2025 Theses Doctoral

Generative Modeling with Sparse Data for Solid Mechanics

Poliner, Jarett Stephen Lo

This thesis introduces a generative artificial intelligence framework for modeling multiscale, path-dependent material behaviors from sparse experimental observations, a setting of critical importance for energy, defense, and infrastructure applications. The central challenge in such settings is the prevention of overfitting with limited data while maintaining robust predictive performance. We address this barrier by combining graph neural networks, latent diffusion models, Bayesian optimization, and projection-based finite element integration into a unified, data-efficient and interpretable modeling pipeline.

Unlike machine learning applications that rely on vast and rich datasets (such as recommender systems), experimental observations and even sub-scale simulations from molecular dynamics or microscopic representative volumes are often costly to obtain. When additional experiments are infeasible, synthetic data generated from artificial intelligence can serve as auxiliary evidence for inference. Chapter 2 presents a data-driven framework that generates synthetic microstructures inferred from real micro-CT images. These microstructures support boundary-value simulations that yield supplementary data for the design-of-experiments and modeling tasks in Chapters 3 and 4. A key technical barrier is the curse of dimensionality: for 3-D voxelized microstructures, producing topologically consistent images with conventional convolutional networks is challenging. We overcome this via a hierarchical divide-and-conquer strategy. At the topological level, we use autoregressive deep generative graphs to construct particle networks with descriptor-defined attributes. At the geometric level, conditional diffusion models generate local particle shapes conditioned on node features, employing classifier-free guidance to align synthetic morphologies with global statistics (e.g., mean curvature and orientation distributions). Validation demonstrates that the framework produces synthetic microstructures that are topologically and geometrically consistent with experimental references.

Chapter 3 addresses data scarcity by optimizing sequential data acquisition. We consider a setting in which training data can be acquired on demand, and the key decision is where within the parameter space additional information would be most valuable to obtain. To this end, we employ Bayesian optimization with maximum-entropy sampling, guided by a continuously updated Gaussian-process surrogate. This strategy efficiently recovers anisotropic yield surfaces with far fewer simulations than baseline heuristics. To further leverage the limited data, we introduce a generative latent diffusion model that infers yield surfaces directly in stress space. This model enables maximum-likelihood estimation of yield points without requiring supervised labels, allowing it to generalize to sparse or incomplete data.

With auxiliary data generated from synthetic microstructures in Chapter 2, and information-optimal sampling and diffusion-driven inference introduced in Chapter 3, Chapter 4 develops an interpretable material model that integrates these components into a predictive constitutive framework. We design a projection-based stress update algorithm tailored for mesh-based simulations, which supports stable, parallel integration without the numerical cost of conventional return-mapping schemes.

Collectively, these contributions establish a data-efficient pipeline that unifies synthetic microstructure generation, information-optimal sampling, and diffusion-driven constitutive inference, together with a projection-based stress update for stable, parallel finite-element integration. The result is a reliable and scalable framework for predicting multiscale, path-dependent material behavior under sparse data regimes.