Retrieval-Augmented Generation with Covariate Time Series

Kenny Ye Liang; Zhongyi Pei; Huan Zhang; Yuhui Liu; Shaoxu Song; Jianmin Wang

cs.AIMar 5, 2026

Retrieval-Augmented Generation with Covariate Time Series

Authors: Kenny Ye Liang, Zhongyi Pei, Huan Zhang, Yuhui Liu, Shaoxu Song, Jianmin Wang

Organizations: Tsinghua University · China Southern Airlines

Abstract

While RAG has greatly enhanced LLMs, extending this paradigm to Time-Series Foundation Models (TSFMs) remains a challenge. This is exemplified in the Predictive Maintenance of the Pressure Regulating and Shut-Off Valve (PRSOV), a high-stakes industrial scenario characterized by (1) data scarcity, (2) short transient sequences, and (3) covariate coupled dynamics. Unfortunately, existing time-series RAG approaches predominantly rely on generated static vector embeddings and learnable context augmenters, which may fail to distinguish similar regimes in such scarce, transient, and covariate coupled scenarios. To address these limitations, we propose RAG4CTS, a regime-aware, training-free RAG framework for Covariate Time-Series. Specifically, we construct a hierarchal time-series native knowledge base to enable lossless storage and physics-informed retrieval of raw historical regimes. We design a two-stage bi-weighted retrieval mechanism that aligns historical trends through point-wise and multivariate similarities. For context augmentation, we introduce an agent-driven strategy to dynamically optimize context in a self-supervised manner. Extensive experiments on PRSOV demonstrate that our framework significantly outperforms state-of-the-art baselines in prediction accuracy. The proposed system is deployed in Apache IoTDB within China Southern Airlines. Since deployment, our method has successfully identified one PRSOV fault in two months with zero false alarm.

Figures & tables

Panel of Figure 1 — Figure 1. Illustration of the PRSOV Scenario. (a) The PRSOV operates under strict pneumatic control logic where the target Manifold Pressure (MP) is primarily influenced by the Engine Speed (N2) and Intermediate Pressure (IP). (b) Example of real world PRSOV: data scarcity (one sample per flight), short transient sequences (18 points in 10 seconds), and complex covariate coupling.

Figure 2. Overall RAG Pipeline. Tail numbers are masked for privacy.

Figure 3. Tree-Structured Knowledge Base. Unlike vector stores, it preserves raw sequences following their physical hierarchy. Tail numbers are masked for privacy.

Figure 4. The Time-Series Native Retrieval Mechanism. It employs a bi-weighted coarse-to-fine strategy. Tail numbers are masked for privacy.

Figure 5. The agentic context augment process. The top-1 sample is used as an agent to self-calibrate the optimal number of context fragments (

k^{*}

). Tail numbers are masked for privacy.

Dataset	Planes	Dim	Len	KB Samples			Query
Dataset	Planes	Dim	Len	Total	Min	Max	Total
B777L	30	3	18	17,573	91	1,050	7,380
B777R	30	3	18	17,573	91	1,050	7,380
A320L	41	3	18	112,932	1,707	3,244	30,013
A320R	41	3	18	112,932	1,707	3,244	30,013

Table 1. Statistics of the CSA-PRSOV Datasets. KB denotes Knowledge Base (2023-2024). Min/Max denotes the minimum and maximum sample counts per plane in KB.

Methods		B777L		B777R		A320L		A320R
Methods		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Learning-based	DLinear	0.254	0.336	0.430	0.467	0.562	0.560	0.600	0.578
	TimeMixer	0.467	0.452	0.580	0.538	0.509	0.512	0.570	0.538
	Pyraformer	0.085	0.176	0.108	0.168	0.376	0.427	0.429	0.457
	iTransformer	0.171	0.252	0.181	0.270	0.471	0.491	0.554	0.530
	PatchTST	0.486	0.461	0.580	0.533	0.564	0.518	0.594	0.538

Table 2. Main performance comparison. The best results are highlighted in bold and the second best are underlined .

Configuration	RAG4CTS (ours)		Chronos-2
Configuration	MSE	MAE	MSE	MAE
0 covariate	0.254	0.315	2.289	1.189
Only N2	0.249	0.319	1.958	0.972
Only IP	0.214	0.296	1.729	1.020
Full covariates	0.187	0.268	1.781	1.020

Table 3. Impact of covariate availability on forecasting performance. Full physical covariates yield the highest accuracy.

