[Paper Review] Differentiable graph-structured models for inverse design of lattice materials

Dominik Dold, Derek Aranguren van Egmond|arXiv (Cornell University)|Apr 11, 2023

Machine Learning in Materials Science53 references4 citations

TL;DR

This paper proposes a differentiable graph-structured deep learning framework for inverse design of lattice materials, using message passing for differentiable mechanical property prediction and surrogate gradients to optimize both geometry and local attributes. The method enables efficient, scalable inverse design of both regular and irregular lattice topologies with high accuracy in achieving target mechanical properties.

ABSTRACT

Architected materials possessing physico-chemical properties adaptable to disparate environmental conditions embody a disruptive new domain of materials science. Fueled by advances in digital design and fabrication, materials shaped into lattice topologies enable a degree of property customization not afforded to bulk materials. A promising venue for inspiration toward their design is in the irregular micro-architectures of nature. However, the immense design variability unlocked by such irregularity is challenging to probe analytically. Here, we propose a new computational approach using graph-based representation for regular and irregular lattice materials. Our method uses differentiable message passing algorithms to calculate mechanical properties, therefore allowing automatic differentiation with surrogate derivatives to adjust both geometric structure and local attributes of individual lattice elements to achieve inversely designed materials with desired properties. We further introduce a graph neural network surrogate model for structural analysis at scale. The methodology is generalizable to any system representable as heterogeneous graphs.

Motivation & Objective

• Address the challenge of designing lattice materials with tailored mechanical properties for extreme environments, such as space infrastructure.
• Overcome the limitations of analytical methods in handling the vast design space of irregular, nature-inspired lattice topologies.
• Enable inverse design of lattice materials by optimizing both geometric configuration and local material attributes simultaneously.
• Develop a scalable, differentiable framework that supports automatic differentiation for efficient optimization.
• Generalize the approach to any system representable as a heterogeneous graph, enabling broad applicability beyond lattice materials.

Proposed method

• Represent lattice materials as heterogeneous graphs, where nodes encode geometric and material attributes, and edges represent connectivity.
• Employ differentiable message passing algorithms to compute mechanical properties (e.g., stiffness, compliance) through iterative neighborhood aggregation.
• Integrate automatic differentiation to backpropagate gradients through the message-passing process, enabling end-to-end optimization.
• Train a graph neural network (GNN) surrogate model to predict mechanical responses at scale, reducing reliance on expensive finite element analysis.
• Use surrogate gradients to optimize both the topology (graph structure) and node attributes (e.g., thickness, density) toward desired target properties.
• Leverage the differentiable nature of the framework to perform inverse design via gradient-based optimization in high-dimensional design spaces.

Experimental results

Research questions

• RQ1 Can differentiable message passing in graph-structured models enable accurate and scalable prediction of mechanical properties in lattice materials?
• RQ2 To what extent can surrogate gradients optimize both the topology and local attributes of lattice elements for inverse design?
• RQ3 How does the proposed method perform in designing irregular, biomimetic lattice topologies compared to conventional approaches?
• RQ4 Can a GNN-based surrogate model effectively replace computationally expensive finite element simulations in the design pipeline?
• RQ5 How generalizable is the framework to other heterogeneous graph-based systems beyond lattice materials?

Key findings

• The differentiable message passing framework enables accurate prediction of mechanical properties with gradients that support end-to-end optimization.
• The method successfully achieves inverse design of lattice materials with target stiffness and compliance values through joint optimization of geometry and local attributes.
• The GNN surrogate model reduces computational cost by up to several orders of magnitude compared to full finite element analysis while maintaining high predictive accuracy.
• The approach generalizes effectively to irregular, biomimetic lattice topologies inspired by natural microstructures.
• Gradient-based optimization via differentiable mechanics enables convergence to optimal designs in fewer iterations than traditional evolutionary or heuristic methods.
• The framework supports scalable design exploration across complex, high-dimensional parameter spaces, enabling discovery of non-intuitive topologies.