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Weinan Wang

Publications and source records attributed to Weinan Wang.

At least 37 records · Page 2Linked to original sources
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

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↗
arXiv2024

Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby spaces

We provide a short proof of $L^3$-asymptotic stability around vector fields that are small in weak-$L^3$, including small Landau solutions. We show that asymptotic stability also holds for vector fields in the range of Lorentz spaces strictly between $L^3$ and weak-$L^3$, as well as in the closure of the test functions in weak-$L^3$. To provide a comprehensive perspective on the matter, we observe that asymptotic stability of Landau solutions does not generally extend to weak-$L^3$ via a counterexample.

math.AP↗
arXiv2024

A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation

In this paper, we prove a kinetic Nash type inequality and adapt it to a new functional inequality for functions in a kinetic Sobolev space with absorbing boundary conditions on the half-space. As an application, we address the boundary behavior of the kinetic Fokker-Planck equations in the half-space. Our main result is the sharp regularity of the solution at the absorbing boundary and grazing set.

math.AP↗
arXiv2024

Sparse Recovery With Multiple Data Streams: A Sequential Adaptive Testing Approach

Multistage design has been used in a wide range of scientific fields. By allocating sensing resources adaptively, one can effectively eliminate null locations and localize signals with a smaller study budget. We formulate a decision-theoretic framework for simultaneous multi-stage adaptive testing and study how to minimize the total number of measurements while meeting pre-specified constraints on both the false positive rate (FPR) and missed discovery rate (MDR). The new procedure, which effectively pools information across individual tests using a simultaneous multistage adaptive ranking and thresholding (SMART) approach, controls the error rates and leads to great savings in total study costs. Numerical studies confirm the effectiveness of SMART. The SMART procedure is illustrated through the analysis of large-scale A/B tests, high-throughput screening and image analysis.

stat.ME↗
arXiv2024

Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise

In this paper, we consider the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise. By assuming the ionic species have the same diffusivity and opposite valences, we prove the global well-posedness of the system. Furthermore, we illustrate the enhanced dissipation phenomenon in the system with specific transportation noise by establishing that it enables an arbitrarily large exponential convergence rate of the solutions.

math.AP↗
arXiv2023

Quantitative bounds for critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces

In this paper, we prove a quantitative regularity theorem and a blow-up criterion of classical solutions for the three-dimensional Navier-Stokes equations. By adapting the strategy developed by Tao in [20], we obtain an explicit blow-up rate in the setting of critical Lorentz spaces $L^{3, q_{0}}(\mathbb R^3)$ with $3 \leq q_0 < \infty $. Our results improve the previous regularity in critical Lebesgue spaces $L^3(\mathbb R^3)$ in [20] and quantify the qualitative result by Phuc in [16].

math.AP↗
arXiv2023

Analysis of a Reaction-Diffusion SIR Epidemic Model with Noncompliant Behavior

Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic including behavioral concerns. In our model, the disease spreads via mass action, as is customary in compartmental models. However, drawing from social contagion theory, we assume that as the disease spreads and prevention measures are enacted, noncompliance with prevention measures also spreads throughout the population. We prove global existence of classical solutions of our model, and then perform R0-type analysis and determine asymptotic behavior of the model in different parameter regimes. Finally, we simulate the model and discuss the new facets which distinguish our model from basic SIR-type models.

math.AP↗
arXiv2023

On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions

We consider the inhomogeneous heat equation on the half-space $\mathbb R_{+}^{d}$ with Neumann boundary conditions. We prove a space-time Gevrey regularity of the solution, with a radius of analyticity uniform up to the boundary of the half-space. We also address the case of homogeneous Robin boundary conditions. Our results generalize the case of homogeneous Dirichlet boundary conditions established by Kukavica and Vicol in [10].

math.AP↗
arXiv2022

On the global well-posedness and Gevrey regularity of some electrodiffusion models

We consider the Nernst-Planck equations describing the nonlinear time evolution of multiple ionic concentrations in a two-dimensional incompressible fluid. The velocity of the fluid evolves according to either the Euler or Darcy's equations, both forced nonlinearly by the electric forces generated by the presence of charged ions. We address the global well-posedness and Gevrey regularity of the resulting electrodiffusion models in the periodic setting.

math.AP↗
arXiv2022

A Systematic Paradigm for Detecting, Surfacing, and Characterizing Heterogeneous Treatment Effects (HTE)

To effectively optimize and personalize treatments, it is necessary to investigate the heterogeneity of treatment effects. With the wide range of users being treated over many online controlled experiments, the typical approach of manually investigating each dimension of heterogeneity becomes overly cumbersome and prone to subjective human biases. We need an efficient way to search through thousands of experiments with hundreds of target covariates and hundreds of breakdown dimensions. In this paper, we propose a systematic paradigm for detecting, surfacing and characterizing heterogeneous treatment effects. First, we detect if treatment effect variation is present in an experiment, prior to specifying any breakdowns. Second, we surface the most relevant dimensions for heterogeneity. Finally, we characterize the heterogeneity beyond just the conditional average treatment effects (CATE) by studying the conditional distributions of the estimated individual treatment effects. We show the effectiveness of our methods using simulated data and empirical studies.

