast decay class. The construction yields quantitative $L^q$ asymptotics for $2\le q\le\infty$ and uniqueness in the prescribed analytic asymptotic classes. The central new ingredients are a nonlinear final-state normal form that removes this long-range coupling and a mixed iteration in particular analytic spaces.

math.AP↗
arXiv2026

The subsonic limit of the 3D Zakharov system

We obtain the optimal convergence rates in the subsonic limit of the three-dimensional Zakharov system for initial data belonging to the low-regularity Sobolev space $\HH^s=H^s\times H^{s-1}\times H^{s-1}$. For the Schr\"odinger component, we prove first-order convergence in $L^2$ for initial data in $\HH^3$, and second-order convergence under the compatibility condition for data in $\HH^4$. For the wave component, we obtain first-order convergence in $L^2$ for data in $\HH^3$ and second-order convergence for data in $\HH^4$. The obtained rates are optimal and coincide with those predicted by the formal asymptotic expansion. No localization assumptions, smallness or high-order regularity hypotheses are required. This improves all previous results on the subsonic limit of the Zakharov system and resolves the optimality issue at the Sobolev regularity level. The proof relies on a uniform local well-posedness theory that remains valid in the subsonic limit. A key ingredient is a refined normal form analysis combined with bilinear Strichartz estimates in atomic function spaces, which allows us to fully exploit the dispersive structure of the Zakharov system at low regularity and to overcome the derivative losses arising from the singular coupling.

math.AP↗
arXiv2026

AI-Native 6G Physical Layer with Cross-Module Optimization and Cooperative Control Agents

In this article, a framework of AI-native cross-module optimized physical layer with cooperative control agents is proposed, which involves optimization across global AI/ML modules of the physical layer with innovative design of multiple enhancement mechanisms and control strategies. Specifically, it achieves simultaneous optimization across global modules of uplink AI/ML-based joint source-channel coding with modulation, and downlink AI/ML-based modulation with precoding and corresponding data detection, reducing traditional inter-module information barriers to facilitate end-to-end optimization toward global objectives. Moreover, multiple enhancement mechanisms are also proposed, including i) an AI/ML-based cross-layer modulation approach with theoretical analysis for downlink transmission that breaks the isolation of inter-layer features to expand the solution space for determining improved constellation, ii) a utility-oriented precoder construction method that shifts the role of the AI/ML-based CSI feedback decoder from recovering the original CSI to directly generating precoding matrices aiming to improve end-to-end performance, and iii) incorporating modulation into AI/ML-based CSI feedback to bypass bit-level bottlenecks that introduce quantization errors, non-differentiable gradients, and limitations in constellation solution spaces. Furthermore, AI/ML based control agents for optimized transmission schemes are proposed that leverage AI/ML to perform model switching according to channel state, thereby enabling integrated control for global throughput optimization. Finally, simulation results demonstrate the superiority of the proposed solutions in terms of BLER and throughput. These extensive simulations employ more practical assumptions that are aligned with the requirements of the 3GPP, which hopefully provides valuable insights for future standardization discussions.

eess.SP↗
arXiv2025

Seamless Interaction: Dyadic Audiovisual Motion Modeling and Large-Scale Dataset

Human communication involves a complex interplay of verbal and nonverbal signals, essential for conveying meaning and achieving interpersonal goals. To develop socially intelligent AI technologies, it is crucial to develop models that can both comprehend and generate dyadic behavioral dynamics. To this end, we introduce the Seamless Interaction Dataset, a large-scale collection of over 4,000 hours of face-to-face interaction footage from over 4,000 participants in diverse contexts. This dataset enables the development of AI technologies that understand dyadic embodied dynamics, unlocking breakthroughs in virtual agents, telepresence experiences, and multimodal content analysis tools. We also develop a suite of models that utilize the dataset to generate dyadic motion gestures and facial expressions aligned with human speech. These models can take as input both the speech and visual behavior of their interlocutors. We present a variant with speech from an LLM model and integrations with 2D and 3D rendering methods, bringing us closer to interactive virtual agents. Additionally, we describe controllable variants of our motion models that can adapt emotional responses and expressivity levels, as well as generating more semantically-relevant gestures. Finally, we discuss methods for assessing the quality of these dyadic motion models, which are demonstrating the potential for more intuitive and responsive human-AI interactions.

