Unsupervised Physics-Informed Neural Network for Digital Twin Construction of LRM Temperature Fields

• Sensor data encoding: Encode the layout information of the LRM surface temperature sensor into a sparse matrix, where the sensor position corresponds to the temperature measurement value, the non-measurement area assigns zero value, and constructs an input tensor with a dimension of n × m; • Physical-informed loss function construction: solve the partial differential equation of heat conduction based on the finite difference method, and optimize the solution steps of the partial differential operator, then establish a physical-network output joint loss function based on the root mean square error to guide network training; • Boundary condition embedding: using mirror filling applies third-order Neumann boundary conditions to ensure the consistency of the numerical solution in the boundary region and the solution domain, while improving the modeling accuracy at the boundary; • Establish deep neural network as substitute model: build U-Net model, optimize the network architecture and set network training parameters. Extract and integrate multi-scale spatial features through codecs and skip link mechanisms, realizing reconstruction from the initial sparse matrix to the n × m full temperature field, as a substitute model for numerical solutions. • Transient and steady-state temperature field construction: Assuming parameters such as thermal conductivity and time step length, determine the key parameters for calculating the optimization matrix. Under a variety of different initial heat source intensity distribution conditions, the model outputs result every several time steps to simulate the evolution of LRM's transient temperature field, and outputs the steady-state temperature field after heat exchange with the environment. In response to the problem that in the health management of line replaceable module (LRM) it is difficult to accurately monitor the complete temperature field in real time due to limited deployment of thermal imagers and sensors, we propose an unsupervised physical-informed neural network that utilizes discrete temperature inputs of thermal sensors to construct a digital twin of LRM temperature field, achieving high-precision modeling of the transient temperature evolution and steady-state distribution of the entire board. The core innovation lies in designing a physical-informed loss function to break through the dependence of supervised learning on image labeled data: use the finite difference method to solve the partial differential equation of heat conduction and optimize the solution steps of the partial differential operator; design a filling strategy that applies third-order Neumann boundary conditions to enable the boundary to satisfy physical equation constraints simultaneously; finally, establish a physical-network output joint loss function based on root mean square error. Meanwhile optimize the U-Net architecture to adapt to the regression task of temperature field images, enabling it to independently learn the mapping relationship from single-point temperature data to two-dimensional temperature cloud map under physical constraints. Experiments show that our method can achieve comparable accuracy to supervised learning without temperature field image label and the calculation time is reduced by about 50% compared with numerical simulation, providing a complete theoretical and low-cost innovative solution for online health management of complex electronic devices.