UC Berkeley

Numerical simulation is a powerful tool that aids scientists in the understanding of the physics of the world around them, but to achieve an understanding of the physics, we must start with a representation of the geometry. Embedded Boundary (EB) simulation provides robust, automatic handling of complex geometries, enabling large scale physics simulations, but it still depends on an initial 3D implicit function representation of said geometry. These geometries are typically user-supplied through 3D design specifications, but for many domains of interest (i.e. outdoor scenes such as cities or forests) no such design specifications exist. This means that simulations of this nature rely on expensive, time consuming, and often noisy measurements from LiDAR or other sources, and because of the cost and lack of quality in the results, there have been relatively few 3D, large scale EB simulations of outdoor scenes.

Recent advances in computer vision, such as Neural Radiance Fields (NeRFs) and their corresponding Neural Signed Distance Functions (NeuS) have made producing 3D implicit functions from images much easier, but they have not yet been studied from the view point of numerical simulation. In this thesis, we present for the first time a 3D simulation using the Embedded Boundary method on a neural-SDF learned from images, demonstrating the feasibility of this approach. In the process, we identify several challenges in bridging the two methods, including differences in how the computer vision community measures error/uncertainty and what types of error/uncertainty actually matter in an EB simulation, and present appropriate alternatives. In the following chapters, we describe several methods for learning 3D geometries from RGB images, discuss their suitability for scientific tasks, and do an in-depth analysis of their error and uncertainty and how those affect a physics simulation. We finally discuss this pipeline through the lens of a high-impact, real-world application: forest management. We reconstruct a forest scene using NeRF that is visibly much more appropriate for simulation than previous examples. We also discuss what challenges this real-world data presents and how the technology presented in this thesis can be used to answer real scientific questions.