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：本文考虑环境波动下反应扩散系统状态演化的微分描述。当仅能获取部分观测数据时，我们致力于估计系统状态。为建立观测值与系统状态间的关联，我们将乘性噪声驱动的动力学过程与观测模型相结合，具体确保观测值受加性噪声误差影响。研究聚焦于别洛乌索夫-扎博京斯基化学反应的状态估计问题，模拟在准二维物理域（如培养皿表面）中进行的反应过程。我们的目标是基于含噪光谱观测值重建涌现的化学模式。为此，采用空间域上的有限差分表示，根据观测站点选择节点。通过分块粒子滤波（一种能够处理该状态空间表示中高维问题的序贯蒙特卡洛方法）来近似求解该状态估计问题。