Can we compile matter - for instance, a pine cone - and derive new active materials, end-to-end from observation to manufacturing? If physical systems can be formalized as composable mathematics, we can point AI that has been shown to resolve long-open mathematical problems at matter itself. Our new work... turns bioinspired engineering from analogy into formal compilation: biology and mechanics become explicit, checkable, and executable, so AI reasoning can produce physical designs. This is the first end-to-end demonstration in which a formally compositional multiscale model is carried from a biological hierarchy, through engineered design and fabrication specification, to executable manufacturing code - and then to a physically tested artifact. Background: Humans have long been inspired by biology to advance technology, but this has usually been an ad hoc process rather than a mathematically rigorous one. Natural materials such as pinecones achieve adaptive behavior through mechanisms organized across many scales. Engineering typically translates those mechanisms by analogy: identify a biological principle, build something inspired by it, and validate each new design as a separate case. This can produce remarkable results, but the knowledge does not readily compound. Instead, we represent each scale as a dynamical module with explicit states, stimuli, governing laws, and interfaces. Every scale-to-scale map must preserve the stimulus - response dynamics: evolve the fine-scale system and then map upward, or map upward first and then evolve. The two paths must agree. Because this condition is preserved under composition, locally valid interfaces remain consistent when assembled into the full hierarchy. We then carry that structure into an engineered system, translate the target behavior into a verified fabrication specification, and compile it into G-code: the toolpaths, deposition sequence, temperatures, speeds, and other commands executed by a 3D printer. The intermediate translations are explicit, checkable, and executable rather than completed through an ad hoc handoff. The formal guarantee is that given valid local models and interfaces, their composition remains valid. Whether those models and manufacturing assumptions accurately capture physical reality remains an empirical question. That is why we fabricated and tested the results. We generated four actuator classes by crossing two stimuli - humidity and heat - with two responses: bending and twisting. The fourth, thermal twisting, required no new pipeline and no separate derivation within the framework. It emerged by composing a thermal stimulus module already validated in one case with a twisting module validated in another. The generated G-code produced the intended motion without manual redesign, and all four predictions fell within one experimental standard deviation of the measured response. Why this matters: 1⃣For AI in science, this provides a physics-aware type system against which generative proposals can be checked - and rejected at the interface - before expensive simulation, fabrication, or experiment. It is roughly analogous to proof checking, but for the composition of physical mechanisms. 2⃣For engineering, the accessible design space can scale with a library of validated components rather than with the number of individually derived cases. 3⃣The mathematics, category theory, carries all the way into a physical object on a print bed. This points toward scientific knowledge as executable infrastructure: models that are not only described in papers, but typed, composable, verifiable, and able to compile into experiments. Excellent work led by my student Lee Marom with Skylar Tibbits & Gioele Zardini. Paper published in J. Mech. Phys. Solids along with code, Grasshopper scripts, and manufacturing G-code below.show more

Markus J. Buehler

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