Accelerated modelling of moisture diffusion controlled drying using coupled physics informed neural network.

A coupled physics informed neural network (CPINN) was used to simulate liquid diffusion controlled drying, an energy intensive process in the food industry. The architecture of the CPINN was designed to permit the prediction of thermo-physical properties and key source and sink terms at the solution boundaries which cause the solution to be highly coupled. The CPINN structure improves upon limitations of using PINNs in low-temperature food drying simulations, most notably allowing multiple and highly coupled variables to be simulated in additional to ensuring dynamic thermo-physical properties updates. The CPINN successfully solved a system 1-D partial differential equations (PDEs), capturing phenomena such as transient moisture diffusion and heat conduction, evaporative and convective heat transfer at the drying surface and moisture loss to the drying air. A benchmark simulation was used to compare the CPINN predicted product temperature, Tˆ _p, and predicted moisture content, Xˆ _p, against a numeric solution. The mean absolute error for the respective comparisons was 0.12 °C and 0.0035 kg _m kg _s ⁻¹. Training the CPINN for the first time was the rate limiting step, requiring the greatest time to solve when compared to the numeric solution, with solution times of t _cpinn = 321 min and t _rk = 82.7 min, respectively, or a time reduction fraction of t _r=3.9, due to generalised initialisation of the CPINN parameters. By utilising a staged transfer learning approach, t _r was reduced to a range of 0.28–0.027 whilst maintaining solution accuracy, representing a 3 to 37 times faster solution. By saving a library of CPINN models, solutions at key drying conditions of interest can be rapidly evaluated at run time, meaning the saved CPINN effectively acted as a method to compress solutions of PDEs. The techniques used here show how CPINNs can be applied to coupled and multi-scale PDEs using a physics-based approach to problems in the food processing and other sectors.