heimdall
HEIMDALL: a grapH-based sEIsMic Detector And Locator for microseismicity
Bagagli, Matteo, Grigoli, Francesco, Bacciu, Davide
In this work, we present a new deep-learning model for microseismicity monitoring that utilizes continuous spatiotemporal relationships between seismic station recordings, forming an end-to-end pipeline for seismic catalog creation. It employs graph theory and state-of-the-art graph neural network architectures to perform phase picking, association, and event location simultaneously over rolling windows, making it suitable for both playback and near-real-time monitoring. As part of the global strategy to reduce carbon emissions within the broader context of a green-energy transition, there has been growing interest in exploiting enhanced geothermal systems. Tested in the complex geothermal area of Iceland's Hengill region using open-access data from a temporary experiment, our model was trained and validated using both manually revised and automatic seismic catalogs. Results showed a significant increase in event detection compared to previously published automatic systems and reference catalogs, including a $4 M_w$ seismic sequence in December 2018 and a single-day sequence in February 2019. Our method reduces false events, minimizes manual oversight, and decreases the need for extensive tuning of pipelines or transfer learning of deep-learning models. Overall, it validates a robust monitoring tool for geothermal seismic regions, complementing existing systems and enhancing operational risk mitigation during geothermal energy exploitation.
Heimdall: test-time scaling on the generative verification
An AI system can create and maintain knowledge only to the extent that it can verify that knowledge itself. Recent work on long Chain-of-Thought reasoning has demonstrated great potential of LLMs on solving competitive problems, but their verification ability remains to be weak and not sufficiently investigated. In this paper, we propose Heimdall, the long CoT verification LLM that can accurately judge the correctness of solutions. With pure reinforcement learning, we boost the verification accuracy from 62.5% to 94.5% on competitive math problems. By scaling with repeated sampling, the accuracy further increases to 97.5%. Through human evaluation, Heimdall demonstrates impressive generalization capabilities, successfully detecting most issues in challenging math proofs, the type of which is not included during training. Furthermore, we propose Pessimistic Verification to extend the functionality of Heimdall to scaling up the problem solving. It calls Heimdall to judge the solutions from a solver model and based on the pessimistic principle, selects the most likely correct solution with the least uncertainty. Taking DeepSeek-R1-Distill-Qwen-32B as the solver model, Pessimistic Verification improves the solution accuracy on AIME2025 from 54.2% to 70.0% with 16x compute budget and to 83.3% with more compute budget. With the stronger solver Gemini 2.5 Pro, the score reaches 93.0%. Finally, we prototype an automatic knowledge discovery system, a ternary system where one poses questions, another provides solutions, and the third verifies the solutions. Using the data synthesis work NuminaMath for the first two components, Heimdall effectively identifies problematic records within the dataset and reveals that nearly half of the data is flawed, which interestingly aligns with the recent ablation studies from NuminaMath.