💻 computer science

Bridging Individual and Collective Realism in LLM-Based Human Mobility Simulation via Mobility Scaling-Law Guidance

This paper introduces COMPASS, a novel framework that bridges individual and collective realism in LLM-based human mobility simulation by leveraging empirical mobility scaling laws as a feedback mechanism to guide prompt construction, thereby ensuring both realistic individual trajectories and accurate population-level regularities.

Original authors: Hua Yan, Heng Tan, Yu Yang

Published 2026-07-15

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Hua Yan, Heng Tan, Yu Yang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to predict how a city breathes. Urban planners, epidemiologists, and traffic engineers need to know how people move: where they go, how far they travel, and how often they visit the same coffee shop. This is called "human mobility." Usually, to get this data, researchers have to ask people to fill out expensive surveys or track their phones, which raises big privacy concerns. So, scientists have started using Artificial Intelligence, specifically Large Language Models (LLMs), to act like digital humans. They give the AI a personality profile (like "a teacher who lives in the suburbs") and ask it to write a day's worth of movements. The problem is that while these AI agents are great at acting like one person, they often fail when you look at the whole crowd. If you simulate a million of them, the group doesn't move like a real city; the traffic jams don't form in the right places, and the distances traveled look weird. It's like having a million actors who are all great at their own lines, but the play falls apart because no one is following the script of the whole cast.

This paper introduces a new method called COMPASS to fix that disconnect. The researchers realized that real human movement follows hidden, mathematical rules called "scaling laws." These are patterns that show up no matter how many people you look at, like how most trips are short and only a few are very long. COMPASS uses these rules as a compass. It simulates a crowd, checks if the group's movement matches the real-world mathematical rules, and then uses an AI to tweak the instructions (prompts) given to individual digital people. It's like a conductor listening to an orchestra, noticing the violins are too loud and the drums are too quiet, and then whispering specific adjustments to just the right musicians until the whole symphony sounds perfect. The paper suggests that by using these population-level rules to guide individual AI agents, we can create much more realistic simulations of how cities work, even when we only have limited or coarse data to start with.

The Problem: Great Soloists, Terrible Choirs

Imagine you are directing a massive choir of one million singers. You want them to sound like a real city's daily rhythm. You hand each singer a sheet of paper with their character's backstory: "You are a nurse," "You are a student," "You are a retiree." You ask an AI to write a song for each person based on their character.

The AI does a fantastic job. The "nurse" sings a believable shift schedule; the "student" sings about rushing to class. But when you play all one million songs at once, the music sounds wrong. Maybe everyone is singing too loudly at noon, or maybe the "nurses" are all walking to the same distant hospital at the exact same time, creating a traffic jam that never happens in real life. The individual singers are perfect, but the collective sound is a mess.

This is exactly what happens with current AI mobility simulations. They are great at making one person look real, but they fail to capture the "group magic" of how real populations move. Real people follow invisible patterns. For instance, most of us take short trips to the grocery store, and only a few of us take long trips across the country. If an AI simulates too many long trips, the whole model breaks. The researchers found that existing AI simulators were making too many long-distance trips and not enough short ones, and they weren't capturing the right mix of people who love exploring new places versus people who stick to their favorite spots.

The Solution: COMPASS and the Magic Compass

The authors created a framework called COMPASS (COllective Multi-Prompt Adjustment guided by Scaling lawS). Think of COMPASS as a super-smart conductor who doesn't just listen to the choir; it has a map of how a real city should sound.

Here is how it works, step-by-step:

The First Draft: The AI generates a crowd of digital people and their movements.
The Reality Check: COMPASS looks at the whole crowd and measures them against "scaling laws." These are the mathematical rules of real movement. For example, it checks: "Do the distances people travel look like a real city's distribution?" or "Do people visit the same places often enough?"
The Diagnosis: If the simulation is off, COMPASS figures out why. Maybe the "nurses" are walking too far, or the "students" are exploring too much.
The Whisper: Instead of rewriting the whole song, COMPASS gives a tiny, specific whisper to the AI. It says, "Hey, for this group of people, tell them to stay closer to home," or "Tell these people to visit the same gym every day."
The Search: The system uses a clever search method (called Monte Carlo Tree Search) to figure out which specific people need which whisper. It's like trying different combinations of instructions to see which mix makes the whole choir sound the most realistic.

