从不规则采样观测预测物理系统长期预测需要稳定、计算高效且无固定时间步假设的模型。本文提出连续时间Koopman自编码器，其潜在动态满足dz/dt = K_cont z，通过闭式推断实现任意时间 horizon τ 的单步预测。这将预测成本与预测长度解耦，并支持数据同化作为基于梯度的优化，其成本不依赖同化窗口。然而，将连续时间Koopman动力学扩展到高维混沌系统会导致潜在不稳定，包括谱崩溃和轨迹发散。相比之下，离散Koopman方法训练一个算子A，使得z_{t+Δt} = A z_t；恢复连续生成器理论上可通过矩阵对数实现，但需要未保证的条件，且近似误差随训练数据中施加的Δt增长。这些方法也要求固定、规则时间步。本文识别出一组经验有效的结构约束——rollout训练、前向-后向一致性、潜在正则化和物理条件化的LoRA——足以实现稳定长周期潜在动态。在具有挑战性的流体基准上，本文方法在长周期预测中优于强大的扩散和算子学习基线，同时实现了110倍的推理加速。
英文摘要：
Forward forecasting and data assimilation are the two important aspects in physical simulation: one propagates the state forward, the other recovers unknown states from sparse observations. Learned surrogates are normally built and benchmarked for forward forecasting, however, whether a surrogate could attain good performance in data assimilation tasks is valuable as well, as inverse problems are of paramount importance in the scientific domain. In this paper, we propose a continuous-time Koopman autoencoder whose latent dynamics obey $\frac{dz}{dt} = \mathbf{K}_{\mathrm{cont}} z$, yielding closed-form inference via $z(τ) = \exp(\mathbf{K}_{\mathrm{cont}} τ) z(0)$ at any horizon $τ$ in a single step. This decouples forecast cost from forecast length at inference time, showing long-term stability and high efficiency in forward simulation, and also supports data assimilation as gradient-based optimization with cost independent of the assimilation window. Experiments are performed on the Kuramoto--Sivashinsky equation and a transient flow, and we compare our method against a range of baselines on the forward problem, including diffusion models and operator-learning models, and obtain a 110x inference speedup over strong diffusion baselines. We further test these baselines on an initial-state inference data assimilation task, and find that a strong forecaster does not guarantee a strong assimilator, while the continuous-time Koopman autoencoder achieves both higher accuracy and efficiency than surrogates of comparable forward performance.
PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems
Hong Kong University of Science and Technology (Guangzhou)（香港理工大学（广州））；Hong Kong University of Science and Technology（香港理工大学）；Shandong University（山东大学）；University of Oxford（牛津大学）
Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferences
Fudan University（复旦大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；The Chinese University of Hong Kong（香港中文大学）；Shanghai Jiaotong University（上海交通大学）；Columbia University（哥伦比亚大学）
Latent assimilation with implicit neural representations for unknown dynamics
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Beijing International Center for Mathematical Research, Peking University（北京国际数学研究中心）；Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）；School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
Deterministic training of generative autoencoders using invertible layers
OnePlanet Research Center（壹星球研究中心）；imec-the Netherlands（荷兰微电子研究中心）；Donders Institute for Brain, Cognition and Behaviour（唐德斯脑、认知与行为研究所）；Radboud University（拉德堡德大学）；UvA-Bosch Delta Lab（阿姆斯特丹大学-博世三角洲实验室）
Accurate and Efficient Hybrid-Ensemble Atmospheric Data Assimilation in Latent Space with Uncertainty Quantification
Department of Earth and Environmental Engineering, School of Engineering and Applied Sciences, Climate School, Columbia University（地球与环境工程系，工程与应用科学学院，气候学院，哥伦比亚大学）；Learning the Earth with Artificial Intelligence and Physics (LEAP) Center, Columbia University（人工智能与物理学习地球中心，哥伦比亚大学）；Shanghai Artificial Intelligence Laboratory, Shanghai, China（上海人工智能实验室，上海，中国）；The Chinese University of Hong Kong, Hong Kong, China（香港中文大学，香港，中国）；Department of Computer Science and Technology, Tsinghua University, Beijing, China（计算机科学与技术系，清华大学，北京，中国）
Simplifying Flow Matching Transformations with Low-Rank Mixture Models
Stanford Intelligent Systems Laboratory in the Department of Aeronautics and Astronautics at Stanford University（斯坦福大学航空航天系智能系统实验室）；Industrial and Systems Engineering Department at King Fahd University of Petroleum and Minerals（科威特石油矿物大学工业与系统工程系）
An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties
Singapore-MIT Alliance for Research and Technology（新加坡-麻省理工学院研究与技术联盟）；National University of Singapore（新加坡国立大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Massachusetts Institute of Technology（麻省理工学院）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Agency for Science, Technology and Research（新加坡科技研究局）；Nanyang Technological University（南洋理工大学）；Shanghai University（上海大学）；Microsoft AI for Good（微软人工智能公益计划）；Toyota Research Institute（丰田研究院）；Tsinghua University（清华大学）
Identification of Nonlinear Latent Hierarchical Models
Carnegie Mellon University（卡内基梅隆大学）；University of California San Diego（加州大学圣迭戈分校）；Beijing Technology and Business University（北京工商大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
Latent Variable Modelling with Hyperbolic Normalizing Flows
McGill University（麦吉尔大学）；Mila（米拉研究所）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
近似后验分布的选择在随机变分推理（SVI）中起着核心作用。一个有效的解决方案是使用归一化流\cut{defined on Euclidean spaces}来构造灵活的后验分布。然而，现有的规范化流的一个关键限制是，它们被限制在欧几里德空间，并且不适合对具有底层层次结构的数据进行建模。为了解决这个基本的限制，我们提出了规范化流的双曲空间的第一个扩展。我们首先提升规范化流双曲空间使用耦合变换定义的切丛，称为切线耦合（$\mathcal{TC}$）。我们进一步介绍了包裹双曲面耦合（$\mathcal{W}\mathbb{H}C$），一个完全可逆的和可学习的变换，明确利用双曲空间的几何结构，允许表达后验，同时是有效的采样。我们证明了我们的新的归一化流的双曲VAE和欧几里得归一化流的功效。我们的方法提高了密度估计的性能，以及表现出分层结构的真实世界图数据的重建。最后，我们表明，我们的方法可以用来权力的生成模型在分层数据使用双曲型潜变量。
Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems
ShanghaiTech University（上海科技大学）；Changsha Institute for Computing and Digital Economy, Peking University（北京大学长沙计算与数字经济研究院）；Louisiana State University（路易斯安那州立大学）
Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Models
Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Carnegie Mellon University（卡内基梅隆大学）；Guangdong University of Technology（广东工业大学）；Beijing Technology and Business University（北京工商大学）；University of Illinois Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校）；Johns Hopkins University（约翰斯·霍普金斯大学）
