Automated Simulation and the Discovery of Mechanical Devices

Abstract

Automatically designing or finding novel devices that accomplish new or existing functions remains one of the greatest unsolved problems in Design Automation. In part, this is due to 1) the interplay of physical form and usage, 2) the emergence of complex behaviors from combinations of simple geometries, and 3) the sparsity and instability of “interesting” physical phenomena with small changes in the design space, which have historically stymied past efforts, since most approaches required 1) human intuition and creativity, 2) infeasibly large amounts of computational power, or 3) a priori targeted desired behavior. In contrast, this dissertation takes a data-driven approach to addressing the general question “What device functionality emerges organically from knowledge of various physical laws?” To make this high-level question more precise, this dissertation tackles three interrelated sub-questions that address challenges that arise when attempting to deploy data-driven methods on function discovery tasks.

First, to generate diverse and high-quality datasets from which an algorithm might find novel behavior, this dissertation asks, “How do we enumerate possible boundary conditions for a given physical law that can lead to well-defined solutions to a given partial differential equation?” Chapter 3 proposes a type-based indexing scheme and two properties of that scheme that can generate valid Finite Element Method (FEM) formulations, resulting in a three-fold increase in the number of simulations we generated from our limited set of boundary conditions. Chapter 4 proposes a regression formulation for predicting physical realizability in Stokes flow simulations as estimated with the magnitude of the pressure field. Second, this dissertation asks, “How do we encapsulate the emergence of complex behaviors from interactions between different components?” Chapter 5 proposes reframing this question as an error regression, using graph neural networks to adjust for the “error” — i.e., emergent behavior — incurred by composing multiple basis Navier-Stokes simulations into one large simulation. Lastly, given solution field data, this dissertation asks, “Under what conditions can we detect novel device behaviors through computer-driven sim-ulation and exploration?” Chapter 6 proposes a boundary representation method and modified a hierarchical clustering approach, called Silhouette-optimized Hierarchical Density-Based Spatial Clustering of Applications with Noise (SHDBSCAN), to identify clusters of fluidic devices with similar behaviors. This chapter shows that the solution field representation has a significantly stronger impact on detecting novel device behaviors than the clustering algorithm used, but that a significant challenge lies in capturing “interesting” behavior in the design space in the first place.

Overall, this dissertation illuminates promising simulation methods for automating functional discovery and initial work on using data-driven methods to analyze such data. It also highlights several challenges, including the curse of dimensionality, that plague such approaches.