• Aditya Balu
• Olga Wodo
• Adarsh Krishnamurthy, Iowa State University
• Baskar Ganapathysubramanian

Machine learning based-approaches in engineering design have seen rapid progress in recent years. Modern ML/AI approaches have transformed a host of application areas that involve assimilating large data streams to make valuable predictions. The next generation of approaches will leverage these advances to analyze, optimize, design, and control complex engineered systems. Researchers have been leveraging novel tools in machine learning–such as deep generative models, deep reinforcement learning–as a computationally efficient paradigm for modeling and simulation of complex engineered systems. However, despite their apparent utility, current AI systems suffer from three key drawbacks:
• Reliance on an abundance of data: Current AI systems tend to let data dictate the narrative entirely. As a result, the data requirements for training such systems are substantial, which may be a significant bottleneck for complex simulations and expensive experiments.
• Lack of generalizability: Current ML/AI systems are of a narrow scope, i.e., they typically only succeed on the task on which they are trained. Additionally, contextual constraints and domain knowledge known from the physical system are usually not incorporated.
• Unsatisfactory parsimony and explainability: Most current ML models are non-parsimonious and un-interpretable. This un-explainability is especially damaging when the end goal–identifying functional relationships in complex systems or constrained explorations of the design space–requires generating insights into the engineered system.

Recent efforts with the advent of physics informed neural networks (PINNs), generative neural network models (such as generative adversarial networks, or GANs) have proven to be of tremendous impact in numerous tasks such as prediction, visualization, and design. These approaches are a significant departure from the typical, data-hungry approach required by the traditional ML training method since the encoded invariances allow for physically meaningful predictions using far less training data. In our view, these approaches are suitable for solving the forward design problem (where one is just solving for physics). While most of the advancement in this area is based on solving the forward problem, inverse design for engineering systems goes beyond the current research efforts. Inverse design models can naturally account for uncertainty, need very few training data pairs, and explicitly account for multiscale physical constraints. We hope to see several other researchers in the community work more closely on this research area. However, there are several unanswered research question; some of the key areas of research include:
• Developing principled approaches for incorporating physics-based constraints into generative models;
• Quantitative guarantees that link model architecture, predictive performance, and generalization;
• Construction of new generative model architectures for physical domains with complex geometries.

Addressing these research questions requires revolutionary advances in AI, physics-based modeling and simulation, optimization, computational science. Further, these ideas can be extended to complex engineering systems, which include physical phenomena such as turbulence, fluid-structure interaction, and complex material dynamics. We hope that our minisymposium would be a suitable forum to share the recent advances in these fields.