Abstract
Many engineering systems involve multiple interacting disciplines or subsystems. For a design or analysis task, unknown linking variables, which are those variables that are outputs of some disciplines and inputs of other disciplines, are obtained by solving the system of implicit interdisciplinary compatibility equations for a given set of system inputs. This study creates surrogate models for linking variables using label-free training with neural networks. The compatibility equations are embedded in the cost function of the model training. They are calculated and are not solved for given input training variables, thereby avoiding label acquisition. To quantify the prediction errors of the surrogate models, we build their error models with Gaussian Process regression, which uses the existing training points and the derivatives of the compatibility equations at the training points. The error models are then used to compensate for the errors of neural network surrogate models of the linking variables, producing more accurate predictions of linking variables with quantified model uncertainty for predicting system responses. The linking variables with quantified model uncertainty are then used to predict the system responses and associated prediction errors. We demonstrate the effectiveness of the proposed method by the application to a propane combustion problem.
