AI Agents for Scientific Computing

Scientific Machine Learning (SciML), which encompasses physics-informed neural networks, neural operators, and hybrid physics–data models, has transformed computational science. Yet designing effective SciML solutions remains a slow, expert-driven process of architecture selection, loss engineering, and iterative tuning. At the same time, large language model (LLM) agents have demonstrated the ability to plan, write and execute code, critique results, and collaborate in structured multi-agent systems. This course explores the emerging synthesis of these two fields: Agentic SciML, in which teams of specialized AI agents autonomously propose, implement, evaluate, and refine scientific machine learning methods.

The course proceeds in three stages. Students first build a working foundation in SciML, implementing PINNs and neural operators and confronting their characteristic failure modes. They then study the architecture of LLM agents, including tool use, planning, reflection, memory, and multi-agent collaboration protocols such as structured debate and proposer–critic loops. The final stage unites the two threads through a close reading of the AgenticSciML framework and related systems for automated method discovery, covering retrieval-augmented method memory, ensemble-guided evolutionary search, integration with classical solvers, and questions of reliability, reproducibility, and safety in autonomous scientific workflows.

15th September ~ 8th December, 2026

Weekday	Time	Venue	Online	ID	Password
Tuesday	08:50 - 12:15	A3-1-101	ZOOM 01	928 682 9093	BIMSA

### Session 1 — Introduction: SciML and the AI-for-Science Landscape
- Why numerical simulation needs ML
- Three paradigms: data-driven, physics-constrained, hybrid
- Course roadmap and the Agentic SciML vision

### Session 2 — Physics-Informed Neural Networks (PINNs)
- Residual losses; soft enforcement of boundary/initial conditions
- Training pathologies: loss weighting, spectral bias
- **Hands-on:** solving the Burgers equation in PyTorch/JAX

### Session 3 — Neural Operators and Operator Learning
- DeepONet, Fourier Neural Operator (FNO)
- Discretization invariance; comparison with classical numerical methods
- **Hands-on:** operator learning for Darcy flow

### Session 4 — SciML Engineering Practice and Failure Modes
- Loss design, sampling strategies, curriculum learning, domain decomposition
- Why SciML tuning is expert-dependent: the motivation for agents

## Part II: Foundations of LLM Agents (Sessions 5–7)

### Session 5 — LLMs and Tool Use
- Prompt engineering, function calling, code generation and execution
- The ReAct paradigm
- **Hands-on:** having an LLM write and run a numerical solver

### Session 6 — Single-Agent Architectures
- Planning, reflection (Reflexion), memory
- Retrieval-augmented generation (RAG)
- Agent evaluation methods

### Session 7 — Multi-Agent Systems
- Role specialization, structured debate, proposer–critic patterns
- Collaboration protocols
- **Hands-on:** frameworks such as AutoGen / LangGraph

## Part III: Agentic SciML Core (Sessions 8–10)

### Session 8 — Deep Dive: The AgenticSciML Framework
- System architecture: explicit agent roles, closed-loop workflows, retrieval-augmented memory
- Coordinating planning, model discovery, experimentation, analysis, and iterative refinement
- Experimental results on physics-informed learning and operator learning benchmarks
- Reading: Jiang & Karniadakis (2025), *AgenticSciML*, arXiv:2511.07262

### Session 9 — Evolutionary Search and Method Discovery
- Ensemble-guided evolutionary strategies
- Hypothesis generation and assessment; building a method-memory library
- Related work: FunSearch, The AI Scientist

### Session 10 — Agentic Scientific Workflows
- Integration with classical solvers (FEM/FDM)
- Automated experimental design, uncertainty quantification
- Reliability, reproducibility, and safety in autonomous workflows

## Part IV: Frontiers and Projects (Sessions 11–12)

### Session 11 — Frontier Topics and Open Problems
- Multi-physics extensions; self-driving laboratories
- Meta-agents for orchestration; interpretable symbolic planning layers
- Application case studies: materials, fluids, biology

### Session 12 — Final Project Presentations
- Team project: an end-to-end agentic SciML pipeline (e.g., agents that automatically design and tune a PINN for a given PDE)
- Presentations, peer review, and course wrap-up

Graduate , Postdoc , Researcher

No

Chinese , English

Dr. Wuyue Yang is currently an Assistant Professor at BIMSA. She received her PhD degree from Tsinghua University in 2022 and was honored as an Outstanding Graduate of Beijing. Her main research directions are artificial intelligence, machine learning theory and applications. She has published papers in internationally renowned academic journals such as "Journal of Computational Physics," "Journal of Chemical Physics," and "Physics of Fluids," with over 1,000 Google citations. She is the PI of a National Natural Science Foundation of China Youth Fund project and has participated as a researcher in National Key R&D Program Special Projects. She serves as a review expert for international journals including "BMC Infectious Diseases" and "AIMS Mathematics." She teaches courses including "Theory and Application of Sparse Identification of Nonlinear Dynamics (SINDy)," "Complex System Dynamics and Control," and "Collective Dynamics of Active Matter."