State-Space Gaussian Process for Drift Estimation in Stochastic Differential Equations

Zhao, Zheng; Tronarp, Filip; Hostettler, Roland; Särkkä, Simo

doi:10.1109/icassp40776.2020.9054472

Cited by 4 publications

(2 citation statements)

References 25 publications

(34 reference statements)

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“…Our trajectory data is of the type for nonparametric regression of f φ . The recent works [42][43][44][45][46][47][48][49][50][51] that use GPs in learning differential equations typically model f φ : R dN → R dN as a Gaussian process. However, the straightforward application of existing approaches may suffer from the well-known curse of dimensionality since f φ is of dimension dN .…”

Section: Connection With Nonparametric Regression and Inverse Problemmentioning

confidence: 99%

Learning particle swarming models from data with Gaussian processes

Feng

Ren

Tang

2021

Preprint

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Interacting particle or agent systems that display a rich variety of collection motions are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and collective behaviors. In this paper, we study the data-driven discovery of distance-based interaction laws in second-order interacting particle systems. We propose a learning approach that models the latent interaction kernel functions as Gaussian processes, which can simultaneously fulfill two inference goals: one is the nonparametric inference of interaction kernel function with the pointwise uncertainty quantification, and the other one is the inference of unknown parameters in the non-collective forces of the system. We formulate learning interaction kernel functions as a statistical inverse problem and provide a detailed analysis of recoverability conditions, establishing that a coercivity condition is sufficient for recoverability. We provide a finite-sample analysis, showing that our posterior mean estimator converges at an optimal rate equal to the one in the classical 1-dimensional Kernel Ridge regression. Numerical results on systems that exhibit different collective behaviors demonstrate efficient learning of our approach from scarce noisy trajectory data.Preprint. Under review.

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Section: Connection With Nonparametric Regression and Inverse Problemmentioning

confidence: 99%

Learning particle swarming models from data with Gaussian processes

Feng

Ren

Tang

2021

Preprint

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“…However, GPs have problems dealing with large amounts of data, as the computational complexity scales cubically with number of data records [67]. Therefore, in practice, the state space modeling of GP is often used for linear computational complexity on temporal data [71]- [73].…”

Section: A Key Requirements Of Ai For Maritime Problemsmentioning

confidence: 99%

Sensors and AI Techniques for Situational Awareness in Autonomous Ships: A Review

Thombre

Zhao

Ramm-Schmidt³

et al. 2022

IEEE Trans. Intell. Transport. Syst.

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114

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Autonomous ships are expected to improve the level of safety and efficiency in future maritime navigation. Such vessels need perception for two purposes: to perform autonomous situational awareness and to monitor the integrity of the sensor system itself. In order to meet these needs, the perception system must fuse data from novel and traditional perception sensors using Artificial Intelligence (AI) techniques. This article overviews the recognized operational requirements that are imposed on regular and autonomous seafaring vessels, and then proceeds to consider suitable sensors and relevant AI techniques for an operational sensor system. The integration of four sensors families is considered: sensors for precise absolute positioning (Global Navigation Satellite System (GNSS) receivers and Inertial Measurement Unit (IMU)), visual sensors (monocular and stereo cameras), audio sensors (microphones), and sensors for remotesensing (RADAR and LiDAR). Additionally, sources of auxiliary data, such as Automatic Identification System (AIS) and external data archives are discussed. The perception tasks are related to well-defined problems, such as situational abnormality detection, vessel classification, and localization, that are solvable using AI techniques. Machine learning methods, such as deep learning and Gaussian processes, are identified to be especially relevant for these problems. The different sensors and AI techniques are characterized keeping in view the operational requirements, and some example state-of-the-art options are compared based on accuracy, complexity, required resources, compatibility and adaptability to maritime environment, and especially towards practical realization of autonomous systems.

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Learning particle swarming models from data with Gaussian processes

Feng,

Kulick,

Ren

et al. 2023

Math. Comp.

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Interacting particle or agent systems that exhibit diverse swarming behaviors are prevalent in science and engineering. Developing effective differential equation models to understand the connection between individual interaction rules and swarming is a fundamental and challenging goal. In this paper, we study the data-driven discovery of a second-order particle swarming model that describes the evolution of N N particles in R d \mathbb {R}^d under radial interactions. We propose a learning approach that models the latent radial interaction function as Gaussian processes, which can simultaneously fulfill two inference goals: one is the nonparametric inference of the interaction function with pointwise uncertainty quantification, and the other is the inference of unknown scalar parameters in the noncollective friction forces of the system. We formulate the learning problem as a statistical inverse learning problem and introduce an operator-theoretic framework that provides a detailed analysis of recoverability conditions, establishing that a coercivity condition is sufficient for recoverability. Given data collected from M M i.i.d trajectories with independent Gaussian observational noise, we provide a finite-sample analysis, showing that our posterior mean estimator converges in a Reproducing Kernel Hilbert Space norm, at an optimal rate in M M equal to the one in the classical 1-dimensional Kernel Ridge regression. As a byproduct, we show we can obtain a parametric learning rate in M M for the posterior marginal variance using L ∞ L^{\infty } norm and that the rate could also involve N N and L L (the number of observation time instances for each trajectory) depending on the condition number of the inverse problem. We provide numerical results on systems exhibiting different swarming behaviors, highlighting the effectiveness of our approach in the scarce, noisy trajectory data regime.

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State-Space Gaussian Process for Drift Estimation in Stochastic Differential Equations

Cited by 4 publications

References 25 publications

Learning particle swarming models from data with Gaussian processes

Learning particle swarming models from data with Gaussian processes

Sensors and AI Techniques for Situational Awareness in Autonomous Ships: A Review

Learning particle swarming models from data with Gaussian processes

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