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Researcher profile

Yixuan Wu

Yixuan Wu contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.NANumerical AnalysisArtificial IntelligenceComputer Visioncs.CYnlin.CDphysics.geo-ph

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Published work

6 published item(s)

preprint2026arXiv

AcademiClaw: When Students Set Challenges for AI Agents

Benchmarks within the OpenClaw ecosystem have thus far evaluated exclusively assistant-level tasks, leaving the academic-level capabilities of OpenClaw largely unexamined. We introduce AcademiClaw, a bilingual benchmark of 80 complex, long-horizon tasks sourced directly from university students' real academic workflows -- homework, research projects, competitions, and personal projects -- that they found current AI agents unable to solve effectively. Curated from 230 student-submitted candidates through rigorous expert review, the final task set spans 25+ professional domains, ranging from olympiad-level mathematics and linguistics problems to GPU-intensive reinforcement learning and full-stack system debugging, with 16 tasks requiring CUDA GPU execution. Each task executes in an isolated Docker sandbox and is scored on task completion by multi-dimensional rubrics combining six complementary techniques, with an independent five-category safety audit providing additional behavioral analysis. Experiments on six frontier models show that even the best achieves only a 55\% pass rate. Further analysis uncovers sharp capability boundaries across task domains, divergent behavioral strategies among models, and a disconnect between token consumption and output quality, providing fine-grained diagnostic signals beyond what aggregate metrics reveal. We hope that AcademiClaw and its open-sourced data and code can serve as a useful resource for the OpenClaw community, driving progress toward agents that are more capable and versatile across the full breadth of real-world academic demands. All data and code are available at https://github.com/GAIR-NLP/AcademiClaw.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

WaveDiffusion: Joint Latent Diffusion for Physically Consistent Seismic and Velocity Generation

Full Waveform Inversion (FWI) is a critical technique in subsurface imaging, aiming to reconstruct high-resolution subsurface properties from surface measurements. Acoustic FWI involves two physical modalities, seismic waveforms and velocity maps, which are governed by the acoustic wave equation. Prior works primarily focus on the inverse problem, modeling the relationship between seismic and velocity as an image-to-image translation task. In this work, we study their relationship from a generative perspective. Our aim is to explore and characterize the latent space structure, and identify latent vectors that generate seismic-velocity pairs consistent with the governing partial differential equation (PDE). Specifically, we model seismic and velocity data jointly from a shared latent space via a diffusion process. In experiments, we find that diffusion progressively refines arbitrary latent vectors into ones that yield approximately physics-consistent seismic-velocity pairs, even without explicit physics constraints. This provides empirical evidence of PDE-consistency in latent diffusion, where sampling is biased toward PDE-valid solutions. In latent space, satisfying the acoustic wave equation can be approximated through sampling and gradient descent. We formalize this physics-consistent latent modeling task and quantify it through extensive experiments. On large-scale OpenFWI benchmarks, our approach produces high-fidelity, diverse, and physically consistent seismic-velocity pairs, demonstrating the potential of a data-driven latent diffusion for physically consistent generation in a complex scientific domain.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis

The paper introduces a new meshfree pseudospectral method based on Gaussian radial basis functions (RBFs) collocation to solve fractional Poisson equations. Hypergeometric functions are used to represent the fractional Laplacian of Gaussian RBFs, enabling an efficient computation of stiffness matrix entries. Unlike existing RBF-based methods, our approach ensures a Toeplitz structure in the stiffness matrix with equally spaced RBF centers, enabling efficient matrix-vector multiplications using fast Fourier transforms. We conduct a comprehensive study on the shape parameter selection, addressing challenges related to ill-conditioning and numerical stability. The main contribution of our work includes rigorous stability analysis and error estimates of the Gaussian RBF collocation method, representing a first attempt at the rigorous analysis of RBF-based methods for fractional PDEs to the best of our knowledge. We conduct numerical experiments to validate our analysis and provide practical insights for implementation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

