Gradient-Based Shape Optimization for Engineering Using Machine Learning

Abstract

Shape design problems are important in engineering, e.g., trajectory planning for robot arms, material distribution optimization, etc. However, existing works usually solve these tasks without the help of gradients, whose efficiency can be limited. We formalize design problems as constrained optimization tasks and propose to use gradient-based optimizers with automatic differentiation to solve them. Specifically, we use the adjoint method when the underlying physical process can be characterized by PDEs. In Chapter 2, we solve for extruder paths of 3D printing that can compensate for the deformation caused by the fiber printing process. As the printing process is complex and difficult to model, we create a synthetic dataset and fit it using a neural network to get a differentiable surrogate of the printing simulator. We further speed up the optimization process by using a neural network to amortize it, sacrificing a bit of accuracy but getting much faster, real-time inferences. In Chapter 3, we study the task of fiber path planning, figuring out where to lay reinforcing fibers in plastic for 3D printing, maximizing the stiffness of the composite. We build a simulator by solving the linear elastic equations and use the adjoint method for gradient calculation and BFGS for fiber path optimization. In Chapter 4, we investigate the problem of dovetail joint shape optimization for stiffness. To model the contact between two parts of a joint, we build a simulator by alternatively solving one side of the joint while fixing the other side. We use the adjoint method for gradient computation and gradient descent for optimization. All methods across the projects are tested both in simulation and real-world experiments, showing our approach produces high-quality designs, and also the amortized approach provides real-time inference while achieving a comparable design quality.