Learning from fracture: Teaching language models to design through physical experience

Bo Ni

Figure 1: FracLearn: learning to design through physical experience. The experience–abstraction–generalization framework is illustrated through a deliberately unfamiliar, Tetris-inspired fracture game. (A) Experience. Language model proposals are coupled with numerical search and fracture simulation to pursue focused optimization. Multiple campaigns, each centered on one design motif (

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N), collectively generate diverse physical experience. Blue and peach denote reinforcement and matrix, respectively; red paths indicate cracks. (B) Abstraction. Experience across campaigns is distilled into a “textbook” of conditional principles and design practices, with supporting evidence and limits. (C) Generalization. The model is challenged to combine lessons in new architectures and surpass the experience-stage record. The schematic performance trajectory illustrates refinement and recovery through hypothesis revision. The dashed line marks the earlier record, and red points identify designs exceeding it. (D) FracLearn. The interlocking puzzle represents our learning strategy for aligning language model reasoning with physical experience, enabling mechanistic understanding and design capability to develop together. Demonstrated here through fracture design, this integration could extend to other physical systems, using the computational scalability of language-model reasoning to expand researchers’ capacity to explore designs and develop explanations grounded in physical feedback.

Figure 2: A fracture-design game connects architectural choices with physical feedback. (A) A bioinspired material system with Tetris-based reinforcement assembly. Mineralized biological composites motivate the compliant matrix (apricot), stiffer and stronger reinforcement (ultramarine), and their elastic and fracture-property contrasts. Thirteen tetrominoes, drawn from seven shapes, occupy 52 cells of a 20

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9 design grid. The architecture is tested in a 100

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50 nm specimen with a 25-nm precrack. White outlines distinguish tetromino groupings; hatched matrix bands are protected against fracture. Opposing boundary displacements, +g and

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g, impose a traveling opening field; solid and dashed profiles indicate successive positions. (B) Composite scoring combines six performance measures with two deductions. The polygon shows the normalized components, annotated with their values and weights. Weighted benefits of 0.5647, less deductions for edge effects and instability, give a composite score of 0.5054. Component definitions are given in Materials and Methods.

Figure 3: FracLearn organizes language-model learning through experience, abstraction, and generalization. (A) A design cycle linking physical hypotheses to fracture evidence. The large language model (LLM) proposes a hypothesis, anticipated responses, and a structured design subspace. A deterministic compiler constructs admissible tetromino layouts, and a numerical selector explores this fixed pool through three batches of five finite-element method (FEM) evaluations. Crack and load responses and score components inform LLM reflection; the harness retains evidence and interpretations for the next cycle. (B) A learning progression connecting focused campaigns to new design tasks. Multiple cycles of (A) form a campaign. Six motif-focused campaigns generate diverse experience in Stage I. Cross-campaign abstraction compares supporting evidence and counterevidence, extracting conditional principles and practices into a textbook with source links, scope, predictions, and proposed tests. In Stage II, the LLM is tasked with combining textbook principles and retained experience in new architectures, assigning mechanical roles and predicting responses. Feedback-based instructions guide refinement, repair, or reconsideration toward exceeding the experience-stage record. Embedded A boxes refer to the shared design cycle. The score trajectory is schematic; the dashed line marks the earlier record. Blue and peach denote reinforcement and matrix; red paths indicate cracks. DOFs, degrees of freedom.

