Deep Generative Modeling for Computational Mechanics: Inverse Design and PDE-Based Simulations

 

Inverse materials design and simulation are at the heart of accelerating innovation in computational materials science. In this talk, we introduce a novel two-part research framework that leverages deep generative modeling to tackle both material discovery and the simulation of underlying physical systems.

 

We first introduce PSP-GEN, a probabilistic generative model for inverse materials design that operates across the full Processing–Structure–Property (PSP) chain. By learning low-dimensional, microstructure- and property-aware latent representations, PSP-GEN enables the generation of process-parameterized microstructures that are both high-performing and physically realizable. This approach is particularly effective under small training data, high-dimensional design spaces, and out-of-distribution target properties, making it a powerful tool for practical material discovery.

 

Next, we present DGenNO (Deep Generative Neural Operator), a novel physics-informed framework for solving parametric PDEs and their associated inverse problems. Unlike existing Deep  Neural Operator (DNO) solvers, DGenNO combines probabilistic generative modeling with neural operator learning to produce fast, uncertainty-aware, and physics-consistent solutions. It employs a new NO architecture, MultiONet, and a physics-driven training strategy that embeds weak-form residuals as virtual observations. This allows DGenNO to learn from both labeled and unlabeled data, significantly improving performance in noisy, discontinuous, and data-limited scenarios.

 

While developed independently, PSP-GEN and DGenNO are fundamentally synergistic. PSP-GEN provides a high-level inverse design framework, while DGenNO serves as a robust, data-efficient solver for the SP (Structure–Property) link by solving PDEs governing material behavior. Their shared foundation in generative, probabilistic modeling paves the way for a future unified framework that combines design, simulation, and uncertainty quantification in a physically consistent loop.

 

This research was conducted in collaboration with Prof. Faidon-Stelios Koutsourelakis at the Technical University of Munich (TUM).