DualWeaver: Synergistic Feature Weaving Surrogates for Multivariate Forecasting with Univariate Time Series Foundation Models

Jinpeng Li; Zhongyi Pei; Huaze Xue; Bojian Zheng; Chen Wang; Jianmin Wang

cs.LGFeb 25, 2026

DualWeaver: Synergistic Feature Weaving Surrogates for Multivariate Forecasting with Univariate Time Series Foundation Models

Authors: Jinpeng Li, Zhongyi Pei, Huaze Xue, Bojian Zheng, Chen Wang, Jianmin Wang

Organizations: School of Software, BNRist, Tsinghua University · Tencent

Abstract

Time-series foundation models (TSFMs) have achieved strong univariate forecasting through large-scale pre-training, yet effectively extending this success to multivariate forecasting remains challenging. To address this, we propose DualWeaver, a novel framework that adapts univariate TSFMs (Uni-TSFMs) for multivariate forecasting by using a pair of learnable, structurally symmetric surrogate series. Generated by a shared auxiliary feature-fusion module that captures cross-variable dependencies, these surrogates are mapped to TSFM-compatible series via the forecasting objective. The symmetric structure enables parameter-free reconstruction of final predictions directly from the surrogates, without additional parametric decoding. A theoretically grounded regularization term is further introduced to enhance robustness against adaptation collapse. Extensive experiments on diverse real-world datasets show that DualWeaver outperforms state-of-the-art multivariate forecasters in both accuracy and stability. We release the code at https://github.com/li-jinpeng/DualWeaver.

Figures & tables

Panel of Figure 1 — Figure 1: The paradigms adapting Uni-TSFM for multivariate forecasting. (a) Channel-independent: each variable is processed separately by Uni-TSFMs, ignoring cross-variable dependencies. (b) Encoder-Decoder: an encoder maps original variables to latent representations, whose predictions are then decoded back; the decoding may mislead the adaptation. (c) Dual-tuned Surrogates (ours): a shared feature-fusion module generates dual surrogates that capture dependencies under distinct optimization directions, reducing overfitting and making adaptation more robust.

Figure 2: The overview of the DualWeaver framework. A shared feature-fusion module first extracts cross-variable dependencies to generate a pair of dual-tuned surrogates ( $\mathbf{S}_{\alpha}$ , $\mathbf{S}_{\beta}$ ). These surrogates are independently processed by a frozen Uni-TSFM, after which the final multivariate predictions are derived via non-parametric reconstruction to neutralize the shared fusion part.

Methods		DualWeaver		AdaPTS		SFT		Vanilla		TimePro		SimpleTM		TimeMixer		iTrans.
Methods		(Ours)		(2025)		SFT		Vanilla		(2025)		(2025)		(2024)		(2024c)
Metric		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
TimerXL	ETTh1	0.406	0.419	0.411	0.433	0.427	0.428	0.419	0.427	0.438	0.438	0.422	0.428	0.458	0.445	0.454	0.447
	ETTh2	0.340	0.386	0.348	0.399	0.349	0.389	0.359	0.396	0.377	0.403	0.353	0.391	0.384	0.407	0.383	0.407
	ETTm1	0.338	0.379	0.347	0.392	0.377	0.390	0.397	0.409	0.391	0.400	0.381	0.396	0.385	0.399	0.407	0.410
	ETTm2	0.260	0.318	0.268	0.336	0.261	0.320	0.288	0.347	0.281	0.326	0.275	0.322	0.278	0.325	0.288	0.332

Table 1: Multivariate forecasting results on public datasets with forecasting horizons

\in\{96,192,336,720\}

. Averaged results are reported here, and full results are provided in Table 10 with the best in bold and the second underlined .

1^{st}

Count represents the number of wins achieved by a method under all prediction lengths and datasets. Results for TimePro, SimpleTM, TimeMixer, and iTransformers are reported in ( Ma et al., 2025 ) and ( Chen et al., 2025 ) . Extended evaluations on additional datasets are provided in Appendix D .

