Scale-PINN: Learning Efficient Physics-Informed Neural Networks Through Sequential Correction

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern numerical solvers. We introduce the Sequential Correction Algorithm for Learning Efficient PINN (Scale-PINN), a learning strategy that bridges modern physics-informed learning with numerical algorithms. Scale-PINN incorporates the iterative residual-correction principle, a cornerstone of numerical solvers, directly into the loss formulation, marking a paradigm shift in how PINN losses can be conceived and constructed. This integration enables Scale-PINN to achieve unprecedented convergence speed across PDE problems from different physics domain, including reducing training time on a challenging fluid-dynamics problem for state-of-the-art PINN from hours to sub-2 minutes while maintaining superior accuracy, and enabling application to representative problems in aerodynamics and urban science. By uniting the rigor of numerical methods with the flexibility of deep learning, Scale-PINN marks a significant leap toward the practical adoption of PINNs in science and engineering through scalable, physics-informed learning. Codes are available at https://github.com/chiuph/SCALE-PINN.

Information Fidelity in Tool-Using LLM Agents: A Martingale Analysis of the Model Context Protocol

As AI agents powered by large language models (LLMs) increasingly use external tools for high-stakes decisions, a critical reliability question arises: how do errors propagate across sequential tool calls? We introduce the first theoretical framework for analyzing error accumulation in Model Context Protocol (MCP) agents, proving that cumulative distortion exhibits linear growth and high-probability deviations bounded by $O(\sqrt{T})$. This concentration property ensures predictable system behavior and rules out exponential failure modes. We develop a hybrid distortion metric combining discrete fact matching with continuous semantic similarity, then establish martingale concentration bounds on error propagation through sequential tool interactions. Experiments across Qwen2-7B, Llama-3-8B, and Mistral-7B validate our theoretical predictions, showing empirical distortion tracks the linear trend with deviations consistently within $O(\sqrt{T})$ envelopes. Key findings include: semantic weighting reduces distortion by 80\%, and periodic re-grounding approximately every 9 steps suffices for error control. We translate these concentration guarantees into actionable deployment principles for trustworthy agent systems.

Agentic Spatio-Temporal Grounding via Collaborative Reasoning

Spatio-Temporal Video Grounding (STVG) aims to retrieve the spatio-temporal tube of a target object or person in a video given a text query. Most existing approaches perform frame-wise spatial localization within a predicted temporal span, resulting in redundant computation, heavy supervision requirements, and limited generalization. Weakly-supervised variants mitigate annotation costs but remain constrained by the dataset-level train-and-fit paradigm with an inferior performance. To address these challenges, we propose the Agentic Spatio-Temporal Grounder (ASTG) framework for the task of STVG towards an open-world and training-free scenario. Specifically, two specialized agents SRA (Spatial Reasoning Agent) and TRA (Temporal Reasoning Agent) constructed leveraging on modern Multimoal Large Language Models (MLLMs) work collaboratively to retrieve the target tube in an autonomous and self-guided manner. Following a propose-and-evaluation paradigm, ASTG duly decouples spatio-temporal reasoning and automates the tube extraction, verification and temporal localization processes. With a dedicate visual memory and dialogue context, the retrieval efficiency is significantly enhanced. Experiments on popular benchmarks demonstrate the superiority of the proposed approach where it outperforms existing weakly-supervised and zero-shot approaches by a margin and is comparable to some of the fully-supervised methods.

