arXiv subjects

Yufei Zhang

Publications and source records attributed to Yufei Zhang.

At least 91 records · Page 5Linked to original sources

arXiv2025

Continuous-time mean field games: a primal-dual characterization

This paper establishes a primal-dual formulation for continuous-time mean field games (MFGs) and provides a complete analytical characterization of the set of all Nash equilibria (NEs). We first show that for any given mean field flow, the representative player's control problem with {\it measurable coefficients} is equivalent to a linear program over the space of occupation measures. We then establish the dual formulation of this linear program as a maximization problem over smooth subsolutions of the associated Hamilton-Jacobi-Bellman (HJB) equation, which plays a fundamental role in characterizing NEs of MFGs. Finally, a complete characterization of \emph{all NEs for MFGs} is established by the strong duality between the linear program and its dual problem. This strong duality is obtained by studying the solvability of the dual problem, and in particular through analyzing the regularity of the associated HJB equation. Compared with existing approaches for MFGs, the primal-dual formulation and its NE characterization do not require the convexity of the associated Hamiltonian or the uniqueness of its optimizer, and remain applicable when the HJB equation lacks classical or even continuous solutions.

math.OC↗

arXiv2025

OccuEMBED: Occupancy Extraction Merged with Building Energy Disaggregation for Occupant-Responsive Operation at Scale

Buildings account for a significant share of global energy consumption and emissions, making it critical to operate them efficiently. As electricity grids become more volatile with renewable penetration, buildings must provide flexibility to support grid stability. Building automation plays a key role in enhancing efficiency and flexibility via centralized operations, but it must prioritize occupant-centric strategies to balance energy and comfort targets. However, incorporating occupant information into large-scale, centralized building operations remains challenging due to data limitations. We investigate the potential of using whole-building smart meter data to infer both occupancy and system operations. Integrating these insights into data-driven building energy analysis allows more occupant-centric energy-saving and flexibility at scale. Specifically, we propose OccuEMBED, a unified framework for occupancy inference and system-level load analysis. It combines two key components: a probabilistic occupancy profile generator, and a controllable and interpretable load disaggregator supported by Kolmogorov-Arnold Networks (KAN). This design embeds knowledge of occupancy patterns and load-occupancy-weather relationships into deep learning models. We conducted comprehensive evaluations to demonstrate its effectiveness across synthetic and real-world datasets compared to various occupancy inference baselines. OccuEMBED always achieved average F1 scores above 0.8 in discrete occupancy inference and RMSE within 0.1-0.2 for continuous occupancy ratios. We further demonstrate how OccuEMBED integrates with building load monitoring platforms to display occupancy profiles, analyze system-level operations, and inform occupant-responsive strategies. Our model lays a robust foundation in scaling occupant-centric building management systems to meet the challenges of an evolving energy system.

eess.SP↗

arXiv2025

An $α$-potential game framework for $N$-player dynamic games

This paper proposes and studies a general form of dynamic $N$-player non-cooperative games called $α$-potential games, where the change of a player's value function upon her unilateral deviation from her strategy is equal to the change of an $α$-potential function up to an error $α$. Analogous to the static potential game (which corresponds to $α=0$), the $α$-potential game framework is shown to reduce the challenging task of finding $α$-Nash equilibria for a dynamic game to minimizing the $α$-potential function. Moreover, an analytical characterization of $α$-potential functions is established, with $α$ represented in terms of the magnitude of the asymmetry of value functions' second-order derivatives. For stochastic differential games in which the state dynamic is a controlled diffusion, $α$ is characterized in terms of the number of players, the choice of admissible strategies, and the intensity of interactions and the level of heterogeneity among players. Two classes of stochastic differential games, namely distributed games and games with mean field interactions, are analyzed to highlight the dependence of $α$ on general game characteristics that are beyond the mean-field paradigm, which focuses on the limit of $N$ with homogeneous players. To analyze the $α$-NE, the associated optimization problem is embedded into a conditional McKean-Vlasov control problem. A verification theorem is established to construct $α$-NE based on solutions to an infinite-dimensional Hamilton-Jacobi-Bellman equation, which is reduced to a system of ordinary differential equations for linear-quadratic games.