cs.CV↗
arXiv2024

High-order asymptotic expansion for the nonlinear Klein-Gordon equation in the non-relativistic limit regime

This paper presents an investigation into the high-order asymptotic expansion for 2D and 3D cubic nonlinear Klein-Gordon equations in the non-relativistic limit regime. There are extensive numerical and analytic results concerning that the solution of NLKG can be approximated by first-order modulated Schrödinger profiles in terms of $e^{i\frac t {\varepsilon^2}}v + c.c. $, where $v$ is the solution of related NLS and ``$c.c.$" denotes the complex conjugate. Particularly, the best analytic result up to now is given in \cite{lei}, which proves that the $L_x^2$ norm of the error can be controlled by $\varepsilon^2 +(\varepsilon^2t)^{\frac α4}$ for $H^α_x$-data, $α\in [1, 4]$. As for the high-order expansion, to our best knowledge, there are only numerical results, while the theoretical one is lacking. In this paper, we extend this study further and give the first high-order analytic result. We introduce the high-order expansion inspired by the numerical experiments in \cite{schratz2020, faou2014a}: \[ e^{i\frac t {\varepsilon^2}}v +\varepsilon^2 \Big( \frac 18 e^{3i\frac t {\varepsilon^2} }v^3 +e^{i\frac t {\varepsilon^2}} w \Big) +c.c., \] where $w$ is the solution to some specific Schrödinger-type equation. We show that the $L_x^2$ estimate of the error is of higher order $\varepsilon^4+\left(\varepsilon^2t\right)^\fracα{4}$ for $H^α_x$-data, $α\in [4, 8]$.

math.AP↗
arXiv2024

Global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation

In this paper, we study the global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation. Recently, Dodson [arXiv:2004.09618] studied the global well-posedness in a critical Sobolev space $\dot{W}^{11/7,7/6}$. In this paper, we aim to show that if the initial data belongs to $\dot H^\frac12$ to guarantee the local existence, then some extra weak space which is subcritical, is sufficient to prove the global well-posedness. More precisely, we prove that if the initial data belongs to $\dot{H}^{1/2}\cap \dot{W}^{s,1}$ for $12/13<s \leqslant 1$, then the corresponding solution exists globally and scatters.

math.AP↗
arXiv2024

Global well-posedness for the defocusing 3D quadratic NLS in the sharp critical space

In this paper, we prove the global well-posedness of defocusing 3D quadratic nonlinear Schrödinger equation \begin{align*} i\partial_t u + \frac12Δu = |u| u, \end{align*} in its sharp critical weighted space $\mathcal F \dot H_x^{1/2}$ for radial data. Killip, Masaki, Murphy, and Visan [2017, NoDEA] have proved its global well-posedness and scattering, if the $\mathcal F \dot H_x^{1/2}$-norm of the solution is bounded in the maximal lifespan. Now, we remove this a priori assumption for the global well-posedness statement in the radial case. Our method is based on the almost conservation of pseudo conformal energy. This energy scales like $\dot H_x^{-1}$, which is supercritical. We are still able to derive the global well-posedness using this monotone quantity. The main observation is that we can establish the local solution in supercritical weighted space when the initial time is away from the origin.

math.AP↗
arXiv2024

Interference Cancellation Based Neural Receiver for Superimposed Pilot in Multi-Layer Transmission

In this paper, an interference cancellation based neural receiver for superimposed pilot (SIP) in multi-layer transmission is proposed, where the data and pilot are non-orthogonally superimposed in the same time-frequency resource. Specifically, to deal with the intra-layer and inter-layer interference of SIP under multi-layer transmission, the interference cancellation with superimposed symbol aided channel estimation is leveraged in the neural receiver, accompanied by the pre-design of pilot code-division orthogonal mechanism at transmitter. In addition, to address the complexity issue for inter-vendor collaboration and the generalization problem in practical deployments, respectively, this paper also provides a fixed SIP (F-SIP) design based on constant pilot power ratio and scalable mechanisms for different modulation and coding schemes (MCSs) and transmission layers. Simulation results demonstrate the superiority of the proposed schemes on the performance of block error rate and throughput compared with existing counterparts.

