Interpretable and versatile data-driven mechanics: from classical theories to the art of data embedding

Feb
11

Interpretable and versatile data-driven mechanics: from classical theories to the art of data embedding

Bahador Bahmani, Johns Hopkins University

3:30 p.m., February 11, 2025   |   B001 Geddes Hall

The field of data-driven mechanics has advanced rapidly, driven by breakthroughs in artificial intelligence (AI) as well as computational hardware and software. One of its greatest promises is the potential to make physics simulations autonomous—an essential development given the significant growth in novel materials and emerging physical phenomena over the past decade, driven by technological progress. However, the interpretability, robustness, extrapolation, and data efficiency of AI-driven methods remain critical challenges, particularly in high-consequence engineering applications.

Bahador Bahmani

Bahador Bahmani,
Johns Hopkins University

In this talk, I will share my contributions to this exciting field, tackling some of these pressing issues. In the first part, I focus on physics-constrained material modeling, where the governing equations of deformable solids are assumed to be known, and the constitutive laws are derived from experimental data or fine-scale simulations. I demonstrate that formulating the search problem within a carefully designed embedding space—whether geometric or thermodynamic—enables the development of scalable algorithms that are fully interpretable, data-efficient, and capable of robust extrapolation.

In the second part, I relax the assumption of known governing equations and present a novel operator learning method to infer parameterized PDEs directly from multi-resolution, multi-fidelity data. I demonstrate how constructing a resolution-independent embedding space—addressing a key limitation of existing approaches—enables a simple, efficient, and interpretable framework with a built-in out-of-distribution metric that supports active learning. Additionally, I extend this method to quantify uncertainty in stochastic operators without requiring prior knowledge about the joint distributions or mutual independence of the underlying random variables. The versatility and impact of these methods will be demonstrated through applications in solid mechanics (soft materials, energetic materials, and granular materials) and broader classes of PDEs.

Bahador Bahmani is a postdoctoral fellow in the Hopkins Extreme Mechanics Institute at Johns Hopkins University. He obtained his Ph.D. in engineering mechanics from Columbia University. His research lies at the intersection of computational mechanics and scientific machine learning with applications to solid mechanics. He also has industrial research experience in computational geometry and machine learning within the additive manufacturing and data privacy sectors. Recognition of his work includes the Mindlin Scholar Award and Dongju Lee Memorial Award from Columbia University’s Fu Foundation School of Engineering and Applied Science, as well as fellowships and travel grants from the NSF, USACM, and ICERM at Brown University.