Gaussian processes (GP) regression is a powerful probabilistic tool for modeling nonlinear dynamical systems. The downside of the method is its cubic computational complexity with respect to the training data that can be partially reduced using pseudo-inputs. The dynamics can be represented with an autoregressive model, which simplifies the training to that of the static case. When simulating an autoregressive model, the uncertainty is propagated through a nonlinear function and the simulation cannot be evaluated in closed-form. This paper combines the variational methods of GP approximations with a nonlinear autoregressive model with exogenous inputs (NARX) to form variational GP (VGP-NARX) models. We show how VGP-NARX models, on average, better approximate a full GP-NARX model than more commonly used GP-NARX (FITC) model on 10 chaotic time-series. The modeling capabilities of VGP-NARX models are compared with the existing approaches on two benchmarks for modeling nonlinear dynamical systems. The advantage of general-purpose computing on graphics processing units (GPGPU) for Monte Carlo simulation on large validation data sets is addressed.

高斯过程（GP）回归是用于建模非线性动力系统的强大概率工具。该方法的缺点是它相对于训练数据的三次计算复杂度，可以使用伪输入来部分减少。动力学可以用自回归模型表示，该模型将训练简化为静态案例的训练。在模拟自回归模型时，不确定性会通过非线性函数传播，并且无法以封闭形式评估模拟。本文将GP近似的变分方法与带有外部输入的非线性自回归模型（NARX）相结合，以形成变分GP（VGP-NARX）模型。我们展示了VGP-NARX平均而言如何 在10个混沌时间序列上，比更常用的GP-NARX（FITC）模型更好地近似完整的GP-NARX模型。将VGP-NARX模型的建模能力与两个基准上的现有方法进行了比较，以对非线性动力系统进行建模。解决了在大型验证数据集上进行蒙特卡洛仿真的图形处理单元（GPGPU）上通用计算的优势。