arXiv subjects

Pei Fu

Publications and source records attributed to Pei Fu.

3 recordsLinked to original sources

arXiv2026

High-Order Discontinuous Cut Finite Element Methods for Scalar Hyperbolic Conservation Laws

In this paper, we present a family of high-order cut finite element methods based on the discontinuous Galerkin (DG) framework for scalar hyperbolic conservation laws on complex domains. Building on our previous work, we develop a multidimensional formulation that combines macro-element stabilization with flux limiting to obtain a scheme that preserves the maximum principle and remains robust with respect to arbitrary boundary cuts of the background mesh. The physical domain is embedded in a regular background mesh, which may produce arbitrarily small cut cells. To avoid the severe time step restrictions typically associated with such cells, ghost penalty stabilization terms are added on interior facets of macro-elements. The resulting method exhibits stability and accuracy properties similar to those of standard DG methods on fitted meshes. An $L^2$-stability result is derived for the semi-discrete scheme under both periodic and inflow-outflow boundary conditions. To enforce the maximum principle and suppress nonphysical oscillations, we adapt limiter techniques from standard DG methods to the CutFEM setting by defining limiting parameters on macro-elements. In particular, we present a macro-element-based parameterized flux limiter together with adaptations of the Zhang-Shu bound-preserving limiter and the Barth-Jespersen slope limiter. Numerical experiments in two and three spatial dimensions demonstrate optimal convergence orders, preservation of the maximum principle, and accurate shock capturing without spurious oscillations, even for challenging cut configurations involving very small-cut cell intersections.

math.NA↗

arXiv2026

DAREBench: Deployment-Aware and Reliable Evaluation of Models as Agents

As large language models evolve from question-answering systems into general-purpose agents, evaluation must move beyond static answer correctness to assess multimodal perception, multi-step execution, tool use, and artifact delivery. However, existing benchmarks are often tied to specific task types, execution environments, or scoring protocols, limiting their comparability, interpretability, and reliability for deployment decisions. We introduce DAREBench (Deployment-Aware and Reliable Evaluation of Models as Agents), a benchmark designed to capture workload variation and support reliable agent evaluation. Built on a shared OpenClaw execution environment, DAREBench organizes 233 tasks selected and adapted from 22 source benchmarks into a $2\times3$ workload matrix defined by input modality and execution form, and evaluates them under a unified contract-based protocol with evidence-based score auditing. We evaluate 23 commercial API models and 12 locally deployed open-weight models over 7,587 model--task runs, reporting accuracy and token consumption alongside reference costs for API models. Results show that no single model dominates all workload groups, text and multimodal tasks exhibit distinct accuracy--cost trade-offs, and local open-weight models are competitive in several groups but still trail frontier commercial models overall. These findings suggest that agent deployment and model selection should consider workload profiles, deployment mode, and accuracy--cost trade-offs rather than rely on a single aggregate score.

cs.AI↗

arXiv2026

Making Every Tool Call Count: Necessary Tool-Evidence Path Rewards for Agentic Vision-Language Models

Modern vision-language models (VLMs) can directly answer many image-grounded questions, yet they often struggle with complex queries requiring fine-grained visual details or external knowledge. To acquire this missing evidence, agentic VLMs invoke tools such as image cropping, image search, and text search. However, existing training paradigms primarily evaluate tool-use based on final answer correctness, leaving evidence acquisition and utilization insufficiently supervised. This leads to two critical shortcomings: (i) models frequently issue redundant or off-target tool calls that fail to gather necessary evidence, and (ii) even when appropriate tools are called, models often fail to extract the necessary information from the resulting observations. To address these limitations, we introduce the NTEP (Necessary Tool-Evidence Path), a novel annotation scheme that explicitly specifies the essential external evidence and corresponding tool calls for each query. Building upon this, we propose NTEP-R (NTEP Reward), a supervision mechanism ensuring that each tool invocation strictly advances the reasoning process toward the final solution. Specifically, our approach rewards the agent for aligning its pre-call intent with a necessary evidence-seeking goal, and for ensuring the information summarized from the post-call observation aligns with the necessary evidence. Furthermore, we introduce a non-repeated-goal regularizer to penalize redundant calls that revisit satisfied NTEP goals. Extensive evaluations on seven image-grounded benchmarks demonstrate that our 8B-parameter instantiation, NTEP-8B, significantly improves both search-oriented accuracy and tool-use efficiency within a unified three-tool framework. These results highlight the critical value of fine-grained tool-evidence path supervision for training robust agentic VLMs.

cs.AI↗