THE FEATHERWEIGHT FORTRESS
Machine learning and 3D printing at the nanoscale have resulted in a lightweight material with one of the highest strength-to-weight ratios ever achieved.
Written by Nicole Imeson

From left to right: An image of the full lattice geometry is juxtaposed with an 18.75-million cell lattice floating on a bubble. Photos: Peter Serles and Tobin Filleter, University of Toronto
WITH THE HELP OF MACHINE LEARNING algorithms, researchers at the University of Toronto have engineered nanoscale building blocks into 3D structures with the compressive strength of carbon steel and the density of Styrofoam.
This nano-architected material the team developed was so strong and lightweight that it outperformed existing materials in its weight class by more than a factor of ten. The final product featured struts measuring just 300 nanometers—about 200 times thinner than a human hair.
Since the early 2010s, research into nano-architecting has boomed, where nano-3D printing combines mechanical structuring and nanoscale strengthening to achieve new material properties. Researchers have explored a wide range of classical materials, geometries, and densities. But rather than relying on brute force for design iterations, this new approach implements a machine learning tool to generate new geometries and a lattice design that avoids stress concentrations with reinforced nodes, tapered struts, and an optimized lattice structure.
“This challenge suited machine learning perfectly,” explained Peter Serles, now a Schmidt Science Fellow at Caltech and co-lead author of “Ultrahigh Specific Strength by Bayesian Optimization of Carbon Nanolattices.”
“We knew a few key structural features, but the machine learning algorithm explored the entire design space, developed brand new designs that were unintuitive for our typical understanding, and led to some outstanding results,” Serles said.

Tobin Filleter (left) and Peter Serles (right). Photos: Daria Perevezentsev and Dewey Chang
MACHINE LEARNING
Co-lead author Jinwook Yeo from the Korea Advanced Institute of Science and Technology led the team in using Multi-objective Bayesian Optimization (MBO) to refine the design. First, the researchers converted its initial 3D lattice shape into mathematical variables, breaking it down into 2D cross-sections. To explore structural variations, they analyzed two lattice configurations: CFCC (crystal face-centered cubic), where nodes sat at cube corners and face centers, and CBCC (crystal body-centered cubic), which positioned nodes at cube corners and the cube center. While the nodes remained fixed, the machine learning algorithm adjusted the struts between them in each iteration.
With their lattice structures defined, the team programmed the algorithm to optimize key objectives, minimize density, and enhance compressive and shear stiffness. The algorithm then systematically altered each geometry, adjusting variables while enhancing mechanical properties and testing the results.
“We didn’t just randomize variables and find the shapes that performed well. The algorithm recognized patterns in what worked and what failed, then generated entirely new geometries,” Serles explained.
In addition to accelerating design iterations, machine learning unlocked possibilities beyond human intuition, producing results well outside the research team’s expectations. “Most of the geometries it started with were terrible,” Serles said. “Random changes created far more bad designs than good ones. But the algorithm learned from these and once the algorithm optimized them, the best structures it produced outperformed everything we had encountered.”

Finite element analysis maps of stress distribution from standard to MBO machine learning design. Image: Peter Serles and Tobin Filleter, University of Toronto

Scanning electron microscopy images of an MBO machine learning designed lattice profile and standard lattice profile. Photo: Peter Serles and Tobin Filleter, University of Toronto
3D PRINTING AND PYROLYZING
Researchers used two-photon polymerization to nano-3D print the design. A printer directs a laser beam into a pool of liquid resin, instantly solidifying material at each precise contact point. The tightly controlled laser beam polymerized only within a 200-nanometer central area, allowing for construction of struts with initial diameters ranging from 800 to 1,000 nanometers.
After printing the structure, the researchers subjected it to pyrolysis, exposing it to intense heat under vacuum that stripped away oxygen and hydrogen atoms, leaving behind a pure carbon framework. The structure uniformly contracted, shrinking to one-fifth its original size without warping. Given the part’s miniscule size, it was placed on stilts to allow it to collapse inward as it shrank rather than getting lost. The final product displayed struts with diameters around 300 nanometers.
While typical two-photon polymerization is quite slow, the team partnered with laser optics researchers at the Karlsruhe Institute of Technology in Germany to employ an ultrafast printer consisting of 49 lasers to produce 18.75 million lattices stacked together. This structure, measuring about 15 cubic millimeters after pyrolysis, can balance on a bubble yet outperformed the strength of other materials in its weight class by multitudes.
MBO machine learning lattice (left) and standard lattice (right) undergoing in situ uniaxial compression in a scanning electron microscope. Video: Peter Serles and Tobin Filleter, University of Toronto
APPLICATIONS
Although 3D printing speeds must improve before commercial use, the material’s design scales effectively by connecting millions of the unit cells together. The most promising application lies in aerospace. The team estimated that replacing a single kilogram on an aircraft with nano-architected materials could save 80 to 100 liters of fuel annually. Scaling this across larger sections of a plane could lead to exponential fuel savings.
Beyond this specific material, the research highlighted machine learning’s power in material design.
“Many challenges stem from material limitations,” explained Tobin Filleter, professor of mechanical engineering at the University of Toronto and senior author of the work. “This work sets the framework for how machine learning can create new materials. With better machine learning tools, we can enhance material properties more effectively, opening doors to dozens of new applications.”
Nicole Imeson is an engineer and writer in Calgary, Alta.

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