MathFlow: Enhancing the Perceptual Flow of MLLMs for Visual Mathematical Problems

Despite impressive performance across diverse tasks, Multimodal Large Language Models (MLLMs) have yet to fully demonstrate their potential in visual mathematical problem-solving, particularly in accurately perceiving and interpreting diagrams. Inspired by typical processes of humans, we hypothesize that the perception capabilities to extract meaningful information from diagrams is crucial, as it directly impacts subsequent inference processes. To validate this hypothesis, we developed FlowVerse, a comprehensive benchmark that categorizes all information used during problem-solving into four components, which are then combined into six problem versions for evaluation. Our preliminary results on FlowVerse reveal that existing MLLMs exhibit substantial limitations when extracting essential information and reasoned property from diagrams and performing complex reasoning based on these visual inputs. In response, we introduce MathFlow, a modular problem-solving pipeline that decouples perception and inference into distinct stages, thereby optimizing each independently. Given the perceptual limitations observed in current MLLMs, we trained MathFlow-P-7B as a dedicated perception model. Experimental results indicate that MathFlow-P-7B yields substantial performance gains when integrated with various closed-source and open-source inference models. This demonstrates the effectiveness of the MathFlow pipeline and its compatibility to diverse inference frameworks. The FlowVerse benchmark and code are available at https://github.com/MathFlow-zju/MathFlow.

PAPM: A Physics-aware Proxy Model for Process Systems

In the context of proxy modeling for process systems, traditional data-driven deep learning approaches frequently encounter significant challenges, such as substantial training costs induced by large amounts of data, and limited generalization capabilities. As a promising alternative, physics-aware models incorporate partial physics knowledge to ameliorate these challenges. Although demonstrating efficacy, they fall short in terms of exploration depth and universality. To address these shortcomings, we introduce a physics-aware proxy model (PAPM) that fully incorporates partial prior physics of process systems, which includes multiple input conditions and the general form of conservation relations, resulting in better out-of-sample generalization. Additionally, PAPM contains a holistic temporal-spatial stepping module for flexible adaptation across various process systems. Through systematic comparisons with state-of-the-art pure data-driven and physics-aware models across five two-dimensional benchmarks in nine generalization tasks, PAPM notably achieves an average performance improvement of 6.7%, while requiring fewer FLOPs, and just 1% of the parameters compared to the prior leading method. The code is available at https://github.com/pengwei07/PAPM.

DSAF: A Dual-Stage Adaptive Framework for Numerical Weather Prediction Downscaling

While widely recognized as one of the most substantial weather forecasting methodologies, Numerical Weather Prediction (NWP) usually suffers from relatively coarse resolution and inevitable bias due to tempo-spatial discretization, physical parametrization process, and computation limitation. With the roaring growth of deep learning-based techniques, we propose the Dual-Stage Adaptive Framework (DSAF), a novel framework to address regional NWP downscaling and bias correction tasks. DSAF uniquely incorporates adaptive elements in its design to ensure a flexible response to evolving weather conditions. Specifically, NWP downscaling and correction are well-decoupled in the framework and can be applied independently, which strategically guides the optimization trajectory of the model. Utilizing a multi-task learning mechanism and an uncertainty-weighted loss function, DSAF facilitates balanced training across various weather factors. Additionally, our specifically designed attention-centric learnable module effectively integrates geographic information, proficiently managing complex interrelationships. Experimental validation on the ECMWF operational forecast (HRES) and reanalysis (ERA5) archive demonstrates DSAF's superior performance over existing state-of-the-art models and shows substantial improvements when existing models are augmented using our proposed modules. Code is publicly available at https://github.com/pengwei07/DSAF.