Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching

Yıldız, Çağatay; Heinonen, Markus; Intosalmi, Jukka; Mannerström, Henrik; Lähdesmäki, Harri

doi:10.1109/mlsp.2018.8516991

Cited by 23 publications

(21 citation statements)

References 21 publications

(41 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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“…An open question is to which extend analytical structured models can be combined with numerical integration schemes such that training of such a combined model is done solely on trajectory data. Recent works discuss how to approximate ODEs using GPs [41,104,108] and NNs [17,63] as well as solve initial‐value problems using GPs [82,83].…”

Section: Conclusion and Future Outlookmentioning

confidence: 99%

Structured learning of rigid‐body dynamics: A survey and unified view from a robotics perspective

Geist

Trimpe

2021

GAMM-Mitteilungen

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Accurate models of mechanical system dynamics are often critical for model‐based control and reinforcement learning. Fully data‐driven dynamics models promise to ease the process of modeling and analysis, but require considerable amounts of data for training and often do not generalize well to unseen parts of the state space. Combining data‐driven modeling with prior analytical knowledge is an attractive alternative as the inclusion of structural knowledge into a regression model improves the model's data efficiency and physical integrity. In this article, we survey supervised regression models that combine rigid‐body mechanics with data‐driven modeling techniques. We analyze the different latent functions (such as kinetic energy or dissipative forces) and operators (such as differential operators and projection matrices) underlying common descriptions of rigid‐body mechanics. Based on this analysis, we provide a unified view on the combination of data‐driven regression models, such as neural networks and Gaussian processes, with analytical model priors. Furthermore, we review and discuss key techniques for designing structured models such as automatic differentiation.

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“…As an illustration, Fig. 3 shows the drift term of the Langevin equation given by applying the Bayesian estimation technique recently introduced in [29] to the time-series across PC1-PC2 in the Seshat data.…”

Section: Comparing Different Historical Trajectories: Flow Mapsmentioning

confidence: 99%