Peizhi Zhao

Tzu-Yen Ma, Bo Zhang, Zichen Tang et al. · princeton

We present THEMIS, a novel multi-task benchmark designed to comprehensively evaluate multimodal large language models (MLLMs) on visual fraud reasoning within real-world academic scenarios. Compared to existing benchmarks, THEMIS introduces three major advances. (1) Real-World Scenarios and Complexity: Our benchmark comprises over 4,000 questions spanning seven scenarios, derived from authentic retracted-paper cases and carefully curated multimodal synthetic data. With 60.47% complex-texture images, THEMIS bridges the critical gap between existing benchmarks and the complexity of real-world academic fraud. (2) Fraud-Type Diversity and Granularity: THEMIS systematically covers five challenging fraud types and introduces 16 fine-grained manipulation operations. On average, each sample undergoes multiple stacked manipulation operations, with the diversity and difficulty of these manipulations demanding a high level of visual fraud reasoning from the models. (3) Multi-Dimensional Capability Evaluation: We establish a mapping from fraud types to five core visual fraud reasoning capabilities, thereby enabling an evaluation that reveals the distinct strengths and specific weaknesses of different models across these core capabilities. Experiments on 16 leading MLLMs show that even the best-performing model, GPT-5, achieves an overall performance of only 56.15%, demonstrating that our benchmark presents a stringent test. We expect THEMIS to advance the development of MLLMs for complex, real-world fraud reasoning tasks.

Zichen Tang, Haihong E, Rongjin Li et al.

We introduce FinMMDocR, a novel bilingual multimodal benchmark for evaluating multimodal large language models (MLLMs) on real-world financial numerical reasoning. Compared to existing benchmarks, our work delivers three major advancements. (1) Scenario Awareness: 57.9% of 1,200 expert-annotated problems incorporate 12 types of implicit financial scenarios (e.g., Portfolio Management), challenging models to perform expert-level reasoning based on assumptions; (2) Document Understanding: 837 Chinese/English documents spanning 9 types (e.g., Company Research) average 50.8 pages with rich visual elements, significantly surpassing existing benchmarks in both breadth and depth of financial documents; (3) Multi-Step Computation: Problems demand 11-step reasoning on average (5.3 extraction + 5.7 calculation steps), with 65.0% requiring cross-page evidence (2.4 pages average). The best-performing MLLM achieves only 58.0% accuracy, and different retrieval-augmented generation (RAG) methods show significant performance variations on this task. We expect FinMMDocR to drive improvements in MLLMs and reasoning-enhanced methods on complex multimodal reasoning tasks in real-world scenarios.

Sen Wang, Peizhi Zhao, Qinglong Ma et al.

Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the field of PINN. The solution of singular perturbation problems often exhibits sharp boundary layers and steep gradients, and traditional PINN cannot achieve approximation of boundary layers. In this manuscript, we propose the General-Kindred Physics-Informed Neural Network (GKPINN) for solving Singular Perturbation Differential Equations (SPDEs). This approach utilizes asymptotic analysis to acquire prior knowledge of the boundary layer from the equation and establishes a novel network to assist PINN in approximating the boundary layer. It is compared with traditional PINN by solving examples of one-dimensional, two-dimensional, and time-varying SPDE equations. The research findings underscore the exceptional performance of our novel approach, GKPINN, which delivers a remarkable enhancement in reducing the $L_2$ error by two to four orders of magnitude compared to the established PINN methodology. This significant improvement is accompanied by a substantial acceleration in convergence rates, without compromising the high precision that is critical for our applications. Furthermore, GKPINN still performs well in extreme cases with perturbation parameters of ${1\times10}^{-38}$, demonstrating its excellent generalization ability.

Sen Wang, Peizhi Zhao, Tao Song

Solving Singularly Perturbed Differential Equations (SPDEs) presents challenges due to the rapid change of their solutions at the boundary layer. In this manuscript, We propose Asymptotic Physics-Informed Neural Networks (ASPINN), a generalization of Physics-Informed Neural Networks (PINN) and General-Kindred Physics-Informed Neural Networks (GKPINN) approaches. This is a decomposition method based on the idea of asymptotic analysis. Compared to PINN, the ASPINN method has a strong fitting ability for solving SPDEs due to the placement of exponential layers at the boundary layer. Unlike GKPINN, ASPINN lessens the number of fully connected layers, thereby reducing the training cost more effectively. Moreover, ASPINN theoretically approximates the solution at the boundary layer more accurately, which accuracy is also improved compared to GKPINN. We demonstrate the effect of ASPINN by solving diverse classes of SPDEs, which clearly shows that the ASPINN method is promising in boundary layer problems. Furthermore, we introduce Chebyshev Kolmogorov-Arnold Networks (Chebyshev-KAN) instead of MLP, achieving better performance in various experiments.

Qinglong Ma, Peizhi Zhao, Sen Wang et al.

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success, such as neural operators. However, the ability of various neural operator solvers to learn low-frequency information still needs improvement. In this study, we propose a Deep Parallel Spectral Neural Operator (DPNO) to enhance the ability to learn low-frequency information. Our method enhances the neural operator's ability to learn low-frequency information through parallel modules. In addition, due to the presence of truncation coefficients, some high-frequency information is lost during the nonlinear learning process. We smooth this information through convolutional mappings, thereby reducing high-frequency errors. We selected several challenging partial differential equation datasets for experimentation, and DPNO performed exceptionally well. As a neural operator, DPNO also possesses the capability of resolution invariance.

Junpeng Ding, Zichen Tang, Haihong E et al.

We introduce SPUR, a comprehensive benchmark for scientific experimental image perception, understanding, and reasoning, comprising 4,264 question-answering (QA) pairs derived from 1,084 expert-curated images. SPUR features three key innovations: (1) Panel-Level Fine-Grained Perception: evaluating the visual perception of multimodal large language models (MLLMs) across three dimensions (numerical, morphological, and information localization) on six fine-grained panel types; (2) Cross-Panel Relation Understanding: utilizing complex images with an average of 14.3 panels per sample to evaluate MLLMs' ability to decipher intricate cross-panel relations; (3) Expert-Level Reasoning: assessment of qualitative and quantitative reasoning across five experimental paradigms to determine if models can infer conclusions from evidence as human experts do. Comprehensive evaluation of 20 MLLMs and four multimodal Chain-of-Thought (MCoT) methods reveals that current models fall significantly short of the expert-level requirements for scientific image interpretation, underscoring a critical bottleneck in AI for Science (AI4S) research.