KB Strategy	B777L		B777R
KB Strategy	MSE	MAE	MSE	MAE
Same Plane	0.103	0.205	0.216	0.314
B777	0.058	0.153	0.095	0.203
Full KB	0.057	0.154	0.096	0.217

Table 4. Impact of Knowledge Base scope on B777. “B777” indicates the same aircraft type as the query.

Retrieval Metric	MSE	MAE
Cosine + DTW	0.103	0.203
Cosine + Euclidean	0.085	0.186
Cosine + Matrix Profile	0.077	0.178
Euclidean + DTW	0.111	0.208
Euclidean + Matrix Profile	0.080	0.181
Matrix Profile + DTW	0.099	0.197

Table 5. Sensitivity of retrieval metrics. The hybrid Cosine + Matrix Profile strategy is the most effective.

Method Setup	Uniform		$W^{\text{point}}$		$W^{\text{point}}\odot W^{\text{cov}}$
Method Setup	MSE	MAE	MSE	MAE	MSE	MAE
$k=0$ (Chronos-2)	1.564	0.910	1.564	0.910	1.564	0.910
$k=1$	1.992	1.145	2.052	1.107	2.132	1.158
$k=2$	0.459	0.501	0.431	0.458	0.433	0.455
$k=3$	0.151	0.306	0.144	0.294	0.141	0.289
$k=6$	0.095	0.220	0.086	0.213	0.084	0.185

Table 6. Ablation on weighting schemes and context length (

k

) on B777. “

W^{\text{point}}

” for Point Weighting and “

W^{\text{cov}}

” for Covariate Weighting.

Figure 6. The distribution of k selected dynamically by our agentic splicing context augment.

Figure 7. The PRSOV predictive maintenance pipeline of China Southern Airlines.

Tail	Fault Type	Identified Date	Actual Fault	Type
B-2**8	PRSOV R	2023-10-15	Yes	Historical
B-2**0	PRSOV R	2023-11-04	Yes	Historical
B-7**5	PRSOV R	2023-12-26	Yes	Historical
B-2**1	PRSOV L	2024-04-01	Yes	Historical
B-2**0	PRSOV R	2024-08-22	Yes	Historical
B-2**9	PRSOV R	2024-09-11	Yes	Historical

Table 7. Predictive maintenance records from the CSA deployment (Starting Nov. 2025). Online visualizations are presented in Appendix A.7 . Tail numbers are masked for privacy.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 8. Visual comparison between the baseline and our RAG approach.

Figure 9. Visualization of covariate ablation studies. We compare prediction trajectories under four settings: (1) No Covariates, (2) Only IP, (3) Only N2, and (4) Full Covariates.

Figure 10. Impact of Knowledge Base (KB) Scope on retrieval and prediction. From top to bottom: Scope 1 (Single Plane), Scope 2 (B777, same aircraft type), and Scope 3 (B777 + A320, cross-Type mixed aircraft).

Figure 11. Comparison of weighting strategies: Uniform (Unweighted), Temporal Weight Only, and our proposed Variable + Temporal strategy.

Figure 12. Visualization of prediction performance with varying context lengths (Top-

K

). The plots display the concatenated input sequences and resulting predictions for

K\in\{1,2,3,4,5\}

Figure 13. The MSE of the B-2**7 PRSOV L in time order. PRSOV L fault notified and detected with our method on plane B-2**7. — Figure 13. The MSE of the B-27 PRSOV L in time order. PRSOV L fault notified and detected with our method on plane B-27.

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Large-scale multivariate time series from heterogeneous IoT sensors demand accurate long-term forecasting for resource scheduling and predictive maintenance. While recent time series foundation models exhibit strong generalization, they rely on static parametric knowledge and lack dynamic access to external historical patterns during inference. Retrieval-Augmented Generation (RAG) offers a potential remedy, yet its application to time series forecasting is challenged by magnitude variations across heterogeneous sources and the mismatch between historical similarity and future consistency. We propose CrossRAG, a retrieval-augmented forecasting framework that integrates Shape-Aware Memory (SAM) with RevIN normalization for magnitude-robust shape-level retrieval, Future-Consistent Contrastive (FCC) learning to distinguish informative references from hard negatives with similar history but divergent futures, and Cross-Attention Temporal Fusion (CATF) to fuse retrieved historical--future reference pairs into the backbone's representations at the representation level. Experiments on seven public benchmarks show that CrossRAG consistently outperforms both parametric-only baselines and existing retrieval-augmented forecasting methods.

Abstract

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