我们提出了DiffusionRollout，一种针对自回归扩散模型的新型选择性rollout规划策略，旨在减轻物理系统由偏微分方程（PDEs） govern 的长时间预测中的误差累积。基于最近已验证的PDE求解概率方法，我们进一步探索其量化预测不确定性的能力，并展示了预测误差与多个样本计算出的标准差之间的强相关性，支持其作为模型预测信心的代理。基于这一观察，我们引入了一种机制，在自回归rollout过程中自适应地选择步长，通过减少对不准确先验输出的依赖，提高长期预测的可靠性。在长时间轨迹PDE预测基准上的广泛评估验证了所提出不确定性度量和自适应规划策略的有效性，这体现在更低的预测误差和更长的预测轨迹，这些轨迹与真实值保持高相关性。
英文摘要：
We propose DiffusionRollout, a novel selective rollout planning strategy for autoregressive diffusion models, aimed at mitigating error accumulation in long-horizon predictions of physical systems governed by partial differential equations (PDEs). Building on the recently validated probabilistic approach to PDE solving, we further explore its ability to quantify predictive uncertainty and demonstrate a strong correlation between prediction errors and standard deviations computed over multiple samples-supporting their use as a proxy for the model's predictive confidence. Based on this observation, we introduce a mechanism that adaptively selects step sizes during autoregressive rollouts, improving long-term prediction reliability by reducing the compounding effect of conditioning on inaccurate prior outputs. Extensive evaluation on long-trajectory PDE prediction benchmarks validates the effectiveness of the proposed uncertainty measure and adaptive planning strategy, as evidenced by lower prediction errors and longer predicted trajectories that retain a high correlation with their ground truths.
Gradient-Informed Temporal Sampling Improves Rollout Accuracy in PDE Surrogate Training
School of Future Technology, South China University of Technology, China（未来技术学院，华南理工大学，中国）；State Key Laboratory of Ocean Sensing & Ocean College, Zhejiang University, China（海洋感知国家重点实验室及海洋学院，浙江大学，中国）；Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, USA（天体物理与空间研究所，麻省理工学院，美国）
Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions
Department of Computer Science, Florida State University（佛罗里达州立大学计算机科学系）；Department of Materials Science and Engineering, Florida State University（佛罗里达州立大学材料科学与工程系）；Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校石油与地质系统工程系）
Autoregression-Free Neural Operators for Time-Dependent PDEs
School of Computer Science and Engineering, University of Electronic Science and Technology of China（电子科技大学计算机科学与工程学院）；School of Robotics and Advanced Manufacture, Harbin Institute of Technology（哈尔滨工业大学机器人与先进制造学院）；School of Mathematical Sciences, Capital Normal University（首都师范大学数学学院）；College of Information and Control Engineering, Xi’an University of Architecture and Technology（西安建筑科技大学信息与控制工程学院）；Laboratory of Intelligent Recognition and Image Processing, School of Computer Science and Engineering, Beihang University（北京航空航天大学智能识别与图像处理实验室）；School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）
HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators
School of Computer Science and Engineering, UESTC（电子科技大学计算机科学与工程学院）；Electronics and Information Convergence Engineering, KHU（明知大学电子信息融合工程系）；Department of Mathematical Sciences, UOL（利物浦大学数学科学系）；School of Computer Science and Technology, XDU（西安电子科技大学计算机科学与技术学院）；School of Mechanical and Electrical Engineering, UESTC（电子科技大学机械与电气工程学院）；College of Computer and Information Engineering, XAUAT（西安建筑科技大学计算机与信息工程学院）
Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction
School of Information and Software Engineering, UESTC（电子科技大学信息与软件工程学院）；Electronics and Information Convergence Engineering, KHU（韩国庆熙大学电子与信息融合工程系）；School of Computer Science and Engineering, UESTC（电子科技大学计算机科学与工程学院）；Department of Mathematical Sciences, UOL（利物浦大学数学科学系）；School of Computer Science and Technology, XDU（西安电子科技大学计算机科学与技术学院）；School of Mechanical and Electrical Engineering, UESTC（电子科技大学机械与电气工程学院）；College of Computer and Information Engineering, XAUAT（西安建筑科技大学计算机与信息工程学院）
Wavelet Flow Matching for Multi-Scale Physics Emulation
Department of Earth and Environmental Engineering（地球与环境工程系）；Columbia University（哥伦比亚大学）；University of Edinburgh（爱丁堡大学）；Courant Institute of Mathematical Sciences（数学科学学院）；New York University（纽约大学）；Scripps Institution of Oceanography（斯克里普斯海洋研究所）；Halıcıoğlu Data Science Institute（哈利奇数据科学研究所）；University of California San Diego（加州大学圣地亚哥分校）；CUNY New York City College of Technology（纽约市立大学纽约技术学院）；Lamont-Doherty Earth Observatory（拉蒙特-多伊蒂地球观测站）
System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting
School of Future Technology, South China University of Technology（华南理工大学未来技术学院）；State Key Laboratory of Ocean Sensing & Ocean College, Zhejiang University（浙江大学海洋学院海洋传感国家重点实验室）；Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理与空间研究所）
CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operators
Graduate Group in Applied Mathematics and Computational Science（应用数学与计算科学联合研究生组）；Department of Mechanical Engineering and Applied Mechanics（机械工程与应用力学系）
