arXiv subjects

Weinan Wang

Publications and source records attributed to Weinan Wang.

At least 19 recordsLinked to original sources

arXiv2026

Uniform bounds for a thermo-diffusive system beyond exponential growth

In this paper, we prove a global-in-time uniform bound for solutions to a thermo-diffusive system in the whole space with bounded nonnegative initial data. The result allows exponential reaction rates and a range of superexponential rates determined by the diffusivities. This extends the recent results of La, Roquejoffre, and Ryzhik \cite{LRR24} and of Leontev and Ryzhik \cite{LR26} beyond their strictly subexponential range.

math.AP↗

arXiv2026

The entropy production is not always monotone for the Kac equation

In 1966, McKean conjectured that the entropy production of Kac's caricature of a Maxwellian gas is nonincreasing in time \cite{McKean66}. We disprove this conjecture for the standard uniform-angle Kac equation. Our counterexamples are smooth, strictly positive, even mixtures of two Gaussians at different temperatures. We also show that every entropy derivative beyond the first violates its expected sign at some time along the same solution. The initial densities can be chosen with unit mass and second moment. mass and second moment.

math.AP↗

arXiv2026

A note on relativistic kinetic Schauder estimates

In this note, motivated by \cite{DW26}, we construct counterexamples to momentum-only Schauder estimates for linear kinetic equations with relativistic transport. The construction exploits a structural compatibility between the nonlinear momentum-to-velocity map and a single fixed pair of smooth diffusion and drift coefficients: after conjugation, the diffusion becomes the Laplacian and all induced first-order terms cancel. Thus the obstruction is realized for one fixed operator, uniformly elliptic on every bounded momentum set, rather than through a frequency-dependent family of coefficients. We further show that the failure persists with zero external forcing by constructing uniformly positive stationary solutions for which the hidden spatial oscillation is encoded in a bounded zeroth-order coefficient whose momentum Hölder seminorm tends to zero. Consequently, the full Lorentzian Hölder control used in \cite{HSTT} cannot in general be replaced by momentum-only Hölder control.

math.AP↗

arXiv2026

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions

We study the three-dimensional incompressible Boussinesq equations on a bounded domain with smooth boundary and Navier boundary conditions. We construct global weak solutions by a Galerkin approximation and establish the associated Leray--Hopf energy inequalities. For nonnegative boundary friction, the total energy decays exponentially when the friction coefficient is positive on a boundary subset of positive surface measure. In the frictionless case, the scalar field and the velocity component orthogonal to the rigid-motion kernel decay exponentially; when the kernel is trivial, this is exponential decay of the total energy. When the scalar initial datum vanishes, this also proves exponential decay for the Navier--Stokes system on solids of revolution for every friction coefficient $α\in L^\infty(\partialΩ)$ such that $α\ge0$ almost everywhere and $α\not\equiv0$, resolving the corresponding case left open in \cite{Kelliher2025}. The proof uses a weighted Korn--Poincaré inequality and a two-time Gronwall-type inequality with an exponentially decaying forcing term.

math.AP↗

arXiv2026

Several counterexamples to kinetic Schauder estimates

In this paper, we construct counterexamples to the Schauder estimate for kinetic Fokker--Planck equations, disproving \cite[Conjecture~1.3]{HW}. The conjectured estimate would control second velocity derivatives using only velocity Hölder regularity of the coefficients and forcing, with no spatial regularity. We also give a zero-forcing variant, where the same {conditions are imposed on} a bounded zeroth-order coefficient. Finally, in dimensions $d\geq 2$, we give endpoint examples showing that bounded velocity-independent forcing may produce bounded distributional stationary solutions whose second velocity derivatives are not locally bounded.

math.AP↗

arXiv2026

RealBench: A Repo-Level Code Generation Benchmark Aligned with Real-World Software Development Practices

