In this work, we consider a differential description of the evolution of the state of a reaction-diffusion system under environmental fluctuations. We are interested in estimating the state of the system when only partial observations are available. To describe how observations and states are related, we combine multiplicative noise-driven dynamics with an observation model. More specifically, we ensure that the observations are subjected to error in the form of additive noise. We focus on the state estimation of a Belousov-Zhabotinskii chemical reaction. We simulate a reaction conducted in a quasi-two-dimensional physical domain, such as on the surface of a Petri dish. We aim at reconstructing the emerging chemical patterns based on noisy spectral observations. For this task, we consider a finite difference representation on the spatial domain, where nodes are chosen according to observation sites. We approximate the solution to this state estimation problem with the Block particle filter, a sequential Monte Carlo method capable of addressing the associated high-dimensionality of this state-space representation.
翻译:在这项工作中,我们考虑了环境波动下反应扩散系统状态演变的微分描述。我们感兴趣的是在只有部分观测可用的情况下估计系统状态。为了描述观测和状态之间的关系,我们将乘性噪声驱动动力学与观测模型相结合。具体而言,我们确保观测受到加性噪声误差的影响。我们侧重于对Belousov-Zhabotinskii化学反应的状态估计。我们模拟了一个在类似于培养皿表面的准二维物理域中进行的反应。我们旨在基于带噪声光谱观测重建出新兴的化学模式。为此,我们考虑了空间域上的有限差分表示,其中节点是根据观测站点选择的。我们使用块粒子滤波器来近似解决这个状态估计问题,这是一种能够应对此状态空间表示的高维度的序贯蒙特卡罗方法。