Short Courses

The rapid convergence of scientific computing and artificial intelligence is reshaping how we model, simulate, and understand complex physical systems. This short course, “From Neural Operators to Scientific Foundation Models,” introduces participants to a new paradigm in scientific machine learning that moves beyond traditional surrogate models toward scalable, generalizable, and data-efficient learning frameworks.

The course begins with an overview of neural operators, which learn mappings between infinite-dimensional function spaces and enable resolution-independent predictions for parametric partial differential equations. Building on this foundation, the course explores recent advances in operator learning architectures, including physics-informed and physics-inspired neural operators, multi-fidelity frameworks, and scalable designs for high-dimensional problems.

A central focus of the course is the transition toward scientific foundation models — large-scale, pre-trained models capable of generalizing across multiple physical systems, domains, and tasks. Participants will gain insights into how ideas from foundation models in natural language processing and computer vision can be reinterpreted for scientific applications, enabling cross-domain transfer, data-physics fusion, and robust uncertainty quantification.

Designed for researchers, advanced graduate students, and industry practitioners, this course provides both conceptual depth and practical perspectives, equipping participants with the tools to contribute to the next generation of AI-driven scientific discovery.

This one-day course introduces AI-empowered CAE tools designed to solve complex engineering challenges that exceed traditional modeling limits. By merging Mechanistic Data Science with physics-based solving, the curriculum demonstrates how to achieve unparalleled precision, enabling accurate, high-dimensional simulations for rapid prototyping and automated design in industrial contexts. 

The program will also demonstrate how these AI-empowered CAE tools are integrated within an agentic AI framework that not only automates the CAE modeling workflow (e.g., CAD cleaning, mesh generation, model setup, solver setup) and mitigates modeling errors including human bias, but also pushes beyond the current technical boundaries of conventional CAE software by overcoming their inherent limitations.

Through hands-on tutorials, participants will gain both conceptual understanding and practical skills in applying agentic AI to real engineering problems, as well as practical proficiency in HIDENN-AI technology (including HiDeNN, C-HiDeNN, and B-INN) to solve extremely large-scale problems (e.g., parametric PDEs on arbitrary geometries). This practical experience equips participants to implement AI-enhanced CAE agents for rapid prototyping (e.g., 2D sketch to 3D CAD), high-fidelity analysis, and automated design exploration.

Course Flyer and Schedule

Large Language Models (LLMs) have rapidly evolved from text completion tools into autonomous agents capable of reasoning, planning, and executing complex multi-step tasks. This short course introduces the emerging paradigm of agentic workflows — systems where AI agents autonomously decompose problems, use tools, write and execute code, and iterate toward solutions — with a focus on applications in computational mechanics and scientific computing.

Participants will gain both conceptual understanding and hands-on experience building agentic systems. We will cover the foundational concepts (LLMs, prompting, retrieval-augmented generation), progress to agent architectures (tool use, planning, memory, multi-agent coordination), and culminate in hands-on sessions where participants build agents that tackle problems relevant to the computational mechanics community — from automating simulation workflows to extracting knowledge from scientific literature.