# Hybrid NARX-LLM for Greenland Iceberg Discharge: Prompt-Driven Residual Correction

arXiv: https://arxiv.org/abs/2606.15288 · HTML: https://mlsanity.com/paper/2606.15288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Time Series Forecasting with LLMs: Understanding and Enhancing Model Capabilities](https://mlsanity.com/paper/2402.10835/) (2024)
- [ClimaQA: An Automated Evaluation Framework for Climate Question Answering Models](https://mlsanity.com/paper/2410.16701/) (2024)
- [Zephyrus: An Agentic Framework for Weather Science](https://mlsanity.com/paper/2510.04017/) (2025)
- [Residual Correction in Real-Time Traffic Forecasting](https://mlsanity.com/paper/2209.05406/) (2022)
- [Reasoning emerges from constrained inference manifolds in large language models](https://mlsanity.com/paper/2605.08142/) (2026)

## Abstract (arXiv)

Greenland iceberg discharge exhibits complex nonlinear dynamics with limited observability, challenging traditional predictive models. We present a Hybrid NARX-LLM framework that combines a nonlinear autoregressive model with exogenous inputs (NARX) and a large language model (LLM) for residual correction. We further propose a Physics-Informed Prompt (PIP) method that transforms unstructured physical knowledge into structured prompts for zero-shot in-context reasoning. The primary objective is to explore the corrective potential of this framework for modeling Greenland iceberg discharge, rather than merely optimizing predictive accuracy. The NARX component captures intrinsic temporal dependencies, while the LLM, guided by PIP, encodes glacier dynamics and environmental drivers and perceives key trend patterns to correct systematic prediction errors. This integration allows the model to reason about unmodeled factors and produce interpretable residuals, enhancing overall predictive accuracy. Applied to Greenland iceberg discharge time series, our approach addresses extreme events that are difficult to predict due to rare variations and nonstationary trends, a limitation often overlooked by traditional methods. By fusing structured time-series modeling with knowledge-driven foundation AI, the framework offers a scalable and interpretable pathway to bridge data-limited climate forecasting with physics-informed LLM reasoning. The code is available.