Physics-Guided Neural Network for the Prediction of Mass Change from Water Diffusion

Machine learning (ML) processes such as neural networks (NN) have strong capabilities in the prediction of the state of a given problem domain. A drawback of NN’s is their inability to generalize predictions outside of the domain of data for which they are trained, a problem exasperated by sparse data sets. For physical processes, this can be remedied by the use of physics-guided neural networks (PGNN). By using physical equations describing the process, approximate outputs of a future state of the process can be generated for inputs outside the domain of measured data as well as optimize coefficients within the equation(s) to match the data via gradient descent.

The PGNN was applied to two polyurethane foam samples contained within a glovebox with controlled pressure, temperature, and varied humidity levels, with the mass of the samples finely measured to 0.01 mg precision over time. The mass of the samples obeys the physics of Fickian water diffusion from the air, which were utilized in the PGNN. Combining the physics approximation with data measured from the glovebox, an algorithm was produced that can approximate the future mass of a sample to within 10% of the measured mass for four differing humidity levels of 0, 5, 30, and 75% as well as optimize coefficients such as the diffusivity per area D/s² for some diffusivity D and unknown material thickness s to physically valid values of polyurethane foam. While future work is necessary to create a realistically applicable PGNN, this study indicates that physics can help guide future prediction regardless of a lack of measured data and outcomes to train upon.