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

2026-02-17

AI Summary

This work addresses the challenges in inverse material design posed by discrete parameters, physical constraints, and solution multiplicity, which often render gradient-based optimization ineffective. To overcome these limitations, the authors propose a differentiable framework that integrates continuous relaxation with guided diffusion. By relaxing the discrete design space into a continuous grid and combining differentiable finite element simulation with implicit differentiation, the method leverages a diffusion model during inference, steered by a multi-objective loss function to generate physically plausible designs. This approach achieves the first integration of implicit differentiation and diffusion priors for multimodal inverse material design. It efficiently produces diverse, physically valid 2D and 3D structures with relative errors below 1%, while simultaneously optimizing multiple performance objectives such as material density.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Diffusion Models for Vision
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT

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 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.

Problem

• inverse design
• material design
• design space constraints
• multi-modal solutions
• gradient-based optimization

Innovation

• guided diffusion
• inverse design
• differentiable simulation
• relaxed parameter space
• multi-objective optimization