From Atoms to Swarms: The Categorical Spine of Multiscale Materials Modeling and Autonomous Discovery
Year: 2026
Type: preprint
Abstract: Many biological materials and material systems-silk, collagen, bone, spider webs and many others-achieve strength, toughness, adaptability, or resilience by organizing weak interactions and limited molecular alphabets hierarchically. In these systems, function often lives in the organization rather than in the components. Working with such materials computationally cannot mean computing at a single scale. It must mean moving information between scales without destroying what matters. Here we review research that has focused on attempts to identify, formalize, and now operationalize the invariants that survive those handoffs across scales, systems and modalities. The difficulty is structural: the invariants rarely coincide with the most visible features. A spider web is not robust because each silk fiber is intrinsically strong, and bone is not tough because mineral platelets are themselves tough; the function emerges from how nonlinear response, hierarchy, and topology compose. Identifying the compositional invariant-and not any single ingredient-is the modeling problem. This Account traces an arc that begins with reactive molecular dynamics of dynamic fracture, the hierarchical mechanics of collagen and silk, and the mechanism-level coupling between molecules, fibrils, and spider webs. It then moves into machine-learning surrogates, generative inverse design, materiomusic, neurosymbolic reasoning, and finally agentic discovery and plannerless scientific swarms. All these can be read as structure-preserving maps between typed objects, and category theory provides a disciplined vocabulary for stating what each map preserves and what it does not. This is a vocabulary, not a source of theorems, and that distinction matters. Its value is operational as it forces us to declare which types survive a coarse-graining step, which symmetries a learned surrogate respects, and where each diagram fails to commute. In a field where modern AI methods readily produce fluent answers without grounding, that discipline is not optional but must be a disciplined component. The claim put forth here is that the durable product of materials discovery is shifting from isolated artifacts to generative algorithms. A protein, composite microstructure, alloy, field predictor, graph, or piece of materiomusic remains a useful output, but the more transferable result is the loop that produced it: an alphabet of primitives, a grammar of composition, a neural generator, symbolic constraints, a verifier, provenance, and an update rule. When such a system can also revise its own grammar and verifier under physical constraints, the discovery loop becomes self-referential. The deepest claim is therefore that future materials discovery will not be organized primarily around one protein, one composite, one alloy, one melody, or one graph, but around self-revising generative algorithms that can compose, test, falsify, and update scientific worlds while remaining tied to physical evidence. The arc of this paper - from physics-grounded simulation through surrogates, generative design, neurosymbolic reasoning, and swarms - is then best read as a single object viewed at progressively higher levels of self-reference.
Source: ChemRxiv
Author: Markus J. Buehler
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160545548