Dynamical systems governed by ordinary differential equations (ODEs) serve as models for a vast number of natural and social phenomena. In this work, we offer a fresh perspective on the classical problem of imputing missing time series data, whose underlying dynamics are assumed to be determined by ODEs. Specifically, we revisit ideas from amortized inference and neural operators, and propose a novel supervised learning framework for zero-shot time series imputation, through parametric functions satisfying some (hidden) ODEs. Our proposal consists of two components. First, a broad probability distribution over the space of ODE solutions, observation times and noise mechanisms, with which we generate a large, synthetic dataset of (hidden) ODE solutions, along with their noisy and sparse observations. Second, a neural recognition model that is trained offline, to map the generated time series onto the spaces of initial conditions and time derivatives of the (hidden) ODE solutions, which we then integrate to impute the missing data. We empirically demonstrate that one and the same (pretrained) recognition model can perform zero-shot imputation across 63 distinct time series with missing values, each sampled from widely different dynamical systems. Likewise, we demonstrate that it can perform zero-shot imputation of missing high-dimensional data in 10 vastly different settings, spanning human motion, air quality, traffic and electricity studies, as well as Navier-Stokes simulations -- without requiring any fine-tuning. What is more, our proposal often outperforms state-of-the-art methods, which are trained on the target datasets.
Our pretrained model, repository and tutorials are available online.
Prediction and Causality of functional MRI and synthetic signal using a Zero-Shot Time-Series Foundation Model
AGH University of Krakow, Poland（克拉科夫AGH大学）；Institut de Neurosciences de la Timone UMR 7289, Aix Marseille Université, CNRS, 13005, Marseille, France（里莫内神经科学研究所）
Towards Foundation Models for Zero-Shot Time Series Anomaly Detection: Leveraging Synthetic Data and Relative Context Discrepancy
Department of Industrial Engineering, Tsinghua University, Beijing, China（清华大学工业工程系）；Datadog AI Research, Paris, France. This work was completed prior to joining Datadog（Datadog AI 研究院）；Lab, Huawei Technologies, ShenZhen, China（华为技术2012实验室）
A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection
Griffith University（格里菲斯大学）；Monash University（莫纳什大学）；Squirrel AI（松鼠AI）；IDSIA（瑞士IDSIA人工智能实验室）；Università della Svizzera italiana（意大利语瑞士大学）；Politecnico di Milano（米兰理工大学）；The Chinese University of Hong Kong（香港中文大学）
TS-RAG: Retrieval-Augmented Generation based Time Series Foundation Models are Stronger Zero-Shot Forecaster
School of Computing, University of Connecticut（康奈尔大学计算机学院）；Department of Machine Learning Research, Morgan Stanley（摩根士丹利机器学习研究部）；Ant Group（蚂蚁集团）；TWG Global（TWG全球）
Deep Learning for Multivariate Time Series Imputation: A Survey
PyPOTS Research（PyPOTS研究机构）；Hong Kong University of Science and Technology（香港理工大学）；University of Oxford（牛津大学）；King’s College London（伦敦大学学院）；Huawei Noah’s Ark Lab（华为诺亚实验室）；Hong Kong University of Science and Technology (Guangzhou)（香港理工大学（广州））；Squirrel Ai Learning（Squirrel Ai学习机构）
Large Language Models for Missing Data Imputation: Understanding Behavior, Hallucination Effects, and Control Mechanisms
Computer Science Division, Aeronautics Institute of Technology（航空技术研究所计算机科学系）；Technology Institute, Federal University of São Paulo（圣保罗联邦大学技术学院）；University of Coimbra, CISUC/LASI – Centre for Informatics and Systems of the University of Coimbra, Department of Informatics Engineering（科英布拉大学）
Navigating Data Scarcity using Foundation Models: A Benchmark of Few-Shot and Zero-Shot Learning Approaches in Medical Imaging
Cluster of Excellence “Machine Learning”（卓越集群“机器学习”）；University of Tübingen（蒂宾根大学）；Faculty of Health Sciences and Medicine, University of Lucerne（卢塞恩大学健康科学与医学院）
Imputation Strategies Under Clinical Presence: Impact on Algorithmic Fairness
MRC Biostatistics Unit（MRC生物统计学单元）；University of Cambridge（剑桥大学）；The Alan Turing Institute（阿兰·图灵研究所）；McCombs School of Business（麦库姆斯商学院）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Rady School of Management（雷迪管理学院）；University of California, San Diego（加利福尼亚大学圣迭戈分校）
WindFM: An Open-Source Foundation Model for Zero-Shot Wind Power Forecasting
School of Economics and Management, North China Electric Power University（经济管理学院，华北电力大学）；Tsinghua University（清华大学）；Institute for Interdisciplinary Information Sciences（交叉信息学院）；Department of Automation（自动化系）；Department of Electrical Engineering（电气工程系）