eess.SP↗
arXiv2023

Wave operator for the generalized derivative nonlinear Schrödinger equation

In this work, we prove the existence of wave operator for the following generalized derivative nonlinear Schrödinger equation \begin{align*} i\partial_t u+\partial_x^2 u +i |u|^{2σ}\partial_x u=0, \end{align*} with $(t,x)\in\mathbb{R}\times\mathbb{R}$, $σ\in \mathbb{N}$, and $σ\geq 3$. The study of wave operators is an important part of the scattering theory, and it is useful in the construction of the nonlinear profile and the large data scattering. The previous argument for small data scattering in \cite{BaiWuXue-JDE}, which is based on the local smoothing effect and maximal function estimates, breaks down when considering the final data problem. The main reason is that the resolution space does not provide smallness near the infinite time. We overcome this difficulty by invoking the gauge transformation and the normal form method.

math.AP↗
arXiv2023

Knowledge-driven Meta-learning for CSI Feedback

Accurate and effective channel state information (CSI) feedback is a key technology for massive multiple-input and multiple-output systems. Recently, deep learning (DL) has been introduced for CSI feedback enhancement through massive collected training data and lengthy training time, which is quite costly and impractical for realistic deployment. In this article, a knowledge-driven meta-learning approach is proposed, where the DL model initialized by the meta model obtained from meta training phase is able to achieve rapid convergence when facing a new scenario during target retraining phase. Specifically, instead of training with massive data collected from various scenarios, the meta task environment is constructed based on the intrinsic knowledge of spatial-frequency characteristics of CSI for meta training. Moreover, the target task dataset is also augmented by exploiting the knowledge of statistical characteristics of wireless channel, so that the DL model can achieve higher performance with small actually collected dataset and short training time. In addition, we provide analyses of rationale for the improvement yielded by the knowledge in both phases. Simulation results demonstrate the superiority of the proposed approach from the perspective of feedback performance and convergence speed.

eess.SP↗
arXiv2023

Scattering for defocusing mass sub-critical NLS

In this paper, we consider the $L_x^2$-scattering of defocusing mass sub-critical nonlinear Schrödinger equations with low weighted initial condition. It is known that the scattering holds with $\mathcal{F} H^1$-data, while the continuity of inverse wave operator breaks down with $L^2$-data. Moreover, for large $\mathcal{F} H^s$-data with $s<1$, there only exists the wave operator result, but scattering results are lacking. Our subject is to study the scattering in low weights space. Our results are divided into two parts. Our first result presents a systematic study on the scattering on $\mathcal{F} H^s$ for certain $s<1$, without any restrictions on smallness or radial symmetry. This extends the previous results to spaces with lower weights. Our second result is the almost sure scattering on $L^2$ by introducing a ``narrowed'' Wiener randomization in physical space. For mass subcritical NLS when $d\ge 2$, this result represents the first scattering result without imposing any conditions related to smallness, radial symmetry, or weighted properties on the initial data.

math.AP↗
arXiv2023

Toward Extending Concentric Tube Robot Kinematics for Large Clearance and Impulse Curvature

Concentric Tube Robots (CTRs) have been proposed to operate within the unstructured environment for minimally invasive surgeries. In this letter, we consider the operation scenario where the tubes travel inside the channels with a large clearance or large curvature, such as aortas or industrial pipes. Accurate kinematic modeling of CTRs is required for the development of advanced control and sensing algorithms. To this end, we extended the conventional CTR kinematics model to a more general case with large tube-to-tube clearance and large centerline curvature. Numerical simulations and experimental validations are conducted to compare our model with respect to the conventional CTR kinematic model. In the physical experiments, our proposed model achieved a tip position error of 1.53 mm in the 2D planer case and 4.36 mm in 3D case, outperforming the state-of-the-art model by 71% and 66%, respectively.

cs.RO↗
arXiv2023

Concentric Tube Robot Redundancy Resolution via Velocity/Compliance Manipulability Optimization

Concentric Tube Robots (CTR) have the potential to enable effective minimally invasive surgeries. While extensive modeling and control schemes have been proposed in the past decade, limited efforts have been made to improve the trajectory tracking performance from the perspective of manipulability , which can be critical to generate safe motion and feasible actuator commands. In this paper, we propose a gradient-based redundancy resolution framework that optimizes velocity/compliance manipulability-based performance indices during trajectory tracking for a kinematically redundant CTR. We efficiently calculate the gradients of manipulabilities by propagating the first- and second-order derivatives of state variables of the Cosserat rod model along the CTR arc length, reducing the gradient computation time by 68\% compared to finite difference method. Task-specific performance indices are optimized by projecting the gradient into the null-space of trajectory tracking. The proposed method is validated in three exemplary scenarios that involve trajectory tracking, obstacle avoidance, and external load compensation, respectively. Simulation results show that the proposed method is able to accomplish the required tasks while commonly used redundancy resolution approaches underperform or even fail.

