计算工程、金融与科学：2025–2026 年度综述

An annual survey of the cs.CE arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 120 papers and organised into 44 chapters, it maps the year by the field's research sub-directions.

Book framework (share of the year's output):

• LLM Agents for Financial and Scientific Reasoning (14.8%) — Develops multi-agent LLM frameworks and benchmarks for trustworthy reasoning in financial markets, materials discovery, and complex chart interpretation.
• Physics-Informed Neural Networks for Simulation (13.4%) — Applies physics-informed and graph neural networks to solve forward and inverse problems in mechanics, energy systems, and spatial prediction.
• Data-Driven Frameworks for Scientific Discovery (12.1%) — Constructs data assimilation, sensor placement, and automated reporting frameworks to accelerate scientific research and engineering design workflows.
• Generative Modeling for Flow and Structure (11.6%) — Utilizes flow matching and diffusion models for high-dimensional spatio-temporal modeling and multi-physics co-simulation in engineering systems.
• Optimization and Topology Design Methods (10.2%) — Advances topology, shape, and portfolio optimization algorithms under uncertainty for manufacturing, facility layout, and material design.
• Foundation Models for Prediction and Reduction (9.1%) — Leverages foundation models and reduced-order modeling techniques for predictive analytics in behavioral, structural, and systemic risk contexts.
• Scientific Machine Learning Algorithms (8.7%) — Evaluates and improves deep reinforcement and probabilistic learning methods for PDE solving, turbulence modeling, and sensitivity analysis.
• Finite Element and Numerical Simulation Methods (7.8%) — Enhances finite element analysis, homogenization, and HPC kernels for dynamic simulations and low-resource computational tasks.
• Time Series Forecasting and Quantum Applications (6.2%) — Develops diffusion and causal discovery models for financial time series forecasting and explores quantum computing for energy materials.
• Large Language Models in Finance and Science (6.2%) — Fine-tunes large language models for financial trend analysis, credit risk assessment, and scientific domain-specific tasks like alloy design.

Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.