Figure 4: Physical experience guides motif-focused architectural refinement. (A) Distinct reinforcement motifs explored in six campaigns. Each specimen is the geometric medoid of the 15 first-cycle designs. Peach and blue denote matrix and reinforcement; white outlines delimit tetrominoes. Black segments mark the 25 nm precrack in each 100

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50 nm specimen. (B) Improvement through successive design cycles. Colored curves show cycle-best scores; the black curve shows their mean across campaigns, rising by 16.2% from cycle 1 to cycle 3. Each cycle evaluates three batches of five candidates, totaling 270 evaluations. (C) Architectural refinement and its mechanical consequences in Campaign 1. The first-batch best (Initial, gray) is compared with the campaign best from cycle 3 (Best, orange). Architectures and final crack paths accompany component scores, total reaction, and connected-crack extension. Red traces mark deleted-element footprints. Polygon axes show energy absorption (EA), total crack length (CS), stable crack growth (SG), peak load (PS), residual load capacity (RL), manufacturing simplicity (MS), and the complements of the edge-effect (1

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E) and instability (1

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I) deductions. Values range from 0 to 1, with favorable values outward; weights and deductions are defined in Methods. Total reaction sums the magnitudes of the upper and lower boundary reactions. Connected-crack extension is measured from the initial crack tip. Histories are plotted against loading-field position.

Figure 5: Abstraction connects diverse fracture experience to conditional design principles. (A) Diverse physical experience. The 270 Stage I architectures are summarized by reinforcement occupancy, crack activity, reaction histories, and score distribution. Occupancy and crack activity give the percentages of designs containing reinforcement at each cell and a deleted element at each mesh location, respectively. (B) Crack–reinforcement interaction in Campaign 4 (movie S1). The cycle-2 specimen (left) shows main-crack arrest with separated fracture traces above the reinforcement band and a higher peak reaction; the cycle-3 specimen (right) develops a more continuous fracture route. (C) Sensitivity to reinforcement placement. Two Campaign 2, cycle-2 variants share 46 of 52 reinforcement cells. Gold outlines mark the six cells relocated between layouts. Fracture follows lower and upper routes around the downstream cluster, accompanied by different peak reactions. (D) Interpreting secondary fracture. Additional fracture traces accompany similar peak reactions but different final load retention. Blue and orange curves correspond to the left and right specimens. Peak reactions are labeled in B and C, and final reactions in D. Reaction is the sum of the magnitudes of the upper and lower boundary forces. S denotes the composite score. In specimen maps, blue denotes reinforcement, peach matrix, and red deleted elements; pale red marks deletions adjoining retained shared nodes. White lines delineate tetrominoes, and black segments indicate initial cracks.

Figure 6: Generalization combines learned principles and revises hypotheses to advance fracture design. (A) Performance beyond experience. Cycle-best scores for four Stage II campaigns (left); black outlines mark results above the dashed Stage I record. Distributions include all evaluations in each stage (right), normalized separately; dashed lines mark means. (B) Combining lessons in a new architecture. Stage I exemplars inform the staggered core, flank guidance, and terminal relief proposed for Campaign 4, cycle 1. The selected design exceeds the Stage I record and retains 25.2% of peak reaction. Arrows indicate transfer of design ideas. (C) Recovery through hypothesis revision (movie S2). Campaign 3, cycles 6–8, compare an earlier best, an unsuccessful refinement with terminal bypass, and renewed crack interception after revision. The dashed arrow denotes recall of cycle 6; boxes locate terminal reinforcement. Cycle 8 exceeds cycle 6's score by 9.4% and retains 34.4% of peak reaction. Blue and peach denote reinforcement and matrix. Red marks fracture accumulated through peak force, including the peak state; gold marks subsequent fracture, and black the precrack. Diamonds and circles identify peak and final reactions. Reaction sums the magnitudes of upper and lower boundary forces; the horizontal coordinate is the traveling opening-field position. Specimen maps use the undeformed geometry and preserve tetromino boundaries.

Constituent parameter	Matrix	Reinforcement
Young’s modulus, E	5 GPa	50 GPa
Poisson’s ratio, $\nu$	0.35	0.28
Critical tensile stress for fracture, $\sigma$ c	0.25 GPa	1.5 GPa

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Figure S1: Homogeneous benchmarks of the fracture test. (A) Final crack maps for matrix-only and reinforcement-only specimens under the prescribed surfing boundary condition. Black segments mark the precracks; colored points locate deleted-element centroids, with color indicating the recorded solver step at deletion. (B) Reaction force versus connected crack extension, normalized by the peak reaction force of the matrix specimen. (C) Energy consumed per projected crack area divided by the corresponding deletion-energy estimate; the dashed line denotes unity. The ratios are 1.049 and 0.943 for matrix and reinforcement, respectively. These benchmarks assess the selected mesh and loading protocol. Definitions and parameters are given in Materials and Methods.

