New Machine Learning Framework Enables Data-Efficient Design of Advanced Metamaterials

Researchers at Northwestern Engineering have developed a scientific machine learning framework that predicts and inversely designs the mechanical behavior of spinodal metamaterials – specially engineered structures with tiny, sponge-like architectures that give them unique mechanical properties – using limited but high-quality experimental data. 

The method offers a way to accelerate the development of lighter, stronger, and more energy-efficient materials, with potential applications in aerospace, defense, biomedical implants, and electronics. It reduces the need for costly and time-intensive trial-and-error testing, which has traditionally slowed innovation in materials science.

“By reducing the number of iterations in materials development, this work lowers costs and shortens the innovation cycle,” said Horacio D. Espinosa, the James N. and Nancy J. Farley Professor in Manufacturing and Entrepreneurship and professor of mechanical engineering at the McCormick School of Engineering. 

The framework models the complex mechanical behavior of spinodal microstructures by combining submicron 3D printing, in-situ electron microscopy testing, and deep learning. It accurately captures nonlinear, directional stress-strain responses with prediction errors as low as 5 to 10 percent.

It also supports inverse design, enabling users to specify the desired mechanical performance and generate a corresponding material structure.

“Our method further enables inverse design of microstructures, matching targeted mechanical responses within one to 15 percent accuracy, which were experimentally validated,” Espinosa said.

Espinosa, Northwestern Engineering’s Sridhar Krishnaswamy, and collaborators from Brown University (Professor George Karniadakis and his team) presented their findings in the paper “Characterization and Inverse Design of Stochastic Mechanical Metamaterials Using Neural Operators,” published April 21 in the journal Advanced Materials. The work was supported by the Air Force Office of Scientific Research, the Office of Naval Research, and the US National Science Foundation.

Most approaches to machine learning-based inverse design require large amounts of simulation or experimental data, which are costly and time-consuming, especially for microscale and nonlinear systems.

“This work overcomes those challenges,” said Krishnaswamy, director of the Center for Smart Structures and Materials and professor of mechanical engineering.

The model is based on a two-step Deep Operator Network (DeepONet) architecture that includes symmetry-preserving features to handle the geometric characteristics of architected materials. The paper introduces a novel architecture tailored for data-scarce, nonlinear mechanical systems; a domain where conventional machine learning approaches fail.

Unlike many previous methods, the model is trained on real-world data instead of simulations.

“It sets a precedent for using real, scarce and sparse experimental data — not simulations — as the foundation for inverse design of architected materials, bridging the gap between theoretical design and fabrication reality,” Espinosa said. 

The framework is designed to be transferable to other material types and use cases. It is also scalable and adaptable to other classes of metamaterials and future multi-functional materials, making it a potentially transformative step toward AI-guided materials-by-design.

This research builds on prior work in spinodal microstructure design, scientific machine learning, and neural operator models for multiscale systems. Looking ahead, the Northwestern team is looking to apply the framework to new classes of materials and expand its design capabilities.

“We are planning to explore other material systems, such as glassy carbon or nanocrystalline metals,” Espinosa said. “We also aim to integrate reduced-order modeling or multi-fidelity approaches to combine low-cost simulations with high-fidelity experimental data.”

Additional goals include expanding the framework to model more than just mechanical behavior. The Northwestern team plans to apply the approach to multifunctional metamaterials with thermal, acoustic, or biological properties, and to develop generative design tools that use machine learning to quickly evaluate design options.