We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound quantifying the estimation rate our algorithm attains and prove matching upper and lower bounds which guarantee its asymptotic optimality, up to constants. In addition, we show that this optimal rate is unattainable when using Gaussian noise to excite the system, even with optimally tuned covariance, and analyze several examples where our algorithm provably improves over rates obtained by playing noise. Our analysis critically relies on a novel result quantifying the error in estimating the parameters of a dynamical system when arbitrary periodic inputs are being played. We conclude with numerical examples that illustrate the effectiveness of our algorithm in practice.
In this paper, we investigate the parameter identification problem in dynamical systems through a deep learning approach. Focusing mainly on second-order, linear time-invariant dynamical systems, the topic of damping factor identification is studied. By utilizing a six-layer deep neural network with different recurrent cells, namely GRUs, LSTMs or BiLSTMs; and by feeding input-output sequence pairs captured from a dynamical system simulator, we search for an effective deep recurrent architecture in order to resolve damping factor identification problem. Our study results show that, although pr…
Riken AIP（理化学研究所革新智能综合研究中心）；LTCI, Télécom Paris, Institut Polytechnique de Paris（巴黎电信学院，巴黎综合理工学院）
Screening rules were recently introduced as a technique for explicitly identifying active structures such as sparsity, in optimization problem arising in machine learning. This has led to new methods of acceleration based on a substantial dimension reduction. We show that screening rules stem from a combination of natural properties of subdifferential sets and optimality conditions, and can hence be understood in a unified way. Under mild assumptions, we analyze the number of iterations needed to identify the optimal active set for any converging algorithm. We show that it only depends on its …
In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing equation identification algorithms assuming the state variables are known a priori and the governing equations lend themselves to sparse, linear expansions in a (nonlinear) basis of the state variables. In the context of the identification of governing equations of nonlinear dynamical systems, one faces the problem of identifiability of model parameters whe…
IDSIA Dalle Molle Institute for Artificial Intelligence（IDSIA达勒莫尔人工智能研究所）；USI-SUPSI, Lugano, Switzerland（瑞士卢加诺的提契诺大学与瑞士南部应用科学与艺术大学）
This paper introduces a network architecture, called dynoNet, utilizing linear dynamical operators as elementary building blocks. Owing to the dynamical nature of these blocks, dynoNet networks are tailored for sequence modeling and system identification purposes. The back-propagation behavior of the linear dynamical operator with respect to both its parameters and its input sequence is defined. This enables end-to-end training of structured networks containing linear dynamical operators and other differentiable units, exploiting existing deep learning software. Examples show the effectiveness…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and actions or for systems that can be identified from data generated by i.i.d. random inputs. Nonetheless, many interesting dynamical systems have continuous states and actions and can only be identified through a judicious choice of inputs. Motivated by practical settings, we study a class of nonlinear dynamical systems whose state transitions depend linearly on…
Active Sensing and Deferred-Decision Trajectory Optimization for Robust Target Identification
Department of Electrical and Computer Engineering, Purdue University（普渡大学电气与计算机工程系）；Department of Electrical Engineering, University of Notre Dame（诺丁汉大学电气工程系）
University of Michigan（密歇根大学）；University of Texas Medical Branch（德克萨斯大学医学部）；Institute for Translational Sciences（转化科学研究所）；Electrical Engineering and Computer Science（电气工程与计算机科学学院）
The problem of active diagnosis arises in several applications such as disease diagnosis, and fault diagnosis in computer networks, where the goal is to rapidly identify the binary states of a set of objects (e.g., faulty or working) by sequentially selecting, and observing, (noisy) responses to binary valued queries. Current algorithms in this area rely on loopy belief propagation for active query selection. These algorithms have an exponential time complexity, making them slow and even intractable in large networks. We propose a rank-based greedy algorithm that sequentially chooses queries s…
ETH Zurich（苏黎世联邦理工学院）；Carnegie Mellon University（卡内基梅隆大学）；Stanford University（斯坦福大学）；University College London（伦敦大学学院）；University of Alberta（阿尔伯塔大学）
Many real-world reinforcement learning tasks require control of complex dynamical systems that involve both costly data acquisition processes and large state spaces. In cases where the transition dynamics can be readily evaluated at specified states (e.g., via a simulator), agents can operate in what is often referred to as planning with a \emph{generative model}. We propose the AE-LSVI algorithm for best-policy identification, a novel variant of the kernelized least-squares value iteration (LSVI) algorithm that combines optimism with pessimism for active exploration (AE). AE-LSVI provably ide…
University of California, Riverside（加州大学河滨分校）；University of Michigan Ann Arbor（密歇根大学安娜堡分校）
Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the system's states and inputs. Under a mild marginal mean-square stability assumption, we identify how much data is needed to estimate the unknown bilinear system up to a desired accuracy with high probability. Our sample complexity and statistical error rates are optimal in terms of the trajectory length, the dimensionality of the system and the input size. Our proo…
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems with non-asymptotic statistical rates depending on the inherent dimensionality (order) $d$ of the system, rather than on the possibly much larger memory length. We propose an algorithm that given a single trajectory of length $T$ with gaussian observation noise, learns the system with a near-optimal rate of $\widetilde O\left(\sqrt\frac{d}{T}\right)$ in $\ma…
This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE) algorithm is adopted, seeking to find the best estimate of unknown model parameters based on noiseless measurements of the state. We are interested in the fundamental limitation of the rate at which unknown parameters can be learned, in the sense of the D-optimality scalarization criterion subject to a quadratic control cost. We first establish a novel conne…
A Sampling Complexity-aware Framework for Discrete-time Fractional-Order Dynamical System Identification
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California（南加州大学明海电气与计算机工程系）；Elmore Family School of Electrical and Computer Engineering, Purdue University（普渡大学埃尔莫尔电气与计算机工程学院）
The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial observations. Here, we address this challenge and investigate variational deep learning schemes. Within the proposed framework, we jointly learn an inference model to reconstruct the true states of the system and the governing laws of these states from series of noisy and partial data. In doing so, this framework bridges classical data assimilation and state-of-th…
University of California, Berkeley（加利福尼亚大学伯克利分校）；Amazon（亚马逊）
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work shows that the eigenspectrum of unknown linear dynamics can be identified without full system identification. We analyze a computationally efficient and provably convergent algorithm to estimate the eigenvalues of the state-transition matrix in a linear dynamical system. When applied to time series clustering, our algorithm can efficiently cluster multi-dimen…
ETH Zürich（苏黎世联邦理工学院）；Max Planck ETH CLS（马克斯·普朗克-苏黎世联邦理工计算与系统神经科学中心）；MPI-IS Tübingen（图宾根马克斯·普朗克智能系统研究所）
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computational cost are well established, a rigorous mathematical framework has been missing. We offer a novel interpretation which leads to a better understanding and improvements in state-of-the-art performance in terms of accuracy for nonlinear dynamical systems.
Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown external sources. In such cases, developing a purely analytical model becomes very difficult and data-driven modeling can be of assistance. In this paper, we present a hybrid framework combining physics-based numerical models with deep learning for source identification and forecasting of spatio-temporal dynamical systems with unobservable time-varying external sou…
Due to the increasing availability of large-scale observation and simulation datasets, data-driven representations arise as efficient and relevant computation representations of dynamical systems for a wide range of applications, where model-driven models based on ordinary differential equation remain the state-of-the-art approaches. In this work, we investigate neural networks (NN) as physically-sound data-driven representations of such systems. Reinterpreting Runge-Kutta methods as graphical models, we consider a residual NN architecture and introduce bilinear layers to embed non-linearities…
Towards Explainable, Safe Autonomous Driving with Language Embeddings for Novelty Identification and Active Learning: Framework and Experimental Analysis with Real-World Data Sets
University of California San Diego（加利福尼亚大学圣迭戈分校）；Laboratory for Intelligent and Safe Automobiles（智能与安全汽车实验室）
Development and Application of Self-Supervised Machine Learning for Smoke Plume and Active Fire Identification from the FIREX-AQ Datasets
Spatial Informatics Group, LLC.（空间信息集团有限公司）；Jet Propulsion Laboratory, California Institute of Technology（喷气推进实验室，加州理工学院）；University of California at Berkeley（加州大学伯克利分校）；Fowler School of Engineering, Chapman University（查普曼大学福勒工程学院）；Machine Learning and Assistive Technology Lab (MLAT), Chapman University（机器学习与辅助技术实验室（MLAT），查普曼大学）
Physics-informed active learning with simultaneous weak-form latent space dynamics identification
ANSYS Inc.（ANSYS公司）；Department of Applied Mathematics, University of Colorado（应用数学系，科罗拉多大学）；Center for Applied Scientific Computing, Lawrence Livermore National Laboratory（应用科学计算中心，劳伦斯利弗莫尔国家实验室）
LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification
Visual Computing Lab, Indian Institute of Science（印度科学院视觉计算实验室）；Department of Electrical and Electronics Engineering, BITS Pilani Hyderabad Campus（BITS Pilani Hyderabad校区电子与电气工程系）
Josef Ressel Centre for Symbolic Regression（约瑟夫·雷塞尔符号回归中心）；Heuristic and Evolutionary Algorithms Laboratory（启发式与进化算法实验室）；University of Applied Sciences Upper Austria（上奥地利应用科学大学）
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential equations (ODE). The novelty is that we add a step of gradient-based optimization of the ODE parameters. For this we calculate the sensitivities of the solution to the initial value problem (IVP) using automatic differentiation. The proposed approach is tested on a set of 19 problem instances taken from the literature which includes datasets from simulated systems a…