Landscape-aware Automated Algorithm Design: An Efficient Framework for Real-world Optimization

The advent of Large Language Models (LLMs) has opened new frontiers in automated algorithm design, giving rise to numerous powerful methods. However, these approaches retain critical limitations: they require extensive evaluation of the target problem to guide the search process, making them impractical for real-world optimization tasks, where each evaluation consumes substantial computational resources. This research proposes an innovative and efficient framework that decouples algorithm discovery from high-cost evaluation. Our core innovation lies in combining a Genetic Programming (GP) function generator with an LLM-driven evolutionary algorithm designer. The evolutionary direction of the GP-based function generator is guided by the similarity between the landscape characteristics of generated proxy functions and those of real-world problems, ensuring that algorithms discovered via proxy functions exhibit comparable performance on real-world problems. Our method enables deep exploration of the algorithmic space before final validation while avoiding costly real-world evaluations. We validated the framework's efficacy across multiple real-world problems, demonstrating its ability to discover high-performance algorithms while substantially reducing expensive evaluations. This approach shows a path to apply LLM-based automated algorithm design to computationally intensive real-world optimization challenges.

From Pixels to Facts (Pix2Fact): Benchmarking Multi-Hop Reasoning for Fine-Grained Visual Fact Checking

Despite progress on general tasks, VLMs struggle with challenges demanding both detailed visual grounding and deliberate knowledge-based reasoning, a synergy not captured by existing benchmarks that evaluate these skills separately. To close this gap, we introduce Pix2Fact, a new visual question-answering benchmark designed to evaluate expert-level perception and knowledge-intensive multi-hop reasoning. Pix2Fact contains 1,000 high-resolution (4K+) images spanning 8 daily-life scenarios and situations, with questions and answers meticulously crafted by annotators holding PhDs from top global universities working in partnership with a professional data annotation firm. Each question requires detailed visual grounding, multi-hop reasoning, and the integration of external knowledge to answer. Our evaluation of 9 state-of-the-art VLMs, including proprietary models like Gemini-3-Pro and GPT-5, reveals the substantial challenge posed by Pix2Fact: the most advanced model achieves only 24.0% average accuracy, in stark contrast to human performance of 56%. This significant gap underscores the limitations of current models in replicating human-level visual comprehension. We believe Pix2Fact will serve as a critical benchmark to drive the development of next-generation multimodal agents that combine fine-grained perception with robust, knowledge-based reasoning.

Out-of-Distribution Generalization for Neural Physics Solvers

Neural physics solvers are increasingly used in scientific discovery, given their potential for rapid in silico insights into physical, materials, or biological systems and their long-time evolution. However, poor generalization beyond their training support limits exploration of novel designs and long-time horizon predictions. We introduce NOVA, a route to generalizable neural physics solvers that can provide rapid, accurate solutions to scenarios even under distributional shifts in partial differential equation parameters, geometries and initial conditions. By learning physics-aligned representations from an initial sparse set of scenarios, NOVA consistently achieves 1-2 orders of magnitude lower out-of-distribution errors than data-driven baselines across complex, nonlinear problems including heat transfer, diffusion-reaction and fluid flow. We further showcase NOVA's dual impact on stabilizing long-time dynamical rollouts and improving generative design through application to the simulation of nonlinear Turing systems and fluidic chip optimization. Unlike neural physics solvers that are constrained to retrieval and/or emulation within an a priori space, NOVA enables reliable extrapolation beyond known regimes, a key capability given the need for exploration of novel hypothesis spaces in scientific discovery

Parametric Expensive Multi-Objective Optimization via Generative Solution Modeling

Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This gives rise to parametric expensive multi-objective optimization problems (P-EMOPs) where each task parameter defines a distinct optimization instance. Current multi-objective Bayesian optimization methods have been widely used for finding finite sets of Pareto optimal solutions for individual tasks. However, P-EMOPs present a fundamental challenge: the continuous task parameter space can contain infinite distinct problems, each requiring separate expensive evaluations. This demands learning an inverse model that can directly predict optimized solutions for any task-preference query without expensive re-evaluation. This paper introduces the first parametric multi-objective Bayesian optimizer that learns this inverse model by alternating between (1) acquisition-driven search leveraging inter-task synergies and (2) generative solution sampling via conditional generative models. This approach enables efficient optimization across related tasks and finally achieves direct solution prediction for unseen parameterized EMOPs without additional expensive evaluations. We theoretically justify the faster convergence by leveraging inter-task synergies through task-aware Gaussian processes. Meanwhile, empirical studies in synthetic and real-world benchmarks further verify the effectiveness of our alternating framework.