Writing code requires significant time and effort in software development. To automate this process, researchers have made substantial progress using Large Language Models (LLMs) for code generation. Many benchmarks like HumanEval and EvoCodeBench have been created to evaluate LLMs by requiring them to generate code from natural language requirements. However, in enterprise applications and team development, developers typically write code based on structured designs or specifications rather than raw natural language descriptions. This gap between existing benchmarks and real industry development practices means that current benchmark scores may not accurately reflect how much code generation can help automate software development tasks. To address this gap, we propose RealBench, a repository-level code generation benchmark aligned with real-world industry software development practices. Each example includes both natural language requirements and UML diagrams as system design, matching how developers typically receive specifications. Based on the constructed benchmarks, we conduct a systematic evaluation of advanced LLMs' code generation capabilities when provided with structured system designs. The experimental results reveal key insights in current LLMs' capabilities for repo-level code generation aligned with real-world software development practices. First, we notice that regarding repo-level code generation, LLMs show much worse performance and there are significant performance gaps among LLMs. Second, LLMs are good at finding and creating modules defined in UML diagrams, but the quality of generated modules is often poor due to grammar and logic errors. Third, generating the entire repository at once is the best generation strategy on smaller repositories, while generating a complex repository with the module-by-module strategy works better compared to other strategies.

cs.SE↗

arXiv2026

Optimal Control of an SIR Model with Noncompliance as a Social Contagion

We propose and study a compartmental model for epidemiology with human behavioral effects. Specifically, our model incorporates governmental prevention measures aimed at lowering the disease infection rate, but we split the population into those who comply with the measures and those who do not comply and therefore do not receive the reduction in infectivity. We then allow the attitude of noncompliance to spread as a social contagion parallel to the disease. We derive the reproductive ratio for our model and provide stability analysis for the disease-free equilibria. We then propose an optimal control scenario wherein a policy-maker with access to control variables representing disease prevention mandates, treatment efforts, and educational campaigns aimed at encouraging compliance minimizes a cost functional incorporating several cost concerns. Via careful analysis of the control-to-state map, we are able to prove existence of optimal controls. Our proof applies to dynamics which can be nonlinear in the control variables and general cost functionals including the case of $L^1$ control costs. We numerically resolve optimal strategies using the sequential quadratic Hamiltonian method, a relatively new numerical method for optimal control which is easy to implement and has good convergence theory, as we demonstrate. We test our model in several parameter regimes with specific interest in observing how the policy-maker's optimal strategies depend on their particular preferences which are expressed via design of different cost functionals.

eess.SY↗

arXiv2026

Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime

In this paper, we propose a perturbation-based conformal prediction framework for uncertainty quantification in operator learning, with a focus on the 2D Navier--Stokes equations. While neural operators provide fast surrogates for expensive PDE solvers, they do not by themselves provide calibrated uncertainty for spatiotemporal field predictions. Our approach wraps a trained Fourier Neural Operator (FNO) with split conformal prediction and constructs the local uncertainty scale by comparing the predictions of two operators trained on nearly identical datasets: one on the original labels and one on labels perturbed by small Gaussian noise. We consider this procedure in the data-scarce regime, where the total label budget is fixed and methods that require a separate uncertainty network must divide training data between multiple models. On the 2D Navier--Stokes benchmark, the perturbation-based method produces substantially narrower conformal bands than existing methods under matched total data budgets while maintaining the target simultaneous coverage. These results suggest that perturbation sensitivity is a practical and sample-efficient uncertainty proxy for conformalized neural operators.

cs.LG↗

arXiv2026

FingerViP: Learning Real-World Dexterous Manipulation with Fingertip Visual Perception

The current practice of dexterous manipulation generally relies on a single wrist-mounted view, which is often occluded and limits performance on tasks requiring multi-view perception. In this work, we present FingerViP, a learning system that utilizes a visuomotor policy with fingertip visual perception for dexterous manipulation. Specifically, we design a vision-enhanced fingertip module with an embedded miniature camera and install the modules on each finger of a multi-fingered hand. The fingertip cameras substantially improve visual perception by providing comprehensive, multi-view feedback of both the hand and its surrounding environment. Building on the integrated fingertip modules, we develop a diffusion-based whole-body visuomotor policy conditioned on a third-view camera and multi-view fingertip vision, which effectively learns complex manipulation skills directly from human demonstrations. To improve view-proprioception alignment and contact awareness, each fingertip visual feature is augmented with its corresponding camera pose encoding and per-finger joint-current encoding. We validate the effectiveness of the multi-view fingertip vision and demonstrate the robustness and adaptability of FingerViP on various challenging real-world tasks, including pressing buttons inside a confined box, retrieving sticks from an unstable support, retrieving objects behind an occluding curtain, and performing long-horizon cabinet opening and object retrieval, achieving an overall success rate of 80.8%. All hardware designs and code will be fully open-sourced.

