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Let's Apply The AI Scientist to the SEIR Model

Introduction

“The AI Scientist” is a system proposed by Sakana AI that aims to fully automate the scientific discovery process using large language models (LLMs).

The strength of The AI Scientist lies in its ability to independently generate ideas, conduct experiments, write, and review without human assistance (with the exception of the initial preparation of the code base). In particular, during the experiment iteration, the model showcases its potential by autonomously modifying code, extracting data from results, and discovering new insights, thereby expanding the capabilities of large language models (LLMs).

In the original paper, they focused on having The AI Scientists conduct research in the field of deep learning. However, as mentioned in the paper, the potential applications of The AI Scientists are open-ended.

Here, I apply The AI Scientists to the SEIR model, a differential equation-based model used to predict the spread of infectious diseases.

Background

The AI Scientist

Overview of The AI Scientist
Overview of The AI Scientist (Fig: https://arxiv.org/abs/2408.06292)

The AI Scientist is a system that aims to fully automate the scientific discovery process using large language models (LLMs).

The process of The AI Scientist is as follows:

The AI Scientist first generate the novel ideas given a seed idea and validate generated ideas with the help of the Semantic Scholar API. Then, The AI Scientist conduct experiment iteration. During the iteration, The AI Scientist automatically modifies the code, executes the code, and extracts data from the results. After the experiment, The AI Scientist writes a paper based on the previous steps. Then, The AI Scientist do paper reviewing.

There are some key components of The AI Scientist:

SEIR Model

The SEIR model is a model used to predict the spread of infectious diseases. The model divides the population into four compartments: Susceptible (SS), Exposed (EE), Infected (II), and Recovered (RR). The model is based on the following differential equations:

dSdt=−βSIdEdt=βSI−σEdIdt=σE−γIdRdt=γI\begin{align*} \frac{dS}{dt} &= -\beta SI \\ \frac{dE}{dt} &= \beta S I - \sigma E \\ \frac{dI}{dt} &= \sigma E - \gamma I \\ \frac{dR}{dt} &= \gamma I \end{align*}

where:

By solving these equations given the initial conditions, we can obtain the population distribution at each time step like the following image.

Baseline Results of SEIR Model
Solution of the SEIR Model

Experiment Setup

I will explain the setup of the experiment in this part. The experimental code used in this experiment can be found at https://github.com/SakanaAI/AI-Scientist/tree/main/templates/seir (My template code was merged into the official repo.🎉)

Template Setup

When we want to conduct custom experiments using The AI Scientist, we need to prepare a template directory that is used as a codebase for LLMs to generate ideas, conduct experiments, and write papers. The template directory is structured as follows:

template/
├── latex/            # contains .tex, .sty, and .bst files for writing papers
├── experiment.py     # codebase to conduct experiments
├── plot.py           # codebase for plotting results for the paper
├── seed_ideas.json   # seed ideas for problems you want to solve
├── ideas.json        # JSON file for storing generated ideas
└── prompt.json       # system and task prompts for The AI Scientist

To apply The AI Scientist to the SEIR model, I prepared the template directory as follows:

Basically, I used the content from official GitHub repository as is, but I modified the bibliography items to focus on the SEIR model. Additionally, I changed the filenames of the images in the tex file.

I prepared a code that solves the SEIR model, using the reference from here. This code solves the SEIR model given the initial conditions of Susceptible: 3000, Exposed: 0, Infected: 5, and Recovered: 0.

And the results of the experiment.py are designed to save the below information:

However, when reporting the experimental results to the base foundation model, I chose not to include the solution in the prompt, as it is a large list that could potentially have negative effects.

I prepared plot.py that generates an image that shows the solution of the SEIR model and saves it as seir_solution_run_0.png. Since it is crucial to mitigate the peak number of infections during an epidemic, a line has been drawn at the peak section. The image of the baseline results is shown below.

Baseline Results of SEIR Model
seir_solution_run_0.png

I prepared the following idea in seed_ideas.json.

[
 {
     "Name": "time_varying_vaccination_seir",
     "Title": "Modeling the Impact of Time-Varying Vaccination on SEIR Dynamics",
     "Experiment": "Enhance the seir_eq function to include a new compartment for vaccinated individuals (V) with a time-varying vaccination rate. Update the equations to reflect individuals transitioning from S to V, allowing the vaccination rate to change at specified intervals. Simulate scenarios with different vaccination strategies and analyze their effects on final infection counts and peak infections. This will offer insights into how dynamic vaccination efforts can influence infection spread.",
     "Interestingness": 9,
     "Feasibility": 7,
     "Novelty": 9
 }
]

I prepared ideas.json as an empty file.

