Guided Diffusion by Optimized Loss Functions on Relaxed Parameters for Inverse Material Design

Jens U. Kreber, Christian Weißenfels, Joerg Stueckler

Keywords: guided diffusion, inverse design, material design

Abstract: Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate step, which is often an optimization problem by itself. In many scenarios, several design parameters can lead to the same or similar output values. For such cases, multi-modal probabilistic approaches are advantageous to obtain diverse solutions. Additional difficulties arise if the design problem is constrained. We propose a novel inverse design method based on diffusion models. The model learns a prior over possible approximate designs in a relaxed parameter space. Parameters are sampled using guided diffusion for which we leverage implicit differentiation of the simulation to evaluate the loss function. A design sample is obtained by backprojecting the sampled parameters. We develop our approach for a composite material design problem where the forward process is modeled as a linear FEM problem. We evaluate with the objective of finding designs that match a specified bulk modulus. We demonstrate that our method can propose diverse designs within 1% relative error margin from medium to high target bulk moduli in 2D and 3D settings. We also demonstrate that the material density of generated samples can be minimized simultaneously by using a multi-objective loss function.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 2149