math.OC↗

arXiv2025

Entropy annealing for policy mirror descent in continuous time and space

Entropy regularization has been widely used in policy optimization algorithms to enhance exploration and the robustness of the optimal control; however it also introduces an additional regularization bias. This work quantifies the impact of entropy regularization on the convergence of policy gradient methods for stochastic exit time control problems. We analyze a continuous-time policy mirror descent dynamics, which updates the policy based on the gradient of an entropy-regularized value function and adjusts the strength of entropy regularization as the algorithm progresses. We prove that with a fixed entropy level, the mirror descent dynamics converges exponentially to the optimal solution of the regularized problem. We further show that when the entropy level decays at suitable polynomial rates, the annealed flow converges to the solution of the unregularized problem at a rate of $\mathcal O(1/S)$ for discrete action spaces and, under suitable conditions, at a rate of $\mathcal O(1/\sqrt{S})$ for general action spaces, with $S$ being the gradient flow running time. The technical challenge lies in analyzing the gradient flow in the infinite-dimensional space of Markov kernels for nonconvex objectives. This paper explains how entropy regularization improves policy optimization, even with the true gradient, from the perspective of convergence rate.

math.OC↗

arXiv2025

Numerical Simulation of Three-dimensional High-Lift Configurations Using Data-Driven Turbulence Model

Traditional Reynolds-averaged Navier-Stokes (RANS) equations often struggle to predict separated flows accurately. Recent studies have employed data-driven methods to enhance predictions by modifying baseline equations, such as field inversion and machine learning (FIML) with symbolic regression. However, data-driven turbulence models exhibit limited adaptability and are rarely applied to complex engineering problems. This study examines the application of data-driven turbulence models to complex three-dimensional high-lift configurations, extending their usability beyond previous applications. First, the generalizability of the SST-CND model, derived from conditioned field inversion and symbolic regression, is validated. Then, the spatially varying correction factor obtained through conditioned field inversion is transferred to the three-equation k-(v^2)-w model. The 30P30N three-element airfoil, the JAXA Standard Model (JSM), and the high-lift version of the NASA Common Research Model (CRM-HL) are numerically simulated. The results indicated that the SST-CND model significantly improves the prediction of stall characteristics, demonstrating satisfactory generalizability. The corrected k-(v^2 )-w-CND model accurately predicts the stall characteristics of CRM-HL, with a relative error of less than 5% compared to experimental results. This confirms the strong transferability of the model correction derived from conditioned field inversion across different turbulence models.

physics.flu-dyn↗

arXiv2025

Reduced Spatial Dependency for More General Video-level Deepfake Detection

As one of the prominent AI-generated content, Deepfake has raised significant safety concerns. Although it has been demonstrated that temporal consistency cues offer better generalization capability, existing methods based on CNNs inevitably introduce spatial bias, which hinders the extraction of intrinsic temporal features. To address this issue, we propose a novel method called Spatial Dependency Reduction (SDR), which integrates common temporal consistency features from multiple spatially-perturbed clusters, to reduce the dependency of the model on spatial information. Specifically, we design multiple Spatial Perturbation Branch (SPB) to construct spatially-perturbed feature clusters. Subsequently, we utilize the theory of mutual information and propose a Task-Relevant Feature Integration (TRFI) module to capture temporal features residing in similar latent space from these clusters. Finally, the integrated feature is fed into a temporal transformer to capture long-range dependencies. Extensive benchmarks and ablation studies demonstrate the effectiveness and rationale of our approach.

cs.CV↗

arXiv2025

Data-driven Turbulence Modeling for Separated Flows Considering Non-Local Effect

This study aims to enhance the generalizability of Reynolds-averaged Navier-Stokes (RANS) turbulence models, which are crucial for engineering applications. Classic RANS turbulence models often struggle to predict separated flows accurately. Recently, Data-driven machine learning approaches for turbulence modeling have been explored to address this issue. However, these models are often criticized for their limited generalizability. In this study, we address this issue by incorporating non-local effects into data-driven turbulence modeling. Specifically, we introduce a transport equation for the correction term \b{eta} of the shear stress transport (SST) model to encode non-local information along the mean streamline. The coefficients of the equation are calibrated using high-fidelity data from the NASA hump and periodic hills. The resulting model, termed the \b{eta}-Transport model, demonstrates high accuracy across various separated flows outside the training set, including periodic hills with different geometries and Reynolds numbers, the curved backward-facing step, a two-dimensional bump, and a three-dimensional simplified car body. In all tested cases, the \b{eta}-Transport model yields smaller or equal prediction errors compared to those from classic local data-driven turbulence models using algebraic relations for \b{eta}. These results indicate improved generalizability for separated flows. Furthermore, the \b{eta}-Transport model shows similar accuracy to the baseline model in basic flows including the mixing layer and the channel flow. Therefore, the non-local modeling approach presented here offers a promising pathway for developing more generalizable data-driven turbulence models.

