# LEIA: Learned Environment for Interactive Architected Materials

arXiv: https://arxiv.org/abs/2605.28368 · HTML: https://mlsanity.com/paper/2605.28368/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 31 of its 69 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 30 of 31)

- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [Learning Interactive Real-World Simulators](https://mlsanity.com/paper/2310.06114/) (2023)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries](https://mlsanity.com/paper/2502.02414/) (2025)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Solving High-Dimensional PDEs with Latent Spectral Models](https://mlsanity.com/paper/2301.12664/) (2023)
- [Latent Neural Operator for Solving Forward and Inverse PDE Problems](https://mlsanity.com/paper/2406.03923/) (2024)
- [AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields](https://mlsanity.com/paper/2406.02176/) (2024)
- [Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators](https://mlsanity.com/paper/2402.12365/) (2024)
- [Derivative-enhanced Deep Operator Network](https://mlsanity.com/paper/2402.19242/) (2024)
- [SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2403.19507/) (2024)
- [VoMP: Predicting Volumetric Mechanical Property Fields](https://mlsanity.com/paper/2510.22975/) (2025)
- [Automotive Crash Dynamics Modeling Accelerated with Machine Learning](https://mlsanity.com/paper/2510.15201/) (2025)
- [MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanics](https://mlsanity.com/paper/2601.23177/) (2026)
- [GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training](https://mlsanity.com/paper/2602.20399/) (2026)
- [Geometry-Informed Neural Operator Transformer](https://mlsanity.com/paper/2504.19452/) (2025)
- [P3D: Scalable Neural Surrogates for High-Resolution 3D Physics Simulations with Global Context](https://mlsanity.com/paper/2509.10186/) (2025)
- [Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization](https://mlsanity.com/paper/2512.14086/) (2025)
- [Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics](https://mlsanity.com/paper/2511.08185/) (2025)
- [Learning Memory and Material Dependent Constitutive Laws](https://mlsanity.com/paper/2502.05463/) (2025)
- [A physics-encoded Fourier neural operator approach for surrogate modeling of divergence-free stress fields in solids](https://mlsanity.com/paper/2408.15408/) (2024)
- [Sobolev acceleration for neural networks](https://mlsanity.com/paper/2509.19773/) (2025)
- [Adaptive Mesh-Quantization for Neural PDE Solvers](https://mlsanity.com/paper/2511.18474/) (2025)
- [Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materials](https://mlsanity.com/paper/2512.01735/) (2025)

## Abstract (arXiv)

World models have enabled interactive exploration of game environments and robotic manipulation, but physical engineering remains beyond their reach: real materials exhibit nonlinear constitutive laws, carry history-dependent internal state, undergo inertial dynamics, and may possess hierarchical structures spanning multiple length scales. We present LEIA (Learned Environment for Interactive Architected materials), a world model that lets engineers apply boundary conditions step by step and observe the resulting deformation and stress fields in real time. LEIA handles large three-dimensional unstructured meshes and generates autoregressive responses to user-specified loading. We introduce MicroPlate, a benchmark of architected plates spanning two regimes of microstructure modeling: architected lattices that resolve microstructure explicitly through three-dimensional geometry, and a homogeneous plate where microstructural change is modeled implicitly through internal degrees of freedom. MicroPlate is used to assess LEIA alongside four baseline methods across both regimes. Finally, we demonstrate that LEIA enables efficient candidate generation and ranking for fast surrogate-guided search for de novo designs of architected materials, with stress-accurate candidate ranking validated by finite element ground truth.