Discretizing stochastic dynamical systems using Lyapunov equations

Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems. Discretization of continuous-time models is hence fundamental. We present a novel algorithm using a combination of Lyapunov equations and analytical solutions, enabling efficient implementation in software. The proposed method circumvents numerical problems exhibited by standard algorithms in the literature. Both theoretical and simulation results are provided

Learning deep dynamical models from image pixels

Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement mapping and the transition mapping (system dynamics) in latent space can be challenging. For linear system dynamics and measurement mappings efficient solutions for system identification are available. However, in practical applications, the linearity assumptions does not hold, requiring non-linear system identification techniques. If additionally the observations are high-dimensional (e.g., images), non-linear system identification is inherently hard. To address the problem of non-linear system identification from high-dimensional observations, we combine recent advances in deep learning and system identification. In particular, we jointly learn a low-dimensional embedding of the observation by means of deep auto-encoders and a predictive transition model in this low-dimensional space. We demonstrate that our model enables learning good predictive models of dynamical systems from pixel information only.Comment: 10 pages, 11 figure

Physics-informed neural networks with unknown measurement noise

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated by weak Gaussian noise. We show that the standard PINN framework breaks down in case of non-Gaussian noise. We give a way of resolving this fundamental issue and we propose to jointly train an energy-based model (EBM) to learn the correct noise distribution. We illustrate the improved performance of our approach using multiple examples

Modeling and interpolation of the ambient magnetic field by Gaussian processes

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.Comment: 17 pages, 12 figures, to appear in IEEE Transactions on Robotic

Совершенствование упаковки товара на ОАО «Мозырьсоль»

Материалы XII Междунар. науч.-техн. конф. студентов, магистрантов и молодых ученых, Гомель, 26–27 апр. 2012 г

Invertible Kernel PCA with Random Fourier Features

Kernel principal component analysis (kPCA) is a widely studied method to construct a low-dimensional data representation after a nonlinear transformation. The prevailing method to reconstruct the original input signal from kPCA -- an important task for denoising -- requires us to solve a supervised learning problem. In this paper, we present an alternative method where the reconstruction follows naturally from the compression step. We first approximate the kernel with random Fourier features. Then, we exploit the fact that the nonlinear transformation is invertible in a certain subdomain. Hence, the name \emph{invertible kernel PCA (ikPCA)}. We experiment with different data modalities and show that ikPCA performs similarly to kPCA with supervised reconstruction on denoising tasks, making it a strong alternative.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl