In this paper, we show how informativity and identifiability for networks of dynamical systems can be investigated using Gröbner bases. We provide a sufficient condition for generic informativity in terms of positive definiteness of the spectrum of external signals and full generic row rank of the transfer function relating the external signals to the inputs of the predictor. Moreover, we show how generic local network identifiability in the algebraic sense can be investigated by computing the dimension of the generic fiber associated with the closed loop transfer function from external measurable signals to the measured outputs.
Data-informativity conditions for structured linear systems with implications for dynamic networks
Eindhoven University of Technology（埃因霍温理工大学）；Delft University of Technology（代尔夫特理工大学）；Flemish Institute for Technological Research (VITO)（佛兰芒技术研究所）；ASML（阿斯麦）；Royal Institute of Technology（皇家理工学院）；University of Calgary（卡尔加里大学）
Identifiability of a single module in a network of transfer functions is determined by whether a particular transfer function in the network can be uniquely distinguished within a network model set, on the basis of data. Whereas previous research has focused on the situations that all network signals are either excited or measured, we develop generalized analysis results for the situation of partial measurement and partial excitation. As identifiability conditions typically require a sufficient number of external excitation signals, this work introduces a novel network model structure such tha…
Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond
University of New South Wales（新南威尔士大学）；Australian Research Council（澳大利亚研究理事会）；Massachusetts Institute of Technology（麻省理工学院）；Australian National University（澳大利亚国立大学）
Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical properties of the measured signals. Conditions for generic identifiability of multiple modules, i.e. a subnetwork, are developed for the situation that all node signals are measured and excitation of the network is provided by both measured excitation signals and unmeasured disturbance inputs. Additionally, the network model set is allowed to contain non-parametrized modules that are fixed, and e.g. refl…
Data-Driven Tensor Decomposition Identification of Homogeneous Polynomial Dynamical Systems
School of Data Science and Society, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校数据科学与社会学院）；Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard（麻省理工学院和哈佛大学博德研究所埃里克和温迪·施密特中心）；Department of Mathematics, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校数学系）；Department of Biostatistics, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校生物统计学系）
This paper deals with the design of Excitation and Measurement Patterns (EMP) for the identification of a class of dynamical networks whose topology has the structure of a Directed Acyclic Graph (DAG). In addition to the by now well known condition that the identifiabiltiy of any dynamical network requires that the sources be excited, the sinks be measured, and all other nodes be either excited or measured, we show that for DAGs two other types of nodes have special excitation and measurement requirements. Armed with this result, we propose a systematic procedure for the design of EMPs that gu…
Identification of Nonlinear Acyclic Networks in Continuous Time from Nonzero Initial Conditions and Full Excitations
Shiv Nadar University（希夫纳德大学）；Université de Lorraine, CNRS, CRAN（洛林大学、法国国家科学研究中心、CRAN）；UCLouvain（鲁汶天主教大学）；University of Namur（纳慕尔大学）；ICTEAM institute, UCLouvain（UCLouvain ICTEAM研究所）；Department of Mathematics, Namur Research Institute for Complex Systems, University of Namur（纳慕尔大学数学系、纳慕尔复杂系统研究所）
A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the existing works on identification can be categorized as special cases of these two phenomena. Several effective criteria for determining the identifiability and the corresponding identification algorithms are proposed. Three important results are derived: (1) If a BN is observable, it is uniquely identifiable; (2) If a BCN is O1-observable, it is uniquely id…
Identification methods for dynamic networks typically require prior knowledge of the network and disturbance topology, and often rely on solving poorly scalable non-convex optimization problems. While methods for estimating network topology are available in the literature, less attention has been paid to estimating the disturbance topology, i.e., the (spatial) noise correlation structure and the noise rank in a filtered white noise representation of the disturbance signal. In this work we present an identification method for dynamic networks, in which an estimation of the disturbance topology …
Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent States
Department of Mechanical & Industrial Engineering, Montana State University（机械与工业工程系，蒙大拿州立大学）；Gianforte School of Computing, Montana State University（计算机学院，蒙大拿州立大学）
Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination. We propose an algorithm that computes a description of the set of differenti…
Massachusetts Institute of Technology（麻省理工学院）；Broad Institute of MIT and Harvard（MIT和哈佛大学Broad研究所）；Basis Research Institute（Basis研究机构）；Eric and Wendy Schmidt Center（埃里克和温迪·施密特中心）；BCAM (Basque Center for Applied Mathematics)（BCAM（巴斯克应用数学中心））；Ikerbasque (Basque Foundation for Science)（Ikerbasque（巴斯克科学基金会））
An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis
Carnegie Mellon University（卡内基梅隆大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；International Max Planck Research School for Intelligent Systems (IMPRS-IS)（马克斯·普朗克智能系统国际研究学校（IMPRS-IS））；European Laboratory for Learning and Intelligent Systems (ELLIS)（欧洲学习与智能系统实验室（ELLIS））
