“What we were missing was a way to connect the mathematical description of a natural system all the way to its physical realization. The goal of this framework is to make that entire chain explicit so we can reason about what has to be preserved at each step,” Marom says.
The framework utilizes tools from category theory, which is a systematic method to compose larger systems from smaller ones in a way that is guaranteed to succeed.
Using category theory, the system maps out how a stimulus, such as humidity, causes a response at each level of the biological hierarchy within an organism like a pine cone. It models each level of the biological hierarchy as a separate building block that is independently validated.
Then the framework constructs a larger system from these building blocks by employing mathematical rules to ensure there is a valid transition between each step in the hierarchy.
It assigns each building block in the natural system to a synthetic counterpart. In this way, the engineered material preserves the stimulus-response interactions that cause the natural organism’s unique behavior.
The work extends a research program in Buehler’s laboratory spanning more than a decade.
Earlier studies used category theory to describe hierarchical materials and determine when building blocks could be replaced while preserving higher-level function. In subsequent work, Buehler and colleagues introduced “categorical prototyping,” using the same mathematics to preserve selected molecular-scale mechanics when translating computational models into large-scale 3D-printed prototypes.
The new framework takes the next step by closing the entire chain, from multiscale biological mechanics, through an engineered realization and fabrication specification, to an experimentally validated, machine-executable design.
“Biological materials derive their extraordinary functionality from relationships that span scales, from molecular and fiber-level mechanisms to whole structures. Category theory gives us a way to make those relationships explicit and transferable. Once that design logic is captured mathematically, nature becomes a library of composable mechanisms that can be translated, recombined, and realized in new material systems,” Buehler says.
Compositional structure
“Once we know that the relationships we mapped are valid, we can start recombining them in new ways. That means the framework isn’t only describing existing systems, it can also help us reason about ones we haven’t built before,” Marom explains.
For instance, the engineers mapped the humidity-driven bending behavior in a pine cone and the humidity-driven twisting behavior of a wheat awn as separate sets of building blocks.
Then they combined some building blocks from each to design and fabricate a new type of actuator that exhibits thermal twisting behavior, without the need to do any new design work. When tested, the twisting actuator performed as the researchers expected.
In the future, engineers could use this framework to reliably combine verified components into new, bio-inspired designs for adaptive materials in applications like robotics, biomedical devices, or wearable technology.
“The systematization of our framework allows you to reuse pieces without needing to start from scratch each time, saving a huge amount of computation. That’s the real-world payoff,” Zardini says.
Now that the researchers have laid the groundwork with this mathematical framework, they can apply it to objects with more complex mechanics. They also plan to incorporate artificial intelligence models into their pipeline to expedite the discovery of new adaptive materials.
“We have shown that the boundaries between disciplines do not matter as much as we think they do. Some of the principles from category theory can be used to guide and empower materials design. These mathematical structures seem to really have no boundaries,” Zardini says.
“The larger vision is physical AI: intelligence that can reason in terms of physical mechanisms and then turn those ideas into matter. Here we are beginning to build the infrastructure for that – composable physical knowledge, mathematical rules for determining what can be combined, and a path from a new design concept all the way to machine instructions and fabrication. Ultimately, this could allow AI not only to discover new materials and mechanisms, but to physically realize and test what it discovers,” Buehler says.
This research was supported, in part, by the MIT Lemelson Engineering Fellowship, Singapore DSO National Laboratories, and the MIT Generative AI Impact Consortium.