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LEIA: Learned Environment for Interactive Architected Materials

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: Physics-informed dynamics learning · 0 citations (OpenAlex)

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Introduces LEIA, an action-conditioned latent world model (Perceiver tokenizer + adaLN transformer dynamics + stress head) for interactive nonlinear 3D solid mechanics on architected materials, with the MicroPlate benchmark and surrogate-guided beam search validated by FEM.

Problem

Neural surrogates for 3D nonlinear solid mechanics on large unstructured meshes, with accurate stress and responsiveness to user-specified loading, are lacking for interactive design of architected materials.

Approach

Combines Perceiver IO tokenization for mesh-size invariance, action-conditioned (adaLN/FiLM-style) latent transformer dynamics for boundary-condition control, and a lightweight linear stress head that directly predicts Cauchy stress rather than deriving it from predicted displacement gradients.

Key results

• On the visco-hyperelastic plate, the stress head lifts von Mises correlation for all four baselines above 0.94 (vs at most 0.26 with indirect prediction), while LEIA reaches 0.986 VM correlation under 100-step AR rollout.
• Stress head + pushforward on lattice tokenizer reaches 4.68% in-distribution displacement L2 error and 0.942 VM correlation at +6% training overhead, versus +1160% for autograd Sobolev.
• Surrogate-guided beam search evaluates 553 candidates in 30 minutes and finds a design with a 3.6x improvement in the design metric validated by FEM.

Surprising findings

• Without a stress head, autoregressive rollout of MeshGraphNets degrades to stress correlation 0.225 alongside displacement collapse, while direct stress supervision lifts all baselines above 0.94 teacher-forced VM correlation.
• Gradient-based autograd Sobolev supervision gives smaller stress gains than cheap tet-shape-function supervision on the lattice regime despite much higher cost.

Limitations

• Evaluated only on cubically symmetric lattice plates with fixed 5x5x1 tiling and a 4-DOF action space; transfer to other geometries or actions is untested.
• No active learning at inference; out-of-distribution reliability relies on a learned confidence head that still misses some in-distribution inaccurate cases.

Experimental setup

Datasets: MicroPlate lattice regime (63 architected lattices, FEM-generated) MicroPlate visco-hyperelastic plate (1,000 FEM trajectories)

Benchmarks: MicroPlate

Metrics: displacement relative L2 error von Mises stress Pearson correlation inference speedup vs FEM FEM-validated design metric improvement

Baselines: MeshGraphNets UPT PointNet Transolver tet Sobolev autograd Sobolev gradient head

Builds on: Perceiver IO DiT adaLN pushforward training Universal Physics Transformers MeshGraphNets

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