permutans/tube-distance-field

Tube Distance Field

A GATv2 encoder + MLP value head trained to predict shortest travel time between any pair of London Underground stations.

Given an origin and destination, the model outputs estimated travel time in minutes. MAE: 0.66 min — 90% of predictions within 30 seconds of the Floyd–Warshall ground truth.

Intended Use

This model is a research artifact demonstrating learned distance estimation on a transit graph. It predicts the shortest travel time in minutes between any two London Underground stations using the graph topology and scheduled edge weights from TfL's GTFS timetable feed.

Architecture

Component	Details
Encoder	16-layer GATv2, d=512, 8 heads
Value head	4-layer MLP with LayerNorm
Graph	490 stations
Parameters	11,352,043
Training signal	Huber loss (δ=2 min) vs. Floyd–Warshall all-pairs shortest times

Evaluation Results

Metric	Value
Mean Absolute Error	0.66 min

Limitations

While the value head is accurate as a distance oracle, Bellman rollout using these predictions achieves only 43% routing success due to error compounding across hops. For routing, use the companion policy model.

Usage

import json, torch
from safetensors.torch import load_file
from huggingface_hub import hf_hub_download

repo = "permutans/tube-distance-field"
config = json.loads(open(hf_hub_download(repo, "config.json")).read())
weights = load_file(hf_hub_download(repo, "model.safetensors"))
metadata = json.loads(open(hf_hub_download(repo, "metadata.json")).read())
# See the project repository for full inference code.

Links

• Code: tubeulator-models
• Companion model: Next-hop policy for optimal routing

Part of the Model Trains series. Trained on GTFS timetable data from Transport for London.