Spatial Modeling of Precipitation Based on Data-Driven Warping of Gaussian Processes

Agou, Vasiliki D.; Pavlides, Andrew; Hristopulos, Dionissios T.

doi:10.3390/e24030321

Cited by 10 publications

(7 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In (10), IFT ω (IFT k ) is the inverse Fourier transform with respect to the temporal (spatial) dimension, and the function…”

Section: Hybrid Spectral Approach For Spatiotemporal Kernel Constructionmentioning

confidence: 99%

“…according to the spatiotemporal Fourier transform decomposition property (10). The temporal Fourier modes, C −ω (k, τ ), of the LDHO kernel are obtained from the respective temporal kernels (9) by replacing the LDHO hyperparameters with the dispersion relations ( 15) and ( 18).…”

Section: B Proofs Of Ldho Covariance Kernel Expressionsmentioning

confidence: 99%

“…Such functions, which are necessary for modeling dynamic phenomena, need to include physically meaningful space-time interactions. Applications of Gaussian processes with spatiotemporal kernels involve object tracking [7], control of dynamic systems [2], systems identification [8], mobile sensor networks [9], and environmental process mapping [10]. In spatial statistics, a predictive framework similar to Gaussian processes has been developed independently based on the theory of random fields and has found many applications in the natural sciences [11,12,13,4].…”

Section: Introductionmentioning

confidence: 99%

“…6. If the temporal Fourier modes are explicitly known by solving the generative ODE (14), the space-time covariance kernel C(r, τ ) can be obtained, according to the decomposition property (10), by calculating the IFT of C(k, ω; θ) with respect to the wavevector k. The latter is given by a multidimensional integral, which in certain cases can be exactly evaluated.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes based on a Hybrid Spectral Method and the Harmonic Oscillator

Hristopulos¹

2023

Preprint

View full text Add to dashboard Cite

Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the predictive distribution. For applications with spatiotemporal datasets, suitable kernels should model joint spatial and temporal dependence. Separable space-time covariance kernels offer simplicity and computational efficiency. However, non-separable kernels include space-time interactions that better capture observed correlations. Most non-separable kernels that admit explicit expressions are based on mathematical considerations (admissibility conditions) rather than firstprinciples derivations. We present a hybrid spectral approach for generating covariance kernels which is based on physical arguments. We use this approach to derive a new class of physically motivated, non-separable covariance kernels which have their roots in the stochastic, linear, damped, harmonic oscillator (LDHO). The new kernels incorporate functions with both monotonic and oscillatory decay of space-time correlations. The LDHO covariance kernels involve space-time interactions which are introduced by dispersion relations that modulate the oscillator coefficients. We derive explicit relations for the spatiotemporal covariance kernels in the three oscillator regimes (underdamping, critical damping, overdamping) and investigate their properties.

show abstract

“…In (10), IFT ω (IFT k ) is the inverse Fourier transform with respect to the temporal (spatial) dimension, and the function…”

Section: Hybrid Spectral Approach For Spatiotemporal Kernel Constructionmentioning

confidence: 99%

Section: B Proofs Of Ldho Covariance Kernel Expressionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes based on a Hybrid Spectral Method and the Harmonic Oscillator

Hristopulos¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Most of these studies focus exclusively on the spatial or on the temporal domain. Recently, spatiotemporal studies and models that combine spatial and temporal input data have started gaining traction in physics and other fields [16][17][18][19][20][21][22][23][24][25][26]. For a review of deep learning spatiotemporal applications, please see [27].…”

Section: Introductionmentioning

confidence: 99%

Deep learning-based spatiotemporal multi-event reconstruction for delay line detectors

Knipfer,

Meier,

Volk

et al. 2024

Mach. Learn.: Sci. Technol.

View full text Add to dashboard Cite

Accurate observation of two or more particles within a very narrow time window has always been a challenge in modern physics. It creates the possibility of correlation experiments, such as the ground-breaking Hanbury Brown-Twiss experiment, leading to new physical insights. For low-energy electrons, one possibility is to use a Microchannel plate with subsequent delay lines for the readout of the incident particle hits, a setup called a Delay Line Detector. The spatial and temporal coordinates of more than one particle can be fully reconstructed outside a region called the dead radius. For interesting events, where two electrons are close in space and time, the determination of the individual positions of the electrons requires elaborate peak finding algorithms. While classical methods work well with single particle hits, they fail to identify and reconstruct events caused by multiple nearby particles.To address this challenge, we present a new spatiotemporal machine learning model to identify and reconstruct the position and time of such multi-hit particle signals. This model achieves a much better resolution for nearby particle hits compared to the classical approach, removing some of the artifacts and reducing the dead radius a factor of eight. We show that machine learning models can be effective in improving the spatiotemporal performance of delay line detectors.

show abstract

Evaluation of Double Fusion Satellite Rainfall Dataset in Establish Rainfall Thresholds for Landslide Occurrences Over Badung Regency-Bali

Aryastana,

Dewi,

Wahyuni

et al. 2024

Advances in Natural and Technological Hazards Research

View full text Add to dashboard Cite

Spatial Modeling of Precipitation Based on Data-Driven Warping of Gaussian Processes

Cited by 10 publications

References 63 publications

Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes based on a Hybrid Spectral Method and the Harmonic Oscillator

Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes based on a Hybrid Spectral Method and the Harmonic Oscillator

Deep learning-based spatiotemporal multi-event reconstruction for delay line detectors

Evaluation of Double Fusion Satellite Rainfall Dataset in Establish Rainfall Thresholds for Landslide Occurrences Over Badung Regency-Bali

Contact Info

Product

Resources

About