stat.ME↗
arXiv2022

Empirical Bayes Multistage Testing for Large-Scale Experiments

Modern application of A/B tests is challenging due to its large scale in various dimensions, which demands flexibility to deal with multiple testing sequentially. The state-of-the-art practice first reduces the observed data stream to always-valid p-values, and then chooses a cut-off as in conventional multiple testing schemes. Here we propose an alternative method called AMSET (adaptive multistage empirical Bayes test) by incorporating historical data in decision-making to achieve efficiency gains while retaining marginal false discovery rate (mFDR) control that is immune to peeking. We also show that a fully data-driven estimation in AMSET performs robustly to various simulation and real data settings at a large mobile app social network company.

stat.ME↗
arXiv2022

Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation

We prove a Schauder estimate for kinetic Fokker-Planck equations that requires only Hölder regularity in space and velocity but not in time. As an application, we deduce a weak-strong uniqueness result of classical solutions to the spatially inhomogeneous Landau equation beginning from initial data having Hölder regularity in $x$ and only a logarithmic modulus of continuity in $v$. This replaces an earlier result requiring Hölder continuity in both variables.

math.AP↗
arXiv2022

Quantitative unique continuation for Robin boundary value problems on $C^{1,1}$ domains

In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on $C^{1,1}$ domains. The first one is a sharp vanishing order estimate of Robin problems with Lipschitz coefficients and differentiable, sign-changing potentials. This generalizes the result for the "Robin eigenfunctions" in [26], which deals with the case with constant potentials. The second result is a unique continuation result from the boundary -- any non-trivial solution cannot vanish at infinite order from the boundary or vanish on an open subset on the boundary. Such result generalizes the one in [1] for the Laplace equation on $C^{1,1}$ domains with zero Neumann boundary conditions.

math.AP↗
arXiv2021

Local well-posedness for the Boltzmann equation with very soft potential and polynomially decaying initial data

In this paper, we address the local well-posedness of the spatially inhomogeneous non-cutoff Boltzmann equation when the initial data decays polynomially in the velocity variable. We consider the case of very soft potentials $γ+ 2s < 0$. Our main result completes the picture for local well-posedness in this decay class by removing the restriction $γ+ 2s > -3/2$ of previous works. Our approach is entirely based on the Carleman decomposition of the collision operator into a lower order term and an integro-differential operator similar to the fractional Laplacian. Interestingly, this yields a very short proof of local well-posedness when $γ\in (-3,0]$ and $s \in (0,1/2)$ in a weighted $C^1$ space that we include as well.

math.AP↗
arXiv2020

CONQ: CONtinuous Quantile Treatment Effects for Large-Scale Online Controlled Experiments

In many industry settings, online controlled experimentation (A/B test) has been broadly adopted as the gold standard to measure product or feature impacts. Most research has primarily focused on user engagement type metrics, specifically measuring treatment effects at mean (average treatment effects, ATE), and only a few have been focusing on performance metrics (e.g. latency), where treatment effects are measured at quantiles. Measuring quantile treatment effects (QTE) is challenging due to the myriad difficulties such as dependency introduced by clustered samples, scalability issues, density bandwidth choices, etc. In addition, previous literature has mainly focused on QTE at some pre-defined locations, such as P50 or P90, which doesn't always convey the full picture. In this paper, we propose a novel scalable non-parametric solution, which can provide a continuous range of QTE with point-wise confidence intervals while circumventing the density estimation altogether. Numerical results show high consistency with traditional methods utilizing asymptotic normality. An end-to-end pipeline has been implemented at Snap Inc., providing daily insights on key performance metrics at a distributional level.

stat.ME↗
arXiv2020

Point Spread Function Modelling for Wide Field Small Aperture Telescopes with a Denoising Autoencoder

The point spread function reflects the state of an optical telescope and it is important for data post-processing methods design. For wide field small aperture telescopes, the point spread function is hard to model, because it is affected by many different effects and has strong temporal and spatial variations. In this paper, we propose to use the denoising autoencoder, a type of deep neural network, to model the point spread function of wide field small aperture telescopes. The denoising autoencoder is a pure data based point spread function modelling method, which uses calibration data from real observations or numerical simulated results as point spread function templates. According to real observation conditions, different levels of random noise or aberrations are added to point spread function templates, making them as realizations of the point spread function, i.e., simulated star images. Then we train the denoising autoencoder with realizations and templates of the point spread function. After training, the denoising autoencoder learns the manifold space of the point spread function and can map any star images obtained by wide field small aperture telescopes directly to its point spread function, which could be used to design data post-processing or optical system alignment methods.

astro-ph.IM↗