cs.RO↗

arXiv2026

2D incompressible inviscid Oldroyd-B equations: ill-posedness, long time existence, and high Weissenberg number limit

In this paper, we consider the high-Weissenberg number limit of a Voigt-regularized two-dimensional Oldroyd-B model for viscoelastic fluids. We first demonstrate that the Euler-Oldroyd-B system is both linearly and nonlinearly ill-posed in Sobolev spaces, exhibiting Hadamard instability. Then, we introduce a Voigt-type regularization on the stress tensor, which stabilizes the system. For the regularized model, we establish long time ($T \sim \mathcal O(\varepsilon^{-2/3})$) well-posedness and uniform energy estimates with respect to the relaxation parameter $\varepsilon>0$. Lastly, we prove that, as $\varepsilon \to 0$, the solutions converge to a solution of the 2-d incompressible Navier-Stokes equations over time intervals of size $\mathcal O(\varepsilon^{-2/3})$. The proof relies on a decomposition of the stress tensor, high-order energy estimates, and a detailed analysis of the nonlinear coupling terms. Our results provide a mathematical justification for the Newtonian limit of a regularized viscoelastic fluid model that is otherwise ill-posed.

math.AP↗

arXiv2026

Learning Contact Policies for SEIR Epidemics on Networks: A Mean-Field Game Approach

In this paper, we develop a mean-field game model for SEIR epidemics on heterogeneous contact networks, where individuals choose state-dependent contact effort to balance infection losses against the social and economic costs of isolation. The Nash equilibrium is characterized by a coupled Hamilton--Jacobi--Bellman/Kolmogorov system across degree classes. An important feature of the SEIR setting is the exposed compartment: the incubation period separates infection from infectiousness and changes incentives after infection occurs. In the baseline formulation, exposed agents optimally maintain full contact, while susceptible agents reduce contact according to an explicit best-response rule driven by infection pressure and the value gap. We also discuss extensions that yield nontrivial exposed precaution by introducing responsibility or compliance incentives. We establish existence of equilibrium via a fixed-point argument and prove the uniqueness under a suitable monotonicity condition. The analysis identifies a delay in the onset of precaution under longer incubation, which can lead to weaker behavioral responses and larger outbreaks. Numerical experiments illustrate how network degree and the cost exponent shape equilibrium policies and epidemic outcomes.

q-bio.PE↗

arXiv2025

A Compartmental Model for Epidemiology with Human Behavior and Stochastic Effects

We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that noncompliance with protocols spreads as a social contagion. We begin by deriving the reproductive ratio for a deterministic version of the model, and use this to fully characterize the local stability of disease free equilibrium points. We then append the deterministic model with stochastic effects, specifically assuming that the transmission rate of the disease and the transmission rate of the social contagion are uncertain. We prove global existence and nonnegativity for our stochastic model. Then using suitably constructed stochastic Lyapunov functions, we analyze the behavior of the stochastic system with respect to certain disease free states. We demonstrate all of our results with numerical simulations.

math.DS↗

arXiv2025

On a partial data inverse problem for the semi-linear wave equation

We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a semi-linear wave equation up to natural obstructions on a Lorentzian manifold with boundary. In particular, we do not impose any geometric or size restrictions on the measurement set. The proof relies on the technique of higher order linearization combined with the construction of Gaussian beams with reflections on the boundary.

math.AP↗

arXiv2025

A Calderón type inverse problem for the active scalar equations with fractional dissipation

