Structural identification with physics-informed neural ordinary differential equations

This paper exploits a new direction of structural identification by means Neural Ordinary Differential Equations (Neural ODEs), particularly constrained domain knowledge, such as dynamics, thus forming Physics-informed ODEs, aiming at governing equations discovery/approximation. Structural problems often entail complex setups featuring high-dimensionality, or stiff which pose difficulties in the training and learning conventional data-driven algorithms who seek to unveil dynamics system interest. In this work, ODEs are re-casted two-level representation involving physics-informed term, that stems from possible prior knowledge dynamical system, discrepancy captured feed-forward neural network. The format is highly adaptive flexible monitoring problems, linear/nonlinear identification, model updating, damage detection, driving force etc. As an added step, for inferring explainable model, we propose adoption sparse nonlinear systems additional tool distill closed-form expressions trained nets, embed more straightforward engineering interpretation. We demonstrate framework on series numerical experimental examples, with latter pertaining behavior, successfully learned proposed framework. comes benefits direct approximation versatile modeling problems.