Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic approach to tackling this problem, using compositions of physics-informed random features, derived from ordinary differential equations. The architecture of our model leverages recent advances in approximate inference for deep Gaussian processes, such as layer-wise weight-space approximations which allow us to incorporate random Fourier features, and stochastic variational inference for approximate Bayesian inference. We provide evidence that our model is capable of capturing highly nonlinear behaviour in real-world multivariate time series data. In addition, we find that our approach achieves comparable performance to a number of other probabilistic models on benchmark regression tasks.
翻译:在高度非线性动态系统中存在有效模型化现象,同时准确量化不确定性是一项具有挑战性的任务,往往需要针对具体问题的技术。我们提出了一种新颖的、领域不可知的方法来解决这一问题,利用物理学知情随机特征的构成,这些特征来自普通的差别方程。我们的模型结构利用了深海高斯过程近似推论的最新进展,例如,从层到层的重量-空间近似值,使我们能够纳入随机的Fourier特征,以及近似Bayesian推理的随机变异推论。我们提供了证据,证明我们的模型能够在现实世界多变时间序列数据中捕捉到高度非线性的行为。此外,我们发现,我们的方法取得了与基准回归任务其他一些概率模型相似的业绩。