physics.flu-dyn↗

arXiv2025

Statistical Learning with Sublinear Regret of Propagator Models

We consider a class of learning problems in which an agent liquidates a risky asset while creating both transient price impact driven by an unknown convolution propagator and linear temporary price impact with an unknown parameter. We characterize the trader's performance as maximization of a revenue-risk functional, where the trader also exploits available information on a price predicting signal. We present a trading algorithm that alternates between exploration and exploitation phases and achieves sublinear regrets with high probability. For the exploration phase we propose a novel approach for non-parametric estimation of the price impact kernel by observing only the visible price process and derive sharp bounds on the convergence rate, which are characterised by the singularity of the propagator. These kernel estimation methods extend existing methods from the area of Tikhonov regularisation for inverse problems and are of independent interest. The bound on the regret in the exploitation phase is obtained by deriving stability results for the optimizer and value function of the associated class of infinite-dimensional stochastic control problems. As a complementary result we propose a regression-based algorithm to estimate the conditional expectation of non-Markovian signals and derive its convergence rate.

q-fin.TR↗

arXiv2025

RDG-GS: Relative Depth Guidance with Gaussian Splatting for Real-time Sparse-View 3D Rendering

Efficiently synthesizing novel views from sparse inputs while maintaining accuracy remains a critical challenge in 3D reconstruction. While advanced techniques like radiance fields and 3D Gaussian Splatting achieve rendering quality and impressive efficiency with dense view inputs, they suffer from significant geometric reconstruction errors when applied to sparse input views. Moreover, although recent methods leverage monocular depth estimation to enhance geometric learning, their dependence on single-view estimated depth often leads to view inconsistency issues across different viewpoints. Consequently, this reliance on absolute depth can introduce inaccuracies in geometric information, ultimately compromising the quality of scene reconstruction with Gaussian splats. In this paper, we present RDG-GS, a novel sparse-view 3D rendering framework with Relative Depth Guidance based on 3D Gaussian Splatting. The core innovation lies in utilizing relative depth guidance to refine the Gaussian field, steering it towards view-consistent spatial geometric representations, thereby enabling the reconstruction of accurate geometric structures and capturing intricate textures. First, we devise refined depth priors to rectify the coarse estimated depth and insert global and fine-grained scene information to regular Gaussians. Building on this, to address spatial geometric inaccuracies from absolute depth, we propose relative depth guidance by optimizing the similarity between spatially correlated patches of depth and images. Additionally, we also directly deal with the sparse areas challenging to converge by the adaptive sampling for quick densification. Across extensive experiments on Mip-NeRF360, LLFF, DTU, and Blender, RDG-GS demonstrates state-of-the-art rendering quality and efficiency, making a significant advancement for real-world application.

cs.CV↗

arXiv2024

Inline-Amplification-Free Time Transfer Utilizing Waveform-Resolved Single-Photon Detection

High-precision time transfer over a long haul of fiber plays a significant role in many fields. The core method, namely cascading relay nodes for the compensation of signal attenuation and dispersion, is however insufficient to deal with crucial point-to-point transfer scenarios, such as harsh environments with extremely deficient infrastructure and emergency conditions. In long-distance signal transmission without any inline amplifiers, the high loss of the optical fiber link becomes the primary limiting factor, and direct use of traditional photodetectors at the receiving end will bring about a significant drop in the stability of detected signals. Here we propose a waveform-resolved single photon detection technique and experimentally perform tomography on the weak transferred signal with an average photon number of just 0.617 per pulse. By adopting this technique, we achieve the time deviation of 95.68 ps and 192.58 ps at 200 km and 300 km respectively at an averaging time of 1 s, overcoming the technical lower bound induced by traditional photodetectors. This work lays the foundation for through-type time transfer with high precision in those significant inline-amplification-free scenarios.

