Physics Knowledge Discovery via Neural Differential Equation Embedding

Despite much interest, physics knowledge discovery from experiment data remains largely a manual trial-and-error process. This paper proposes neural differential equation embedding (NeuraDiff), an end-to-end approach to learn a physics model characterized by a set of partial differential equations directly from experiment data. The key idea is the integration of two neural networks – one recognition net extracting the values of physics model variables from experimental data, and the other neural differential equation net simulating the temporal evolution of the physics model. Learning is completed by matching the outcomes of the two neural networks. We apply NeuraDiff to the real-world application of tracking and learning the physics model of nano-scale defects in crystalline materials under irradiation and high temperature. Experimental results demonstrate that NeuraDiff produces highly accurate tracking results while capturing the correct dynamics of nano-scale defects.