The Secret Weapon: Crumbs from the Cookie Jar

One of the coolest parts of this paper is how it handles data. Usually, to get these scaling laws, you need perfect, detailed data on every single person's movement. But that data is often private or hard to get.

The researchers discovered something amazing: You don't need perfect data. You can use "coarse-grained" data. Imagine you have a cookie. You don't need to see every crumb to know it's a chocolate chip cookie; you just need a few crumbs. COMPASS can use rough summaries of movement (like "people travel an average of X miles") or even just the mathematical formulas of movement found in old studies to guide the AI.

They tested this with three types of data:

Detailed but anonymous: Data with user IDs but coarse locations.
No IDs: Just a pile of movement paths without knowing who they belong to.
Just Statistics: Just the numbers and formulas, no actual movement paths at all.

Even with just the statistics (the "crumbs"), COMPASS was able to guide the AI to create much more realistic simulations. This is huge because it means we can build better city models without needing to invade anyone's privacy or wait for perfect datasets.

The Results: A Symphony of Realism

The team tested COMPASS on real-world data from Beijing and New York City. They compared their method against other top AI simulators.

The results were clear: COMPASS won.

In Beijing, it improved the realism of travel distances by up to 74.79% compared to the best previous method.
It also got better at predicting how often people return to the same places (a behavior called "preferential return") and how much they explore new areas.
Even when using the "just statistics" data (the third type), it still beat all other methods, proving that you don't need a crystal ball to get a good picture of the future.

The researchers also found that they didn't need to adjust every single person in the simulation. By tweaking just 15% of the digital people and then copying those changes to similar people, they could fix the whole crowd. This saves a massive amount of computer power.

Why This Matters

This isn't just about making a better video game. If we can simulate how people move realistically, we can:

Plan better cities: Design roads and public transit that actually match how people travel.
Predict disease spread: Understand how a virus might move through a crowd if we know the real patterns of movement.
Protect privacy: We can study these patterns without needing to spy on real people's phones.

The paper suggests that by listening to the "mathematical music" of how crowds move, we can teach AI to act like a real society, not just a collection of lonely individuals. It's a reminder that sometimes, to understand the whole, you have to listen to the rules that govern the group, not just the voice of the individual.

Technical Summary: Bridging Individual and Collective Realism in LLM-Based Human Mobility Simulation via Mobility Scaling-Law Guidance

Problem Statement

Human mobility data is critical for geospatial applications such as urban planning, epidemic forecasting, and transportation modeling. However, acquiring real-world data at scale is hindered by high collection costs, uneven coverage, and privacy concerns. While Large Language Models (LLMs) offer a scalable alternative by simulating individual agents based on user profiles, current LLM-based approaches suffer from a fundamental disconnect: they model individual cognitive processes in isolation without population-level coordination. Consequently, while individual trajectories may appear plausible, the aggregate output fails to reproduce the collective regularities (scaling laws) observed in real-world data, such as specific distributions of travel distances, visitation frequencies, and spatial ranges. Existing methods lack a mechanism to bridge the gap between individual-level generation and collective realism.

Methodology: The COMPASS Framework

The authors propose COMPASS (COllective Multi-Prompt Adjustment framework guided by Scaling lawS), a framework that leverages empirical mobility scaling laws from shared data as feedback signals to guide prompt construction. The core innovation is treating prompt adjustment as a multi-objective, multi-prompt optimization problem formulated as a Markov Decision Process (MDP) and solved via Monte Carlo Tree Search (MCTS).

1. Problem Formulation:
The goal is to find an optimal set of personalized prompts $\mathcal{P} = \{p_1, \dots, p_n\}$ for a population of $n$ individuals. Each prompt is augmented with specific persona descriptions and behavioral constraints to jointly optimize multiple scaling-law metrics (e.g., travel distance, radius of gyration, visitation frequency) derived from shared data.

