Physics-Informed Spatial Fuzzy System and Its Applications in Modeling

Physics-informed machine learning (PIML) has proven to be a valuable approach for overcoming data scarcity challenges by incorporating physical models into machine learning methods. However, PIML faces limitations in handling complex spatial relationships, as its process information is obtained from disordered collocation points. Fuzzy systems, based on expert knowledge, can provide an interpretable way for tackling strong process nonlinearities. This article proposes a brand-new physics-informed spatial fuzzy system framework (PiFuz) to capture the essential system information of complex distributed parameter systems. PiFuz utilizes spatial membership functions to transform collocation points into a 3-D fuzzy input. This input is processed by the inference mechanism, leveraging its 3-D nature to produce fuzzy outputs with distinctive spatial characteristics. A feature fusion module is utilized to integrate these characteristics and generate the distributed system state. Utilizing the known physical knowledge base, the proposed framework undergoes automatic tuning while preserving process interpretability, resulting in an optimal model that aligns with the actual physical process. A reliable prediction of strong spatial nonlinear behaviors is achieved without the dependency of process data. For modeling higher dimensional spatiotemporal problems, the extension, a multikernel PiFuz framework (MKPiFuz), is further developed to improve the representation of heterogeneous time-varying nonlinear behaviors. By incorporating spatial and wavelet kernels, MKPiFuz extracts underlying features from spatial and temporal dimensions, respectively. Experimental investigations on thermal process of the battery module demonstrate the good accuracy in modeling complex spatiotemporal systems.