Accurate analysis and optimization of components, structures and shapes is very computationally expensive. We are working on reduced-order modeling methodology via deep convolutional neural networks (CNNs) for shape optimization applications. The CNN provides a nonlinear mapping between the shapes and their associated attributes while conserving the equivariance of these attributes to the shape translations. The CNN-based reduced-order model (ROM) is constructed in a completely data-driven manner thus well suited for non-intrusive applications. The CNN-ROM-based shape optimization algorithm exhibits significant computational efficiency compared to the full-order model-based online optimization applications.
Mallik, W., Farvolden, N., Jelovica, J., Jaiman, R.K. “Deep convolutional neural network for shape optimization using level-set approach“, arXiv:2201.06210
Machine learning (ML) is increasingly employed for mechanistic problems, but the black-box nature of conventional ML architectures lacks the physical knowledge to infer unforeseen input conditions. This implies both severe overfitting during a dearth of training data and inadequate physical interpretability. Therefore, we are developing a new kinematically consistent, physics-based ML models. We perform physically interpretable learning of inverse problems without suffering overfitting restrictions. We employ long short-term memory (LSTM) networks endowed with a physical, hyperparameter-driven regularizer.
Mallik, W., Jaiman, R.K., Jelovica, J. “Kinematically consistent recurrent neural networks for learning inverse problems in wave propagation”, arXiv preprint arXiv:2110.03903, October 8, 2021