## 1 Introduction
In practical applications, essentially infinite dimensional systems require model simplification to obtain lower-order ordinary differential equations. However, model simplification can lead to unmodeled dynamics and unknown nonlinearity [10]. Intelligent methods like neural networks, extreme learning machines, and fuzzy systems have been incorporated into DPS modeling as well. References [9; 11; 12; 13] combined neural networks with space-time separation methods and achieved good experimental results on parabolic DPS modeling problems. [PERSON] et al. [11] used a nonlinear PCA method to obtain space base functions. After space-time separation and dimension reduction, a neural network was used to identify the time coefficients. [PERSON] et al. [12] used the PCA algorithm to obtain space base functions. After space-time separation and dimension reduction, the time model was decomposed into linear and nonlinear parts. The ARX model was used to model the linear part, and the RBF neural network was employed to model the nonlinear part. [PERSON] et al. [9] used the KL decomposition method to obtain space base functions. After space-time separation and dimension reduction, a mixed time series model of long short-term memory network and multi-layer perceptron was used to model the time coefficients. [PERSON] et al. [13] employed the incremental KL method to estimate the spatial basis function, and utilized the RBF neural network to establish the time model. After linearization, the spatiotemporal model was used for the model predictive control of an oven. [PERSON] et al. [14] mainly solved the problem of using many sensors in KL decomposition-based modeling, and proposed a two-step modeling method. Firstly, the KL method was used to obtain the spatial basis function by using many sensors offline; then the sensors were reduced, the spatial mapping filtering method was used to obtain the output information without sensor points, and the incremental KL method was used to update the spatial basis function; finally, the extreme learning machine was used to learn time model. Unlike the KL decomposition method, [PERSON] et al. [15] first used the locally linear embedding technique to reduce the dimension and obtain the time coefficient; then they used extreme learning machine to establish the time model, and finally used the kernel-based extreme learning machine to reconstruct the spatiotemporal coupling output. However, the aforementioned modeling methods still require dimension reduction. Three-dimensional fuzzy modeling [10; 16] is a new type of DPS modeling method that has developed in the past five years. In three-dimensional fuzzy model, the functions of space-time separation and space-time reconstruction are naturally integrated into three-dimensional fuzzy rules. In each three-dimensional fuzzy rule, space-time separation is naturally achieved, where the preceding component is computed as the time factor, and the resulting component is regarded as the space base function. In the combination operation of multiple excited three-dimensional fuzzy rules, space-time reconstruction is naturally achieved. Compared with traditional modeling methods of distributed parameter systems, the three-dimensional fuzzy modeling method has two advantages: it does not rely on model dimension reduction and has language interpretability. At present, the three-dimensional fuzzy model has been applied in the modeling of DPS such as rapid thermal processing and chemical reactors. [PERSON] et al. [10] introduced a three-dimensional fuzzy modeling approach utilizing clustering and support vector regression, where the nearest neighbor clustering (NNC) method and similarity analysis technique were employed for mining and condensing the initial preceding components in the three-dimensional fuzzy rules, and support vector regression machines were employed to acquire knowledge about the space base functions of the resulting components in the three-dimensional fuzzy rules.