87450 - Models and Numerical Methods in Physics

Learning outcomes

"At the end of the course the student will acquire the tools to build up dynamical models for the evolution of the classical physical systems formed by interacting particles under the influence of external fields. He/she will be able to use numerical techniques for the solution of the corresponding differential equation even in the case of fluctuating fields. In particular, in the limit of a large number of particles the kinetic and the fluid approximations will be developed; in the case of long range interactions the average field equations will be considered, together with self-consistent solutions and collision models based on stochastic processes."

Course contents

“From Conway to LangGraph: Agent Systems for Physicists in the LLM Era”

This year this 48-hour master-level course traces a single intellectual thread — local rules giving rise to emergent global behaviour — from the classical cellular automata of von Neumann, Ulam and Conway to today’s multi-agent frameworks that wrap large-language models in autonomous tool-using workflows.

Drawing on a physicist’s toolkit (statistical mechanics, dynamical systems, graph theory), students will learn how to formalise, simulate and analyse agent-based systems; how to couple them to learning algorithms (reinforcement, evolutionary); and how to embed modern foundation-model capabilities (reasoning, code generation, memory) inside those agents with libraries such as LangGraph.

Weekly hands-on labs in Mesa and Python/Jupyter move from first principles to deployable prototypes, preparing participants to apply agentic thinking to research problems in physics.

WEEKLY TOPICS OUTLINE (in progress)

Week 1,2: Emergence from Local Rules

• Classical cellular automata: von Neumann, Ulam, Conway
• Concepts of emergence and complexity
• Lab: Implementing 1D and 2D cellular automata in NetLogo

Week 3,4: Statistical Mechanics of Agent Systems

• Micro-macro mappings, phase transitions, criticality
• Mean-field approximations and Monte Carlo dynamics
• Lab: Simulate self-organizing criticality in Mesa (Python)

Week 5,6: Reinforcement and Evolutionary Learning

• Reinforcement Learning in multi-agent systems
• Evolutionary algorithms and adaptive behaviour
• Lab: Q-learning agents in gridworld + genetic algorithms

Week 7,8: Foundation Models as Cognitive Primitives

• Overview of LLMs, code generation, and few-shot learning
• LLMs as tools vs agents: prompting vs chaining
• Lab: Use OpenAI API to build an LLM-based calculator/planner

Week 9,10: LangChain and LangGraph Fundamentals

• Memory, tools, agents, chains and graphs
• Control flows, multi-step reasoning, branching logic
• Lab: Build a tool-using LangGraph agent with memory

Week 10,11: Multi-Agent LangGraph Systems

• Agent collaboration and competition
• Coordination via messages, tools, or shared memory
• Lab: Implement a multi-agent scientific assistant (LangGraph)

Readings/Bibliography

In preparation....

Teaching methods

Lectures and Numerical Simulations (with Python)

Assessment methods

Design, implementation and discussion of a project

Teaching tools

Students with Specific Learning Disabilities (SLD) or temporary or permanent disabilities are advised to contact the University office in charge in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/en ). The office will be responsible for proposing any necessary accommodations to the students concerned. These accommodations must be submitted to the instructor for approval at least 15 days in advance, who will assess their appropriateness in relation to the learning objectives of the course.

Office hours

See the website of Mirko Degli Esposti