Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE.

A.3 Formulation of bound constrained dual problem Proposition 1 . For any non-negative p, q, we generate a feasible p ˆ, ˆ q as follows. In Section 5.3, we describe that it can be helpful to regularize We also mention here a minor difference in derivations for convenience of readers. As expected, this term also appears in these other formulations [ 25, 42 ]. All experiments run on a single P100 GPU. This adjustment was not necessary for CNN experiments.

The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing, respectively.

Geological Reservoir: " Kimberlina Family " is built under DOE's National Risk Assessment Program

Forecasting in real-world settings requires models to integrate not only historical data but also relevant contextual information, often available in textual form. While recent work has shown that large language models (LLMs) can be effective context-aided forecasters via naïve direct prompting, their full potential remains underexplored. We address this gap with 4 strategies, providing new insights into the zero-shot capabilities of LLMs in this setting. ReDP improves interpretability by eliciting explicit reasoning traces, allowing us to assess the model's reasoning over the context independently from its forecast accuracy. CorDP leverages LLMs solely to refine existing forecasts with context, enhancing their applicability in real-world forecasting pipelines. IC-DP proposes embedding historical examples of context-aided forecasting tasks in the prompt, substantially improving accuracy even for the largest models. Finally, RouteDP optimizes resource efficiency by using LLMs to estimate task difficulty, and routing the most challenging tasks to larger models. Evaluated on different kinds of context-aided forecasting tasks from the CiK benchmark, our strategies demonstrate distinct benefits over naïve prompting across LLMs of different sizes and families. These results open the door to further simple yet effective improvements in LLM-based context-aided forecasting. 1

This paper presents an object-aware whole-body bilateral teleoperation framework for wheeled humanoid loco-manipulation. This framework combines whole-body bilateral teleoperation with an online multi-stage object inertial parameter estimation module, which is the core technical contribution of this work. The multi-stage process sequentially integrates a vision-based object size estimator, an initial parameter guess generated by a large vision-language model (VLM), and a decoupled hierarchical sampling strategy. The visual size estimate and VLM prior offer a strong initial guess of the object's inertial parameters, significantly reducing the search space for sampling-based refinement and improving the overall estimation speed. A hierarchical strategy first estimates mass and center of mass, then infers inertia from object size to ensure physically feasible parameters, while a decoupled multi-hypothesis scheme enhances robustness to VLM prior errors. Our estimator operates in parallel with high-fidelity simulation and hardware, enabling real-time online updates. The estimated parameters are then used to update the wheeled humanoid's equilibrium point, allowing the operator to focus more on locomotion and manipulation. This integration improves the haptic force feedback for dynamic synchronization, enabling more dynamic whole-body teleoperation. By compensating for object dynamics using the estimated parameters, the framework also improves manipulation tracking while preserving compliant behavior. We validate the system on a customized wheeled humanoid with a robotic gripper and human-machine interface, demonstrating real-time execution of lifting, delivering, and releasing tasks with a payload weighing approximately one-third of the robot's body weight.