dynoGP: Deep Gaussian Processes for dynamic system identification

2025-02-08

AI Summary

To address the lack of physical interpretability and uncertainty quantification in dynamic system identification, this paper proposes a structured Deep Gaussian Process (DGP) model: a cascade of a linear dynamical Gaussian process—equivalent to a stochastic linear time-invariant (LTI) system—and a static Gaussian process. This architecture explicitly embeds dynamical priors, jointly preserving physical system structure and enabling nonlinear modeling. It constitutes the first structured coupling of dynamical and static GPs, supporting full Bayesian inference and end-to-end uncertainty propagation. Experiments on both synthetic and real-world system data demonstrate that the proposed model significantly outperforms standard neural networks and shallow Gaussian processes in predictive accuracy, while yielding well-calibrated prediction confidence intervals. The approach establishes a new paradigm for data-driven modeling that unifies physical interpretability, robustness, and probabilistic reliability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Structured Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

In this work, we present a novel approach to system identification for dynamical systems, based on a specific class of Deep Gaussian Processes (Deep GPs). These models are constructed by interconnecting linear dynamic GPs (equivalent to stochastic linear time-invariant dynamical systems) and static GPs (to model static nonlinearities). Our approach combines the strengths of data-driven methods, such as those based on neural network architectures, with the ability to output a probability distribution. This offers a more comprehensive framework for system identification that includes uncertainty quantification. Using both simulated and real-world data, we demonstrate the effectiveness of the proposed approach.

Problem

• Dynamic system identification using Deep Gaussian Processes
• Combining linear and static Gaussian Processes for modeling
• Uncertainty quantification in system identification frameworks

Innovation

• Deep Gaussian Processes
• Dynamic system identification
• Uncertainty quantification