physics.optics↗

arXiv2024

Semantic Convergence: Harmonizing Recommender Systems via Two-Stage Alignment and Behavioral Semantic Tokenization

Large language models (LLMs), endowed with exceptional reasoning capabilities, are adept at discerning profound user interests from historical behaviors, thereby presenting a promising avenue for the advancement of recommendation systems. However, a notable discrepancy persists between the sparse collaborative semantics typically found in recommendation systems and the dense token representations within LLMs. In our study, we propose a novel framework that harmoniously merges traditional recommendation models with the prowess of LLMs. We initiate this integration by transforming ItemIDs into sequences that align semantically with the LLMs space, through the proposed Alignment Tokenization module. Additionally, we design a series of specialized supervised learning tasks aimed at aligning collaborative signals with the subtleties of natural language semantics. To ensure practical applicability, we optimize online inference by pre-caching the top-K results for each user, reducing latency and improving effciency. Extensive experimental evidence indicates that our model markedly improves recall metrics and displays remarkable scalability of recommendation systems.

cs.IR↗

arXiv2024

High Quality QCD Axion via Electric-Magnetic Duality

We propose a novel paradigm for the QCD axion with high-quality Peccei-Quinn (PQ) symmetry on the basis of electric-magnetic duality in the conformal window of a supersymmetric gauge theory. PQ breaking fields, that contain the QCD axion, emerge in the magnetic theory and possess a large anomalous dimension, which leads to not only generation of an intermediate scale of spontaneous PQ breaking but also significant suppression of explicit PQ symmetry breaking operators. The high PQ quality and the absence of a Landau pole in the color gauge coupling are achieved. The parameter space to realize the correct abundance of the axion dark matter (DM) predicts explicit PQ violation which may be probed by future measurements of the neutron electric dipole moment. In the other viable parameter space, the lightest supersymmetric particle can become a DM candidate. Since the model naturally accommodates a mechanism to suppress the axion isocurvature fluctuation, it provides a complete solution to the strong CP problem as well as the identity of DM.

hep-ph↗

arXiv2024

Development of a Generalizable Data-driven Turbulence Model: Conditioned Field Inversion and Symbolic Regression

This paper addresses the issue of predicting separated flows with Reynolds-averaged Navier-Stokes (RANS) turbulence models, which are essential for many engineering tasks. Traditional RANS models usually struggle with this task, so recent efforts have focused on data-driven methods such as field inversion and machine learning (FIML) to correct this issue by adjusting the baseline equations. However, these FIML methods often reduce accuracy in attached boundary layers. To address this issue, we developed a "conditioned field inversion" technique. This method adjusts the corrective factor \b{eta} (used by FIML) in the shear-stress transport (SST) model. It multiplies \b{eta} with a shield function f_d that is off in the boundary layer and on elsewhere. This maintains the accuracy of the baseline model for the attached flows. We applied both conditioned and classic field inversion to the NASA hump and a curved backward-facing step (CBFS), creating two datasets. These datasets were used to train two models: SR-CND (from our new method) and SR-CLS (from the traditional method). The SR-CND model matches the SR-CLS model in predicting separated flows in various scenarios, such as periodic hills, the NLR7301 airfoil, the 3D SAE car model, and the 3D Ahmed body, and outperforms the baseline SST model in the cases presented in the paper. Importantly, the SR-CND model maintains accuracy in the attached boundary layers, whereas the SR-CLS model does not. Therefore, the proposed method improves separated flow predictions while maintaining the accuracy of the original model for attached flows, offering a better way to create data-driven turbulence models.

physics.flu-dyn↗

arXiv2024

Rapid aerodynamic prediction of swept wings via physics-embedded transfer learning

Machine learning-based models provide a promising way to rapidly acquire transonic swept wing flow fields but suffer from large computational costs in establishing training datasets. Here, we propose a physics-embedded transfer learning framework to efficiently train the model by leveraging the idea that a three-dimensional flow field around wings can be analyzed with two-dimensional flow fields around cross-sectional airfoils. An airfoil aerodynamics prediction model is pretrained with airfoil samples. Then, an airfoil-to-wing transfer model is fine-tuned with a few wing samples to predict three-dimensional flow fields based on two-dimensional results on each spanwise cross section. Sweep theory is embedded when determining the corresponding airfoil geometry and operating conditions, and to obtain the sectional airfoil lift coefficient, which is one of the operating conditions, the low-fidelity vortex lattice method and data-driven methods are proposed and evaluated. Compared to a nontransfer model, introducing the pretrained model reduces the error by 30%, while introducing sweep theory further reduces the error by 9%. When reducing the dataset size, less than half of the wing training samples are need to reach the same error level as the nontransfer framework, which makes establishing the model much easier.

