Title: Guided Diffusion by Optimized Loss Functions on Relaxed Parameters for Inverse Material Design
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
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. However, finding design parameters that achieve some desired output quantities can be ill-posed, if several design parameters can lead to the same or similar output values. For such cases, multi-modal probabilistic approaches are advantageous. The difficulties are exacerbated by the fact that the design problem can be 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 and evaluate our approach for a composite material design problem where the forward process is modeled as a linear FEM problem. 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.