2. MDP Formulation:

State ( $S$ ): The current set of prompts assigned to all individuals.
Action ( $A$ ): Coarse-grained adjustment strategies generated by an LLM. These strategies are derived by comparing simulated scaling-law metrics against target metrics from shared data. The LLM partitions the population into behaviorally coherent groups and proposes tailored strategies for each.
Transition ( $T$ ): An action selects a fraction $\rho$ of users within a target group. A prompt-rewriting LLM updates their prompts based on the strategy, while others remain unchanged.
Reward ( $r$ ): A multi-objective reward function that measures the improvement in aggregated scaling-law metrics. It utilizes a geometric mean of normalized utilities across different metrics to ensure balanced improvements without degrading any single objective.

3. Optimization via Two-Level MCTS:
To navigate the complex search space efficiently, COMPASS employs a two-level MCTS procedure:

Strategy-Level Selection: Uses Upper Confidence Bound (UCT) to select promising adjustment strategies.
User-Level Selection: Uses a per-user Upper Confidence Bound (UCB) bandit to identify specific individuals within a group who are most responsive to a given strategy.
Candidate Filtering: To reduce computational cost, a count-conditioned global action value estimator filters the action space before expensive trajectory regeneration.
Generalization: The framework optimizes prompts on a small subset of the population and generalizes the resulting adjustments to the full population based on profile similarity, significantly reducing search overhead.

4. Data Guidance:
COMPASS is designed to operate with varying levels of data granularity, including:

Coarse-grained trajectories with user IDs.
Coarse-grained trajectories without user IDs.
Pure statistical summaries (e.g., power-law exponents) without trajectory data.

Key Contributions

Conceptual Bridge: The paper introduces the novel idea of using human mobility scaling laws from shared data as a guidance mechanism to align individual LLM-generated trajectories with collective population patterns.
COMPASS Framework: The authors design a multi-prompt adjustment framework that utilizes a two-level MCTS search to simultaneously determine which adjustment strategies to apply and which individuals should receive them. This transforms coarse group strategies into fine-grained, individual-level adaptations.
Empirical Validation: Extensive experiments on two public datasets (Beijing and New York City) demonstrate that COMPASS outperforms state-of-the-art LLM-based simulators (including CoPB, Urban-Mobility-LLM, LLMob, and CitySim). Improvements range from 10.70% to 74.79% across multiple metrics (e.g., travel distance, exploration, preferential return).
Robustness to Data Scarcity: The study shows that even statistical summaries without trajectory-level information can effectively guide simulations, enhancing the framework's practical deployability in data-constrained environments.

Results

Performance: On the Beijing dataset, COMPASS achieved the best performance across all metrics, with significant reductions in Jensen–Shannon divergence (JSD) compared to baselines. For instance, it improved the "Return" metric by 74.79% and "Exploration" by 41.17% over the best baseline.
Scaling Law Reproduction: Visual analysis confirmed that COMPASS successfully corrected the distribution of travel distances and preferential return behaviors, bringing them closer to real-world truncated power laws and heterogeneous user behaviors.
Ablation Studies: Removing the user-bandit selection or the count-conditioned UCB significantly degraded performance, validating the necessity of the two-level search. Similarly, replacing MCTS with random search led to substantial performance drops, highlighting the importance of the search algorithm.
Generalization: Optimizing prompts on a subset (30% of users) and scaling them to the full population yielded performance comparable to optimizing on the full dataset, confirming the method's efficiency.
Model Agnosticism: The framework performed well across different LLM backbones (GPT-5.2, GPT-4o-mini, LLaMA 3.3, Qwen 2.5), indicating that its effectiveness does not rely on a specific proprietary model.

Significance and Claims

The paper claims that COMPASS addresses a critical limitation in current LLM-based mobility simulations: the failure to reproduce collective regularities. By integrating scaling laws as a feedback loop, the framework ensures that individual agents, while simulated in isolation, collectively generate realistic population-level flows. The authors emphasize that this approach is particularly significant because it:

Enables high-fidelity simulation without requiring access to sensitive, individual-level real-world data.
Operates effectively even when only coarse-grained or statistical data is available for guidance.
Provides a scalable solution for downstream tasks like epidemic modeling and urban planning, where accurate aggregate flows are more critical than individual trajectory perfection.

The work concludes that leveraging scaling laws is a viable and effective strategy for bridging the gap between individual realism and collective coherence in generative AI simulations.