I use the same content as in the official template code.

{
   "system": "You are an ambitious AI researcher who is looking to publish a paper that will contribute significantly to the field.",
   "task_description": "You are given the following file to work with, which run the SEIR infection model."
}

Configuration

$ python launch_scientist.py --model "gpt-4o-mini-2024-07-18" --experiment seir --num-ideas 2

Result

Idea Generations

The generated ideas are shown below:

The novelty scores may be too high, but they appear to be good ideas.

In the following parts, I will focus on the results of the ‘network_based_seir’ idea, as it generated the most well-written paper.

Experiment Iteration

In the first run, The AI Scientist added code to calculate the average degree of the randomly generated network graph and multiply beta by the average degree. However, since beta is not used afterward, there is no change in the results compared to the baseline. The added lines by The AI Scientist are expressed with the prefix ”+” in the code below.

import os
import json
import numpy as np
import argparse
+ import networkx as nx
from scipy.integrate import odeint

# -----------------------------------------------------------------------------
# SEIR model is a differential equation model that describes the dynamics of infectious diseases such as COVID-19.
# The model divides the population into four compartments: S (susceptible), E (exposed), I (infectious), and R (recovered).
# -----------------------------------------------------------------------------


parser = argparse.ArgumentParser(description="Run experiment")
parser.add_argument("--out_dir", type=str, default="run_0", help="Output directory")
args = parser.parse_args()

if __name__ == "__main__":
    out_dir = args.out_dir
    os.makedirs(out_dir, exist_ok=True)

    def seir_eq(v, t, beta, lp, ip):
        """Differential equation of SEIR model
        v: [S, E, I, R] Distribution of people in each state
        t: Time
        beta: Infection rate
        lp: Latent period
        ip: Infectious period
        """
        dS = -beta * v[0] * v[2]
        dE = beta * v[0] * v[2] - (1 / lp) * v[1]
        dI = (1 / lp) * v[1] - (1 / ip) * v[2]
        dR = (1 / ip) * v[2]
        return np.array([dS, dE, dI, dR])

+
+     # Create a random graph
+     num_nodes = 1000
+     edge_creation_prob = 0.01
+     G = nx.erdos_renyi_graph(num_nodes, edge_creation_prob)
+
+     # Calculate the average degree
+     avg_degree = np.mean([deg for node, deg in G.degree()])
+
+     # Adjust infection rate based on average degree
+     beta = 0.001 * avg_degree  # Scale infection rate by average degree

    # Solve SEIR model
    init_state = np.array([3000, 0, 5, 0])
    solution = odeint(
        seir_eq,
        init_state,
        t=np.arange(0, 100, 1),
        args=(0.001, 14, 7),
    )

    final_info = {
        "solution": solution.tolist(),
        "infected_peak_day": np.argmax(solution[:, 2]).item(),
        "infected_peak": np.max(solution[:, 2]).item(),
        "tolal_infected": solution[-1, 3].item(),
    }
    with open(os.path.join(out_dir, "final_info.json"), "w") as f:
        json.dump(final_info, f)

In the second run to tha last run, similar modifications to the code were made as in the first run, and since beta was not used thereafter, all experiments produced the same results.

Paper Write-Up

The following pdf was generated in this part. The full paper can be found here

page1 page2 page3
page4 page5 page6
Incorporating Network Structures in SEIR Dynamics (generated by The AI Scientist)

The generated paper looks good. However, there are some obvious mistakes. Some examples are listed below:

page7
Blank Section in the Paper

Findings

When creating base code, it’s better to prepare a single function rather than defining multiple small functions. This is because when functions are separated for each process, maintaining consistency between the function definition parameters and the arguments when calling the function becomes necessary during editing. This increases the number of places that need to be edited, leading to more mistakes. This issue might be resolved with higher-performance models than the gpt-4o-mini used in this case.

Conclusion

In this post, I applied “The AI Scientist” to the SEIR Model. In the experiment, a well-written paper was generated, but the experiment conducted by the LLM was not successful and the quality of the paper was not good. Although it’s not yet perfect, I’ve discovered that the AI Scientist can not only handle deep learning but also manipulate differential equations to perform various simulations. As differential equations are used in various fields, such as physics and economics, we may see a future where people like policy makers and fund managers can quickly make decisions based on the insights and outcomes generated by The AI Scientists.

References

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