Simulation of variational Gaussian process NARX models with GPGPU.

Area of Science:

• Machine Learning
• Dynamical Systems Modeling
• Probabilistic Methods

Background:

• Gaussian Process (GP) regression is effective for nonlinear systems but suffers from cubic computational complexity.
• Existing methods like FITC offer partial solutions but can be improved.
• Simulating autoregressive models involves complex uncertainty propagation.

Purpose of the Study:

• To introduce Variational Gaussian Process (GP) Nonlinear Autoregressive Models with Exogenous Inputs (VGP-NARX).
• To evaluate VGP-NARX models against established methods for nonlinear dynamical systems.
• To demonstrate the superior approximation capabilities of VGP-NARX models.

Main Methods:

• Combining variational GP approximations with Nonlinear Autoregressive Models with Exogenous Inputs (NARX).
• Utilizing pseudo-inputs to mitigate computational complexity.
• Employing Monte Carlo simulations on graphics processing units (GPGPU) for large datasets.

Main Results:

• VGP-NARX models demonstrate, on average, better approximations of full GP-NARX models compared to the FITC approach.
• The models were tested on 10 chaotic time-series and two benchmark nonlinear dynamical systems.
• The performance of VGP-NARX models was validated against existing approaches.

Conclusions:

• VGP-NARX models present a more accurate and efficient approach for modeling nonlinear dynamical systems.
• The proposed method offers significant improvements over commonly used GP-NARX approximations.
• The study highlights the potential of VGP-NARX for complex time-series analysis.