Description
- Abstract:
- The objective of this research is to address two fundamental bottlenecks in modern engineering design: the prohibitive cost of high-fidelity physical simulations and the need for efficient design workflows. The research is presented in two interconnected parts. Part I develops a new generation of data-driven surrogates, geometry-aware neural operators, capable of delivering rapid and accurate physical predictions across varying designs. Part II shifts focus from simulation tools to the design process itself, developing Large Language Model (LLM) powered multi-agent frameworks to automate, augment, and reason through complex engineering tasks. Part I addresses a critical limitation of traditional neural operators: their inability to generalize across varying geometric domains, a necessity for design exploration. We progressively build this capability through novel neural operator frameworks. We first establish the Multi-Task DeepONet (MT-DeepONet) for synergistic learning across multiple geometries and PDE parameters. We then introduce Fusion-DeepONet, a highly data-efficient operator that proves robust in learning complex hypersonic flows for aerospace applications, enhanced by a derivative-aware loss to accurately predict critical surface quantities. Finally, a hybrid DeepONet-Transolver framework demonstrates versatility by capturing the highly nonlinear buckling behavior of complex structures. Collectively, these contributions deliver accurate, geometry-aware surrogates applicable across fluid and solid mechanics. Part II addresses the cognitive and collaborative aspects of the engineering design process by leveraging the reasoning capabilities of LLMs. This work evolves from a single-assistant model that orchestrates scientific machine learning workflows to a sophisticated multi-agent paradigm mirroring human teams in practice. We introduce a framework of specialized AI agents engaging in iterative design-and-review loops, grounded in domain knowledge via knowledge graphs. This system is then extended by integrating a set-based design philosophy and formal risk management. Here, a team of agents systematically prunes the design space using quantitative metrics like Conditional Value-at-Risk (CVaR), resulting in a curated set of risk-assessed designs to a human expert. In summary, by developing both advanced simulation surrogates and the autonomous design reasoning frameworks, this research establishes a new paradigm where AI systems act as effective partners to human engineers, enhancing the efficiency, creativity, and robustness of the entire design process.
- Notes:
- Thesis (Ph. D.)--Brown University, 2026
Citation
Kumar, Varun,
"Bridging Rapid Simulation and Intelligent Reasoning: Geometry-Aware Neural Operators and Multi-Agent LLM Frameworks for Engineering Design"
(2026).
Engineering Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:rtcg2d7c/