Campaign and motif	Architectural hypothesis	Anticipated fracture response
1 — Midspan stagger	A broad interior reinforcement region near midspan, with variations in horizontal placement and staggering.	Central interception may promote repeated deflection and segmented crack advance while limiting reliance on boundary-adjacent reinforcement.
2 — Protected channel	Two interior reinforcement lobes separated by a reinforcement-free matrix channel, with varied alignment and channel width.	Interaction with the lobes may increase crack tortuosity and distributed crack formation while preserving a matrix route through the central region.
3 — Terminal hook	An asymmetric reinforcement region in the downstream half, organized as a diagonal chain.	Delayed engagement may produce a late kink or hooked crack path, increasing path length without extensive off-path damage.
4 — Left-entry ladder	An oblique reinforcement chain extending from the crack-entry region toward midspan.	Earlier engagement may guide the crack through successive local kinks while maintaining connected advance through the reinforced region.
5 — Split-band gate	Upper and lower interior reinforcement bands arranged around a narrow matrix gate.	The crack may pass the gate and engage the offset bands sequentially, promoting reorientation and distributed crack formation.
6 — Diagonal + notch	An interior diagonal reinforcement chain interrupted near its midpoint by a small matrix-filled notch.	The interruption may promote staged engagement of upstream and downstream features, with directional changes near the notch instead of one uninterrupted barrier.

Table 9

LLM wording (verbatim)	Mechanical interpretation	Representative evidence	Implication for design and assessment
P1. “Guided main-crack interaction dominates simple obstruction”	Control how reinforcement impedes and redirects the advancing crack, including arrest and associated daughter-crack formation.	Fig. 5 B: left, main-crack arrest and separated fracture traces; right, a more continuous fracture route. Peak reactions are 3.65 and 3.26 nN, respectively. Additional element failure accompanies a force drop while the left main crack remains arrested.	Supports the mechanical value of arrest and renucleation ( 53 ) . The comparison does not establish that guidance generally outperforms obstruction.
P2. “Realized interaction field and placement are first-order mechanics variables”	Evaluate actual reinforcement placement, spacing, and alignment relative to the evolving crack and remaining load paths.	Fig. 5 C: relocating six cells switches the fracture route around the downstream cluster; peak reaction changes from 2.65 to 4.11 nN despite 46 shared reinforcement cells.	Place reinforcement to engage the evolving crack route. Local geometry and alignment provide more useful mechanical guidance than a cluster-count or motif label alone ( 54 , 55 ) .
P3. “Secondary fracture is evidence, not a verdict”	Interpret additional cracks using their accompanying fracture and load histories before assigning a mechanical benefit.	Fig. 5 D: secondary traces coexist with final reactions of 0.087 and 0.865 nN despite similar peak reactions.	Assess how the location of secondary cracks relates to remaining load transfer. Similar fracture features can coexist with different residual responses; their presence alone does not determine their mechanical role.
P4. “Metrics are diagnostic readouts with a strict hierarchy”	Check rule validity, interpret fracture behavior, and assess the full score together with its component measures.	Fig. 5 C: local placement changes fracture routing and peak reaction. Fig. 5 D: secondary traces and similar peak reactions accompany markedly different final load retention.	Use complementary observables to assess the intended mechanism. Fracture-surface creation and effective toughness are distinct ( 56 , 52 ) , and a combined objective retains trade-offs among responses.

Table 10

Learning from fracture: Teaching language models to design through physical experience

Abstract

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