论文库

Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation. While recent geometry-adaptive neural operators have made substantial progress, they are mainly designed for forward problems in which inputs and outputs share the same spatial domain. This limits their applicability for boundary value problems (BVPs) and inverse problems, where inputs and outputs may live on different domains. We introduce the Geometry-Adaptive Integral Autoencoder (GAIA), an operator learning model that encodes the domain boundary and the interior field distribution into geometry tokens, and conditions integral transform layers on these tokens via cross-attention, allowing the kernel to adapt locally to geometric features. This yields an architecture capable of learning solution operators for forward and inverse problems on arbitrary domains, solving each in a single pass at inference without per-domain optimization, iterative refinement, or graph construction. We evaluate GAIA on seven 2D and 3D benchmarks, four of which are new or substantially extended benchmarks for inverse problems and BVP: electrical impedance tomography, optical tomography, 3D Darcy flow on varying geometries, and a modified setting of the Poisson BVP on mechanical components benchmark (MCB). GAIA sets new state-of-the-art results on every inverse and BVP task, reducing median relative $L^2$ error by 64% on airfoil flow reconstruction and 22% on EIT relative to the next best amortized method, and outperforming all baselines on every shape category of MCB. On other forward problems, GAIA is competitive with specialized solvers while maintaining stable accuracy across point resolutions on which transformer-based baselines degrade.

We introduce Sage-Taiyi, a metacognition-inspired architecture that uses accumulated scientific understanding to guide what to investigate next and how to investigate it. Through explicit monitoring and control, the system revises its understanding of evidence, assumptions, and unresolved questions, then uses these assessments to adapt research targets and select reusable reasoning methods. On Taiyi-Bench, an AI co-scientist ideation benchmark comprising 265 tasks from 50 papers across ten disciplines, Sage-Taiyi ranks first on all eight metrics of historical rediscovery and open-ended ideation, achieving an Overall score of 54.0 compared with 47.9 for the strongest baseline, AI Scientist-v2. It also performs well on two external scientific ideation benchmarks. Five expert-guided collaborations further connect its proposals to experimental and computational validation across chemistry, materials science, and engineering. In chemistry, reaction-condition optimization raises the yield of cobalt-catalyzed carbonylation from trace amounts to 84% and photocatalytic allylic amination from 13% to 69%. These results support metacognitive regulation as an approach to scientific ideation and its progression toward practical validation.

Vision-Language-Action models (VLAs) enable general-purpose embodied intelligence, but their performance is brittle under distribution shift, where unanticipated failures can damage equipment or endanger people. Deploying VLAs in real-world systems therefore requires a runtime monitor that is timely, calibrated, and informative while being efficient enough to run on the edge. Existing methods fail to fulfill these requirements. We present VLA-Tug, a lightweight probe over the latent layers of a VLA backbone that improves early failure detection and bounds the missed-detection and false-alarm rates, with minimal inference overhead. We show that supervising on the pre-failure segment of a trajectory increases early failure detection at matched false-positive rates by up to 30% over the strongest learned baseline. Under shift to unseen tasks, the bounds on missed-detection and false-alarm rates remain valid in up to 86% of runs, versus at most 21% for baselines. Unlike existing methods, VLA-Tug predicts the failure mode to enable corrective actions, raising top-3 accuracy on unseen tasks by up to 44% over a majority baseline. VLA-Tug enables real-time monitoring where the well-timed and informative probe supports lightweight steering that improves task success. We release a dataset of 3,180 annotated manipulation episodes to support future work on latent failure detection in VLAs at https://vla-tug.github.io.

Mathematical modeling turns an open-ended real-world problem into assumptions, a model, a solution, and a defended recommendation, and its answers matter only if they are both close to a credible reference and physically feasible; existing benchmarks either score solver fragments or grade reports with an LLM judge, leaving those numbers unchecked. We introduce TB-MathModel (the Terminal-style Mathematical Modeling Bench), the first benchmark to make complete contest-style modeling problems agentic, verifiable, and terminal at once, over 18 real CUMCM and MCM problems (2023--2025). Each task ships the verbatim statement, official attachments, and figures in a containerized terminal; the agent returns one JSON artifact, scored on the numeric core of the final question against a reproduction of the Outstanding-award paper. Two design choices distinguish it: direction-aware, one-sided scoring, which never penalises beating the anchor, and two-layer feasibility verification---a programmatic gate over six decidable invariant forms plus 624 Lean~4 obligations---with a hard gate that zeroes infeasible answers. Each task is scored against a panel of human outstanding papers rather than one, so a model must be close to many accepted answers; across seven multimodal entries (three seeds each) the strongest reach a multi-reference O-Eval of 64.58\%, while the \$2.54 open model holds 59.81\% at $1/100$ the cost. TB-MathModel turns the numeric core of modeling into a reproducible, machine-checkable signal for measuring long-horizon modeling competence and for collecting agent trajectories. The source code is available at https://github.com/wxj630/terminal-bench-math-modeling.

Self-Driving Chemical Laboratories (SDCLs) are moving chemical experimentation toward embodied automation, where machines must perceive laboratory scenes, reason about experimental states, and act under physical, procedural, and safety constraints. Although Multimodal Large Language Models (MLLMs) are increasingly considered as embodied brains for such systems, existing laboratory benchmarks mainly focus on safety, anomaly detection, or general scientific understanding, leaving their execution-oriented embodied capabilities underexplored. To fill this gap, we introduce BEAKER, a Benchmark for evaluating Embodied Actionability, Knowledge, Experimentation, and Reasoning in SDCLs. BEAKER contains 1,000 expert-curated question-answer samples across 11 image and video task types, covering key judgments required for chemical laboratory execution, including affordance grounding, trajectory planning, equipment, state, and safety recognition, apparatus setup, operation and step reasoning, and temporal procedure reasoning. All questions and annotations are manually created and reviewed by chemistry and embodied Artificial Intelligence (AI) experts, without AI-assisted generation or annotation. We evaluate 28 general-purpose, science-oriented, chemistry-specialized, and embodied MLLMs in an offline, single-turn setting. Results show that current models can follow coarse experimental procedures in videos, but still struggle to ground actions into operable regions and feasible trajectories, to recognize fine-grained laboratory apparatus, states, and safety norms, and to order steps in mid-length procedures. BEAKER thus reveals a clear gap between coarse procedural understanding and the precise, action-grounded perception required for laboratory execution, providing a diagnostic benchmark for future MLLMs in SDCLs.