cs.RO↗
arXiv2023

A Knowledge-Driven Meta-Learning Method for CSI Feedback

Accurate and effective channel state information (CSI) feedback is a key technology for massive multiple-input and multiple-output (MIMO) systems. Recently, deep learning (DL) has been introduced to enhance CSI feedback in massive MIMO application, where the massive collected training data and lengthy training time are costly and impractical for realistic deployment. In this paper, a knowledge-driven meta-learning solution for CSI feedback is proposed, where the DL model initialized by the meta model obtained from meta training phase is able to achieve rapid convergence when facing a new scenario during the target retraining phase. Specifically, instead of training with massive data collected from various scenarios, the meta task environment is constructed based on the intrinsic knowledge of spatial-frequency characteristics of CSI for meta training. Moreover, the target task dataset is also augmented by exploiting the knowledge of statistical characteristics of channel, so that the DL model initialized by meta training can rapidly fit into a new target scenario with higher performance using only a few actually collected data in the target retraining phase. The method greatly reduces the demand for the number of actual collected data, as well as the cost of training time for realistic deployment. Simulation results demonstrate the superiority of the proposed approach from the perspective of feedback performance and convergence speed.

eess.SP↗
arXiv2022

Almost sure well-posedness and scattering of the 3D cubic nonlinear Schrödinger equation

We study the random data problem for 3D, defocusing, cubic nonlinear Schrödinger equation in $H_x^s(\mathbb{R}^3)$ with $s<\frac 12$. First, we prove that the almost sure local well-posedness holds when $\frac{1}{6}\leqslant s<\frac 12$ in the sense that the Duhamel term belongs to $H_x^{1/2}(\mathbb{R}^3)$. Furthermore, we prove that the global well-posedness and scattering hold for randomized, radial, large data $f\in H_x^{s}(\mathbb{R}^3)$ when $\frac{17}{40}< s<\frac 12$. The key ingredient is to control the energy increment including the terms where the first order derivative acts on the linear flow, and our argument can lower down the order of derivative more than $\frac12$. To our best knowledge, this is the first almost sure large data global result for this model.

math.AP↗
arXiv2022

AI Enlightens Wireless Communication: A Transformer Backbone for CSI Feedback

This paper is based on the background of the 2nd Wireless Communication Artificial Intelligence (AI) Competition (WAIC) which is hosted by IMT-2020(5G) Promotion Group 5G+AIWork Group, where the framework of the eigenvector-based channel state information (CSI) feedback problem is firstly provided. Then a basic Transformer backbone for CSI feedback referred to EVCsiNet-T is proposed. Moreover, a series of potential enhancements for deep learning based (DL-based) CSI feedback including i) data augmentation, ii) loss function design, iii) training strategy, and iv) model ensemble are introduced. The experimental results involving the comparison between EVCsiNet-T and traditional codebook methods over different channels are further provided, which show the advanced performance and a promising prospect of Transformer on DL-based CSI feedback problem.

eess.SP↗
arXiv2021

Large global solutions for energy-critical nonlinear Schrödinger equation

In this work, we consider the 3D defocusing energy-critical nonlinear Schrödinger equation $i\partial_t u+Δu =|u|^4 u,\quad (t,x)\in \mathbb{R}\times \mathbb{R}^3$. Applying the outgoing and incoming decomposition presented in the recent work \cite{BECEANU-DENG-SOFFER-WU-2021}, we prove that any radial function $f$ with $χ_{\leq1}f\in H^1$ and $χ_{\geq1}f\in H^{s_0}$ with $\frac{5}{6}<s_0<1$, there exists an outgoing component $f_+$ (or incoming component $f_-$) of $f$, such that when the initial data is $f_+$, then the corresponding solution is globally well-posed and scatters forward in time; when the initial data is $f_-$, then the corresponding solution is globally well-posed and scatters backward in time.

math.AP↗