Haiqian Yang

Haiqian Yang, Yuan Cao, Markus J. Buehler

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.

Haiqian Yang, Vishaal Krishnan, Sumit Sinha et al.

Controlling the evolution of a many-body stochastic system from a disordered reference state to a structured target ensemble, characterized empirically through samples, arises naturally in non-equilibrium statistical mechanics and stochastic control. The natural relaxation of such a system - driven by diffusion - runs from the structured target toward the disordered reference. The natural question is then: what is the minimum-work stochastic process that reverses this relaxation, given a pathwise cost functional combining spatial penalties and control effort? Computing this optimal process requires knowledge of trajectories that already sample the target ensemble - precisely the object one is trying to construct. We resolve this by establishing a time-reversal duality: the value function governing the hard backward dynamics satisfies an equivalent forward-in-time HJB equation, whose solution can be read off directly from the tractable forward relaxation trajectories. Via the Cole-Hopf transformation and its associated Feynman-Kac representation, this forward potential is computed as a path-space free energy averaged over these forward trajectories - the same relaxation paths that are easy to simulate - without any backward simulation or knowledge of the target beyond samples. The resulting framework provides a physically interpretable description of stochastic transport in terms of path-space free energy, risk-sensitive control, and spatial cost geometry. We illustrate the theory with numerical examples that visualize the learned value function and the induced controlled diffusions, demonstrating how spatial cost fields shape transport geometry analogously to Fermat's Principle in inhomogeneous media. Our results establish a unifying connection between stochastic optimal control, Schrödinger bridge theory, and non-equilibrium statistical mechanics.

Haiqian Yang, Anh Q. Nguyen, Dapeng Bi et al.

During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology that defines how living organisms form. Establishing tissue-level morphology critically relies on how every single cell decides to position itself relative to its neighboring cells. Despite its importance, it remains a major challenge to understand and predict the behavior of every cell within the living tissue over time during such intricate processes. To tackle this question, we propose a geometric deep learning model that can predict multicellular folding and embryogenesis, accurately capturing the highly convoluted spatial interactions among cells. We demonstrate that multicellular data can be represented with both granular and foam-like physical pictures through a unified graph data structure, considering both cellular interactions and cell junction networks. We successfully use our model to achieve two important tasks, interpretable 4-D morphological sequence alignment, and predicting local cell rearrangements before they occur at single-cell resolution. Furthermore, using an activation map and ablation studies, we demonstrate that cell geometries and cell junction networks together regulate local cell rearrangement which is critical for embryo morphogenesis. This approach provides a novel paradigm to study morphogenesis, highlighting a unified data structure and harnessing the power of geometric deep learning to accurately model the mechanisms and behaviors of cells during development. It offers a pathway toward creating a unified dynamic morphological atlas for a variety of developmental processes such as embryogenesis.

Haiqian Yang, Florian Meyer, Shaoxun Huang et al.

Multicellular self-assembly into functional structures is a dynamic process that is critical in the development and diseases, including embryo development, organ formation, tumor invasion, and others. Being able to infer collective cell migratory dynamics from their static configuration is valuable for both understanding and predicting these complex processes. However, the identification of structural features that can indicate multicellular motion has been difficult, and existing metrics largely rely on physical instincts. Here we show that using a graph neural network (GNN), the motion of multicellular collectives can be inferred from a static snapshot of cell positions, in both experimental and synthetic datasets.