In this paper, we are interested in an inverse problem for the active scalar equations with fractional dissipation on the torus. We perform a second order linearization to relate our model to the linear fractional diffusion equation. Our approach to solving the inverse problem relies on nonlocal phenomena such as the unique continuation property of the fractional Laplacian and its associated Runge approximation property. A remarkable feature of our model is that the divergence-free structure in the nonlinear term plays an important role in both forward and inverse problems.

math.AP↗

arXiv2025

Optimal Control of a Reaction-Diffusion Epidemic Model with Noncompliance

In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a portion of the population does not comply with them, and this noncompliance affects the spread of the disease. Drawing from social contagion theory, our model allows for the spread of noncompliance parallel to the spread of the disease. The quantities of interest for control are the reduction in infection rate among the compliant population, the rate of spread of noncompliance, and the rate at which non-compliant individuals become compliant after, e.g., receiving more or better information about the underlying disease. We prove the existence of global-in-time solutions for fixed controls and study the regularity properties of the resulting control-to-state map. The existence of optimal control is then established in an abstract framework for a fairly general class of objective functions. Necessary first--order optimality conditions are obtained via a Lagrangian based stationarity system. We conclude with a discussion regarding minimization of the size of infected and non-compliant populations and present simulations with various parameters values to demonstrate the behavior of the model.

math.AP↗

arXiv2025

A new method of petroleum well logging

This paper presents a new petroleum well logging method - electrical impedance logging for shaly sand reservoirs - through theoretical and petrophysical experimental research. Electrical impedance logging measures the electrical impedance of shaly sand reservoirs, extracts resistivity information from the real part, and uses it to determine the oil saturation of the reservoir quantitatively. The study shows that the resistivity, extracted from the real part of the electrical impedance in shaly sands, has characteristics similar to those of the pure sandstone formation resistivity and can be directly used in Archie's law for oil-bearing interpretation of reservoirs.

physics.geo-ph↗

arXiv2024

Model and theory of dark photons in the visible light range

This paper explores the possibility of the existence of dark photons within the visible light range and provides evidence for their existence through a thought experiment. A new model of dark photons is established based on extensive theoretical research, forming a comprehensive theory of dark photons. This theory provides a reasonable explanation for certain perplexing optical phenomena, such as the wave-particle duality of light, Young's double-slit experiment, as well as phenomena like dark matter, dark energy, stellar spectral redshift, and negative time. Furthermore, this theory holds reference value for studying the properties of other fundamental particles and exploring quantum gravity.

physics.optics↗

arXiv2024

ChatBCI: A P300 Speller BCI Leveraging Large Language Models for Improved Sentence Composition in Realistic Scenarios

P300 speller BCIs allow users to compose sentences by selecting target keys on a GUI through the detection of P300 component in their EEG signals following visual stimuli. Most P300 speller BCIs require users to spell words letter by letter, or the first few initial letters, resulting in high keystroke demands that increase time, cognitive load, and fatigue. This highlights the need for more efficient, user-friendly methods for faster sentence composition. In this work, we introduce ChatBCI, a P300 speller BCI that leverages the zero-shot learning capabilities of large language models (LLMs) to suggest words from user-spelled initial letters or predict the subsequent word(s), reducing keystrokes and accelerating sentence composition. ChatBCI retrieves word suggestions through remote queries to the GPT-3.5 API. A new GUI, displaying GPT-3.5 word suggestions as extra keys is designed. SWLDA is used for the P300 classification. Seven subjects completed two online spelling tasks: 1) copy-spelling a self-composed sentence using ChatBCI, and 2) improvising a sentence using ChatBCI's word suggestions. Results demonstrate that in Task 1, on average, ChatBCI outperforms letter-by-letter BCI spellers, reducing time and keystrokes by 62.14% and 53.22%, respectively, and increasing information transfer rate by 198.96%. In Task 2, ChatBCI achieves 80.68% keystroke savings and a record 8.53 characters/min for typing speed. Overall, ChatBCI, by employing remote LLM queries, enhances sentence composition in realistic scenarios, significantly outperforming traditional spellers without requiring local model training or storage. ChatBCI's (multi-) word predictions, combined with its new GUI, pave the way for developing next-generation speller BCIs that are efficient and effective for real-time communication, especially for users with communication and motor disabilities.

cs.HC↗