A Physics-Enhanced Separation Framework for Spatiotemporal Modeling of Distributed Parameter Systems With Multi-Fidelity Data

Many industrial processes are typically distributed parameter systems (DPSs) described by partial differential equations. Data-driven methods have become popular for spatiotemporal modeling of DPSs, which is crucial for system understanding, simulation, and control improvement. However, current data-driven methods rely heavily on data volume and fidelity. With limited high-fidelity data, they exhibit unsatisfactory long-term predictions for out-of-sample scenarios. To remedy this issue, a novel physics-enhanced separation framework (called PhysiT/S) is proposed. PhysiT/S is composed of a physics-enhanced spatiotemporal unit and a coefficient network. By enhancing physics utilization through the physics-enhanced spatiotemporal unit, PhysiT/S becomes less data-dependent while computationally efficient. Multi-fidelity learning of the coefficient network further alleviates the request for a large volume of high-fidelity data. As a result, PhysiT/S can accurately predict out-of-sample distributions, even when only limited high-fidelity data is available. PhysiT/S introduces a novel way of combining physics with multi-fidelity data for spatiotemporal modeling of DPSs. Extensive simulations on two benchmark DPSs and the thermal process of lithium-ion batteries demonstrate the merits of PhysiT/S. Note to Practitioners—This paper is motivated by the problem of data-driven spatiotemporal modeling of DPSs, which is also applicable to other prediction tasks for complex spatiotemporal systems. Existing data-driven approaches rely heavily on high-fidelity data, while physics-informed approaches struggle to extract coupled spatiotemporal features. These drawbacks limit their practical applications to engineering modeling. In this paper, we propose a new generic modeling framework that integrates physics with data through the theory of time/space separation. It aims to achieve accurate long-term predictions for out-of-sample scenarios by constructing spatiotemporal enhancement units and using multi-fidelity data to decrease reliance on high-fidelity datasets. We have applied the proposed method to the thermal processes of a catalytic rod and a cylindrical lithium-ion battery. Preliminary results show that this method is feasible with better predictions than others, but it is untested in production. Future research will address online modeling in practical engineering.