NeuSpring: Neural Spring Fields for Reconstruction and Simulation of Deformable Objects from Videos

In this paper, we aim to create physical digital twins of deformable objects under interaction. Existing methods focus more on the physical learning of current state modeling, but generalize worse to future prediction. This is because existing methods ignore the intrinsic physical properties of deformable objects, resulting in the limited physical learning in the current state modeling. To address this, we present NeuSpring, a neural spring field for the reconstruction and simulation of deformable objects from videos. Built upon spring-mass models for realistic physical simulation, our method consists of two major innovations: 1) a piecewise topology solution that efficiently models multi-region spring connection topologies using zero-order optimization, which considers the material heterogeneity of real-world objects. 2) a neural spring field that represents spring physical properties across different frames using a canonical coordinate-based neural network, which effectively leverages the spatial associativity of springs for physical learning. Experiments on real-world datasets demonstrate that our NeuSping achieves superior reconstruction and simulation performance for current state modeling and future prediction, with Chamfer distance improved by 20% and 25%, respectively.

Distributional Multi-objective Black-box Optimization for Diffusion-model Inference-time Multi-Target Generation

Diffusion models have been successful in learning complex data distributions. This capability has driven their application to high-dimensional multi-objective black-box optimization problem. Existing approaches often employ an external optimization loop, such as an evolutionary algorithm, to the diffusion model. However, these approaches treat the diffusion model as a black-box refiner, which overlooks the internal distribution transition of the diffusion generation process, limiting their efficiency. To address these challenges, we propose the Inference-time Multi-target Generation (IMG) algorithm, which optimizes the diffusion process at inference-time to generate samples that simultaneously satisfy multiple objectives. Specifically, our IMG performs weighted resampling during the diffusion generation process according to the expected aggregated multi-objective values. This weighted resampling strategy ensures the diffusion-generated samples are distributed according to our desired multi-target Boltzmann distribution. We further derive that the multi-target Boltzmann distribution has an interesting log-likelihood interpretation, where it is the optimal solution to the distributional multi-objective optimization problem. We implemented IMG for a multi-objective molecule generation task. Experiments show that IMG, requiring only a single generation pass, achieves a significantly higher hypervolume than baseline optimization algorithms that often require hundreds of diffusion generations. Notably, our algorithm can be viewed as an optimized diffusion process and can be integrated into existing methods to further improve their performance.

Lightweight and Accurate Multi-View Stereo with Confidence-Aware Diffusion Model

To reconstruct the 3D geometry from calibrated images, learning-based multi-view stereo (MVS) methods typically perform multi-view depth estimation and then fuse depth maps into a mesh or point cloud. To improve the computational efficiency, many methods initialize a coarse depth map and then gradually refine it in higher resolutions. Recently, diffusion models achieve great success in generation tasks. Starting from a random noise, diffusion models gradually recover the sample with an iterative denoising process. In this paper, we propose a novel MVS framework, which introduces diffusion models in MVS. Specifically, we formulate depth refinement as a conditional diffusion process. Considering the discriminative characteristic of depth estimation, we design a condition encoder to guide the diffusion process. To improve efficiency, we propose a novel diffusion network combining lightweight 2D U-Net and convolutional GRU. Moreover, we propose a novel confidence-based sampling strategy to adaptively sample depth hypotheses based on the confidence estimated by diffusion model. Based on our novel MVS framework, we propose two novel MVS methods, DiffMVS and CasDiffMVS. DiffMVS achieves competitive performance with state-of-the-art efficiency in run-time and GPU memory. CasDiffMVS achieves state-of-the-art performance on DTU, Tanks & Temples and ETH3D. Code is available at: https://github.com/cvg/diffmvs.