arXiv subjects

Jiansheng Fan

Publications and source records attributed to Jiansheng Fan.

5 recordsLinked to original sources

arXiv2026

Beyond Arbitrary Geometry: Topology Generalization In neural PDE Operators

Neural operators that accept arbitrary meshes are often treated as geometry-general, but unseen domain topology changes both the invariant and decaying subspaces of a PDE operator. We use Hodge heat flow as a controlled lens on this distinction and introduce TopoBox-3D, where tunnels and cavities vary Betti support while the exact Hodge decomposition separates the harmonic kernel from the positive spectrum. Across six architectures, models that infer topology implicitly suffer excess matched degradation in 37 of 45 model--task topology-OOD cells, yet cases that change harmonic dimension are not more strongly penalized on average. The dominant difficulty is instead spectral: the initial Rayleigh quotient is the most stable predictor of error, and spectral broadening adds information for edge and face cochains. Most strikingly, controlled probes show that explicit incidence and harmonic coordinates do not yield the best kernel-identity accuracy; nevertheless, TNO ranks first in mixed-input nonharmonic accuracy on all six tasks with nontrivial harmonic support. Together, these results establish topology as a distinct generalization axis beyond arbitrary-geometry compatibility and show that its influence extends across the Hodge spectrum rather than remaining confined to the harmonic kernel. More broadly, they suggest that global, low-frequency structural priors may help organize predictions in the faster-decaying complementary component, offering a new perspective on how neural operators may generalize across topology as well as geometry.

cs.LG↗

arXiv2026

BlueprintAgent: Constraint-Triggered Targeted Revisits for Simulation-Ready Generation from Scanned Structural Blueprints

Converting in-service reinforced-concrete (RC) building blueprints into simulation-ready models---structured frame representations that support deterministic FEM export and qualified-engineer review---underpins safety assessment and seismic retrofit, but the process remains manual. Direct prompting of a multimodal large language model (MLLM) over a scanned sheet is unreliable: outputs often violate engineering constraints on beam--column support, span count, or 3D continuity. We present BlueprintAgent (BPA), a constraint-triggered multimodal agent for simulation-ready frame extraction from scanned blueprints. BPA treats the MLLM as the primary reader and decision maker, with OCR and computer vision supplying localized evidence. Its central mechanism realizes engineering constraints as callable validators whose entity-level conflict reports trigger targeted MLLM revisits over the local region---an inference-time control distinct from fixed pipelines and free-form self-reflection. We evaluate BPA on 300 real scanned blueprint sheets from 20 anonymized RC frame projects, against five baselines and six ablations. BPA reaches a macro-averaged Beam F1 of 0.994, against 0.301 for single-MLLM zero-shot and 0.820 for a fixed pipeline; removing MLLM-led axis adjudication collapses Beam and Column F1 on complex multi-sheet projects. For dense technical drawings, engineering constraints are best deployed as triggers for entity-level targeted revisits rather than as post-hoc output filters.

cs.CL↗

arXiv2026

Leakage-Free Evaluation and Distribution-Robust Spatio-Temporal Graph Learning for Inductive Kriging

Inductive kriging estimates values at unobserved locations from sparse sensor data, enabling continuous field reconstruction when dense deployment is impractical. However, common 2 x 2 and 2 x 3 evaluation protocols can leak spatial information through model selection and obscure true out-of-distribution (OOD) behavior. We propose a leakage-free 3 x 3 partition that separates training, validation, and testing in both space and time, so that model fitting, checkpoint selection, and final reporting are performed on distinct spatio-temporal domains. Under this stricter setting, we introduce DRIK (Distribution-Robust Inductive Kriging), a framework with three task-specific mechanisms: Spatial Continuity Regularization (SCR) perturbs coordinates to reduce dependence on one discretized graph; Masked Flow Disambiguation (MFD) prunes ambiguous propagation from zero-padded masked nodes; and Structural Domain Expansion (SDE) uses validation-node topology without labels to reduce train-inference structural mismatch. Experiments on six spatio-temporal datasets show that DRIK consistently outperforms state-of-the-art baselines, reducing MAE by up to 12.48% and achieving lower test-to-validation MAE ratios under leakage-free evaluation. These results indicate that robust inductive kriging requires both leakage-free evaluation and mechanisms that explicitly address the structural shifts introduced by unseen nodes.

cs.LG↗

arXiv2026

PhysMind: From Video to Executable Worlds for Training-Free Physical Reasoning

Reliable physical reasoning from video requires understanding how objects move, interact, and respond to interventions. Existing vision-language models (VLMs) often struggle to interpret these dynamics and reason reliably about future and counterfactual outcomes. We introduce PhysMind, a training-free agentic framework that constructs one reusable, question-agnostic executable world per video. PhysMind recovers a temporally consistent dynamic scene through object segmentation, mesh reconstruction, and 6D pose tracking, then fits analytic continuous-time dynamics and latent physical parameters without unrolling a time-stepped simulator. Given a question, it inspects, continues, or edits the world and answers from the resulting trajectories and interactions. Relative to direct chain-of-thought (CoT) reasoning with the same VLM, PhysMind improves accuracy by 38.23 points on CLEVRER and 8.08 points on Physion++. On counterfactual questions, it exceeds the strongest evaluated VLM baseline, GPT-5.5, by 19.25 points.

cs.CV↗

arXiv2026

Thinking in Structures: Evaluating Spatial Intelligence in Constraint-Governed Spaces

Spatial intelligence is crucial for vision--language models (VLMs), yet many scene-centric benchmarks evaluate unconstrained environments where a single image may admit multiple plausible 3D interpretations. We introduce SSI-Bench, a VQA benchmark for Structure-Centric Spatial Reasoning (SCSR) in constraint-governed spaces. Built from complex real-world 3D structures, it uses structural constraints from geometry, topology, and physical feasibility to make component relations more determinate from visual evidence. The benchmark contains 1,000 ranking questions spanning geometric and topological reasoning, where correct ordering requires resolving all candidate-wise 3D relations, imposing stronger demands on spatial understanding. It is created through a fully human-centered pipeline with over 400 researcher-hours of image curation, component annotation, and question design. Evaluating 31 VLMs reveals a large gap to humans: the best open-source model achieves 22.2% accuracy and the strongest closed-source model reaches 33.6%, while humans score 91.6%. Further results show that chain-of-thought reasoning brings only marginal gains, and error analysis reveals fundamental limitations in current models' spatial understanding within constraint-governed spaces. Project page: https://ssi-bench.github.io.

cs.CV↗