FAST-DeepONet: Factor-Augmented Branch Representations for High-Dimensional PDE Inputs in the Small-Sample Regime

Deep operator networks can become statistically unstable when partial differential equation inputs are observed at thousands of strongly correlated sensors but only a small number of operator samples is available. We introduce FAST-DeepONet, a branch representation combining a fixed spectral path with a regularized projection of the orthogonal residual, in which the directional penalty acts on the effective residual map after each of its rows is normalized. On Navier--Stokes flow a plain DeepONet degrades from $0.0394$ to $0.1556$ mean relative $L_2$ error as the branch grows from $129$ to $8193$ coordinates, while FAST-DeepONet stays near $0.04$, so the sensor grid can be refined without a statistical penalty. Across independent test sets for Navier--Stokes flow, Darcy flow, and signed terminal wavefield prediction it lowers mean relative $L_2$ error by $4.7\%$ to $37.0\%$ with three to seven times fewer trainable parameters. A spectral-only branch sharing the same basis separates the two paths: the fixed spectral path carries the improvement on Navier--Stokes and Darcy, while terminal wave prediction requires the residual path together with its directional penalty. FAST-DeepONet targets coordinate-query architectures and trains on solution values alone.

GraspMeanFlow: SE(3)-Equivariant MeanFlow for Few-Step 6-DoF Grasp Generation

Recent data-driven methods for synthesizing 6-DoF grasp poses use generative models to learn complex grasp pose distributions and generate diverse candidate poses. In particular, SE(3)-equivariant flow-based models generate grasp poses that transform consistently with object rotations and translations. However, these methods sample by iterative numerical integration, requiring tens of function evaluations per grasp and limiting their use in real-time manipulation. We propose GraspMeanFlow, an SE(3)-equivariant MeanFlow framework for few-step 6-DoF grasp generation. Our method learns the average velocity over a finite time interval, defined through the time-ordered exponential so that it reproduces exactly the rigid-body displacement accumulated over that interval. We prove that a point-cloud-conditioned distribution transported by an equivariant average-velocity flow map remains invariant, so equivariance is retained under few-step sampling, and we condition the field on a pair of times by lifting both to equivariant vectors, leaving the backbone otherwise unchanged. For stable training, we pair a flow-matching boundary term with either of two consistency terms: the differential MeanFlow identity, whose target requires a Jacobian-vector product, or an equivalent semigroup loss that avoids it. Experiments on ACRONYM show that a single function evaluation of GraspMeanFlow reaches the EMD that an iterative SE(3) flow model needs five steps to approach, that a second instantiation of the same framework improves grasp success by up to 24.3 points in the few-step regime, and that both generate grasp distributions transforming exactly with the object.

AIVV: Neuro-Symbolic LLM Agent-Integrated Verification and Validation for Trustworthy Autonomous Systems

Deep learning models excel at detecting anomaly patterns in normal data. However, they do not provide a direct solution for anomaly classification and scalability across diverse control systems, frequently failing to distinguish genuine faults from nuisance faults caused by noise or the control system's large transient response. Consequently, because algorithmic fault validation remains unscalable, full Verification and Validation (V\&V) operations are still managed by Human-in-the-Loop (HITL) analysis, resulting in an unsustainable manual workload. To automate this essential oversight, we propose Agent-Integrated Verification and Validation (AIVV), a hybrid framework that deploys Large Language Models (LLMs) as a deliberative outer loop. Because rigorous system verification strictly depends on accurate validation, AIVV escalates mathematically flagged anomalies to a role-specialized LLM council. The council agents perform collaborative validation by semantically validating nuisance and true failures based on natural-language (NL) requirements to secure a high-fidelity system-verification baseline. Building on this foundation, the council then performs system verification by assessing post-fault responses against NL operational tolerances, ultimately generating actionable V\&V artifacts, such as gain-tuning proposals. Experiments on a time-series simulator for Unmanned Underwater Vehicles (UUVs) demonstrate that AIVV successfully digitizes the HITL V\&V process, overcoming the limitations of rule-based fault classification and offering a scalable blueprint for LLM-mediated oversight in time-series data domains.

ATLAS : Adaptive Self-Evolutionary Research Agent with Task-Distributed Multi-LLM Supporters

Recent multi-LLM agent systems perform well in prompt optimization and automated problem-solving, but many either keep the solver frozen after fine-tuning or rely on a static preference-optimization loop, which becomes intractable for long-horizon tasks. We propose ATLAS (Adaptive Task-distributed Learning for Agentic Self-evolution), a task-distributed framework that iteratively develops a lightweight research agent while delegating complementary roles to specialized supporter agents for exploration, hyperparameter tuning, and reference policy management. Our core algorithm, Evolving Direct Preference Optimization (EvoDPO), adaptively updates the phase-indexed reference policy. We provide a theoretical regret analysis for a preference-based contextual bandit under concept drift. In addition, experiments were conducted on non-stationary linear contextual bandits and scientific machine learning (SciML) loss reweighting for the 1D Burgers' equation. Both results show that ATLAS improves stability and performance over a static single-agent baseline.