physics.flu-dyn↗

arXiv2024

Dual-comb-enhanced microwave clock synchronization over commercial fiber

The large-scale clock network is the key ingredient to obtain high precision in many scenarios, from fundamental research to cutting-edge applications. The advantage of the time synchronization among microwave clocks is their cost, size, and accessibility. Here, we demonstrate a femtosecond-level time synchronization of microwave clocks through a commercial link of 205.86 km via dual-comb-enhanced optical two-way time transfer, which achieves a 6.23-fs residual time deviation between synchronized timescales at 1 s and an instability below 6E-18 at 10,000 s. Further, the high-precision time synchronization of microwave clocks significantly enhances the probe ability of subtle reciprocity changes of fiber to the sub-picosecond level. This work provides a path toward secure fiber time-frequency networks to support future microwave-clock-based precise timing and sensing systems.

physics.optics↗

arXiv2024

Optimal Investment with Costly Expert Opinions

We consider the Merton problem of optimizing expected power utility of terminal wealth in the case of an unobservable Markov-modulated drift. What makes the model special is that the agent is allowed to purchase costly expert opinions of varying quality on the current state of the drift, leading to a mixed stochastic control problem with regular and impulse controls involving random consequences. Using ideas from filtering theory, we first embed the original problem with unobservable drift into a full information problem on a larger state space. The value function of the full information problem is characterized as the unique viscosity solution of the dynamic programming PDE. This characterization is achieved by a new variant of the stochastic Perron's method, which additionally allows us to show that, in between purchases of expert opinions, the problem reduces to an exit time control problem which is known to admit an optimal feedback control. Under the assumption of sufficient regularity of this feedback map, we are able to construct optimal trading and expert opinion strategies.

q-fin.PM↗

arXiv2024

Towards An Analytical Framework for Dynamic Potential Games

Potential game is an emerging notion and framework for studying N-player games, especially with heterogeneous players. In this paper, we build an analytical framework for dynamic potential games. We prove that a game is a dynamic potential game if and only if each player's value function can be decomposed as a potential function and a residual term which is solely dependent on other players' policies. This decomposition is consistent with the result in the static setting and enables us to identify and analyze an important and new class of dynamic potential games called the distributed game. Moreover, we prove that a game is a dynamic potential game if the value function has a symmetric Jacobian. This generalizes the differential characterization for static potential games by replacing the classical derivative with a new notation of functional derivative with respect to Markov policies. For a general class of continuous-time stochastic games, we explicitly characterize their potential functions. In particular, we show that the potential function of linear-quadratic games can be studied through a system of linear ODEs. Furthermore, under a rank condition on control coefficients, we prove a linear-quadratic game is a Markov potential game if and only if all players have identical cost functions.

math.OC↗

arXiv2024

Pricing and hedging of decentralised lending contracts

We study the loan contracts offered by decentralised loan protocols (DLPs) through the lens of financial derivatives. DLPs, which effectively are clearinghouses, facilitate transactions between option buyers (i.e. borrowers) and option sellers (i.e. lenders). The loan-to-value at which the contract is initiated determines the option premium borrowers pay for entering the contract, and this can be deduced from the non-arbitrage pricing theory. We show that when there are no market frictions, and there is no spread between lending and borrowing rates, it is optimal to never enter the lending contract. Next, by accounting for the spread between rates and transactional costs, we develop a deep neural network-based algorithm for learning trading strategies on the external markets that allow us to replicate the payoff of the lending contracts that are not necessarily optimally exercised. This allows hedge the risk lenders carry by issuing options sold to the borrowers, which can complement (or even replace) the liquidations mechanism used to protect lenders' capital. Our approach can also be used to exploit (statistical) arbitrage opportunities that may arise when DLP allow users to enter lending contracts with loan-to-value, which is not appropriately calibrated to market conditions or/and when different markets price risk differently. We present thorough simulation experiments using historical data and simulations to validate our approach.

q-fin.PR↗