Guided Diffusion by Optimized Loss Functions on Relaxed Parameters for Inverse Material Design
This addresses the challenge of inverse design for engineers and materials scientists by enabling efficient, gradient-based optimization in discrete parameter spaces, though it is incremental as it builds on existing diffusion models and differentiable simulation techniques.
The paper tackled the inverse design problem in materials science by proposing a diffusion model method that relaxes discrete design spaces into continuous representations, enabling gradient-based optimization through differentiable simulations. It demonstrated the ability to generate diverse composite material designs matching target bulk moduli within 1% relative error in 2D and 3D settings, while also minimizing material density with multi-objective loss functions.
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 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. A major difficulty in inverse design stems from the structure of the design space, since discrete parameters or further constraints disallow the direct use of gradient-based optimization. To tackle this problem, we propose a novel inverse design method based on diffusion models. Our approach relaxes the original design space into a continuous grid representation, where gradients can be computed by implicit differentiation in the forward simulation. A diffusion model is trained on this relaxed parameter space in order to serve as a prior for plausible relaxed designs. Parameters are sampled by guided diffusion using gradients that are propagated from an objective function specified at inference time through the differentiable simulation. A design sample is obtained by backprojection into the original parameter space. We develop our approach for a composite material design problem where the forward process is modeled as a linear FEM problem. We evaluate the performance of our approach in 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.