D-Former: A U-shaped Dilated Transformer for 3D Medical Image Segmentation

Computer-aided medical image segmentation has been applied widely in diagnosis and treatment to obtain clinically useful information of shapes and volumes of target organs and tissues. In the past several years, convolutional neural network (CNN) based methods (e.g., U-Net) have dominated this area, but still suffered from inadequate long-range information capturing. Hence, recent work presented computer vision Transformer variants for medical image segmentation tasks and obtained promising performances. Such Transformers model long-range dependency by computing pair-wise patch relations. However, they incur prohibitive computational costs, especially on 3D medical images (e.g., CT and MRI). In this paper, we propose a new method called Dilated Transformer, which conducts self-attention for pair-wise patch relations captured alternately in local and global scopes. Inspired by dilated convolution kernels, we conduct the global self-attention in a dilated manner, enlarging receptive fields without increasing the patches involved and thus reducing computational costs. Based on this design of Dilated Transformer, we construct a U-shaped encoder-decoder hierarchical architecture called D-Former for 3D medical image segmentation. Experiments on the Synapse and ACDC datasets show that our D-Former model, trained from scratch, outperforms various competitive CNN-based or Transformer-based segmentation models at a low computational cost without time-consuming per-training process.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A universal solution scheme for fractional and classical PDEs

We propose a unified meshless method to solve classical and fractional PDE problems with $(-Δ)^{\fracα{2}}$ for $α\in (0, 2]$. The classical ($α= 2$) and fractional ($α< 2$) Laplacians, one local and the other nonlocal, have distinct properties. Therefore, their numerical methods and computer implementations are usually incompatible. We notice that for any $α\ge 0$, the Laplacian $(-Δ)^{\fracα{2}}$ of generalized inverse multiquadric (GIMQ) functions can be analytically written by the Gauss hypergeometric function, and thus propose a GIMQ-based method. Our method unifies the discretization of classical and fractional Laplacians and also bypasses numerical approximation to the hypersingular integral of fractional Laplacian. These two merits distinguish our method from other existing methods for the fractional Laplacian. Extensive numerical experiments are carried out to test the performance of our method. Compared to other methods, our method can achieve high accuracy with fewer number of unknowns, which effectively reduces the storage and computational requirements in simulations of fractional PDEs. Moreover, the meshfree nature makes it free of geometric constraints and enables simple implementation for any dimension $d \ge 1$. Additionally, two approaches of selecting shape parameters, including condition number-indicated method and random-perturbed method, are studied to avoid the ill-conditioning issues when large number of points.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization

In this paper, we propose a new class of operator factorization methods to discretize the integral fractional Laplacian $(-Δ)^\fracα{2}$ for $α\in (0, 2)$. The main advantage of our method is to easily increase numerical accuracy by using high-degree Lagrange basis functions, but remain the scheme structure and computer implementation unchanged. Moreover, our discretization of the fractional Laplacian results in a symmetric (multilevel) Toeplitz differentiation matrix, which not only saves memory cost in simulations but enables efficient computations via the fast Fourier transforms. The performance of our method in both approximating the fractional Laplacian and solving the fractional Poisson problems was detailedly examined. It shows that our method has an optimal accuracy of ${\mathcal O}(h^2)$ for constant or linear basis functions, while ${\mathcal O}(h^4)$ if quadratic basis functions are used, with $h$ a small mesh size. Note that this accuracy holds for any $α\in (0, 2)$ and can be further increased if higher-degree basis functions are used. If the solution of fractional Poisson problem satisfies $u \in C^{m, l}(\barΩ)$ for $m \in {\mathbb N}$ and $0 < l < 1$, then our method has an accuracy of ${\mathcal O}\big(h^{\min\{m+l,\, 2\}}\big)$ for constant and linear basis functions, while ${\mathcal O}\big(h^{\min\{m+l,\, 4\}}\big)$ for quadratic basis functions. Additionally, our method can be readily applied to study generalized fractional Laplacians with a symmetric kernel function, and numerical study on the tempered fractional Poisson problem demonstrates its efficiency.

0 citations0 reviewsNo code linkedOpen access