Figure 3: Performance comparison between Sundial (128M) and Chronos-2 (119M). While Chronos-2 benefits from cross-variable interactions in certain scenarios, DualWeaver enables the adapted Sundial to approach or exceed such performance.

Measurement	ETTh1	ETTh2	ETTm1	ETTm2	Weather
correlations	0.0238	0.0334	0.0314	0.0420	0.0007

Table 2: Cross-Time Cross-Variate Correlation Coefficient

Figure 4: Predictive stability under increasing noise. DualWeaver remains robust to additional noise, outperforming baselines that degrade progressively. Done with forecasting horizon at 96.

Figure 5: Predictability enhancement in the surrogate space. DualWeaver transforms complex multivariate signals into predictable surrogates, yielding an average reduction of 85.44% in MSE and 61.58% in MAE compared to the original input space.

Figure 6: Training efficiency and scalability comparison by training time per epoch (s) and peak memory consumption (GB) on the ETTh1 dataset using TimerXL. While AdaPTS exhibits linear growth in computational costs, DualWeaver maintains a near-constant resource footprint across varying hidden dimensions.

Figure 7: Impact of the regularization on training stability. Without the theoretical constraint (Eq. 13 ), the model experiences catastrophic divergence after epoch 10, with validation error increasing by four orders of magnitude. Using our proposed regularization ensures consistent stability and performance.

Figure 8: Dimensionality Scalability on ECL Dataset. Comparison of performance gains (MSE reduction) achieved by DualWeaver and AdaPTS on TimerXL as the number of variables

N

increases. While AdaPTS exhibits sensitivity to increasing dimensionality with declining returns, DualWeaver demonstrates superior robustness and stable predictive gains even as

N

reaches 321.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Dim	Dataset Size	Frequency
ETTh1	7	(8545, 2881, 2881)	Hourly
ETTh2	7	(8545, 2881, 2881)	Hourly
ETTm1	7	(34465, 11521, 11521)	15min
ETTm2	7	(34465, 11521, 11521)	15min
Weather	21	(36792, 5271, 10540)	10min
ECL	321	(18317, 2633, 5261)	Hourly

Appendix

Table 3: Detailed dataset descriptions.

Methods		DualWeaver		AdaPTS		Vanilla
Metric		MSE	MAE	MSE	MAE	MSE	MAE
TimerXL	ETTh1	0.409	0.418	0.407	0.429	0.419	0.427
	ETTh2	0.341	0.386	0.344	0.397	0.359	0.396
	ETTm1	0.368	0.397	0.360	0.400	0.397	0.409
	ETTm2	0.276	0.335	0.273	0.344	0.288	0.347
	Weather	0.245	0.289	0.244	0.304	0.255	0.302

Appendix

Table 4: Multivariate forecasting results on vanilla Uni-TSFMs with forecasting horizons

\in\{96,192,336,720\}

. Averaged results are reported here with the best in bold .

Methods		WeaverCNN		AdaPTS		Vanilla
Metric		MSE	MAE	MSE	MAE	MSE	MAE
TimerXL	ETTh1	0.406	0.419	0.411	0.433	0.419	0.427
	ETTh2	0.342	0.386	0.348	0.39	0.359	0.396
	ETTm1	0.336	0.388	0.347	0.392	0.397	0.409
	ETTm2	0.260	0.318	0.268	0.336	0.288	0.347
	Weather	0.228	0.273	0.227	0.284	0.255	0.302

Appendix

Table 5: Multivariate forecasting results of CNN-variant DualWeaver with forecasting horizons

\in\{96,192,336,720\}

. Averaged results are reported here with the best in bold .

Dataset	Dim	Dataset Size	Frequency
Exchange	8	(5120, 665, 1422)	Daily
Solar-Energy	137	(36601, 5161, 10417)	10 min
IEAC	5	(70000, 10000, 20000)	5s

Appendix

Table 6: Detailed additional dataset descriptions.

Methods	DualWeaver		AdaPTS		SFT		Vanilla
Metric	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Exchange	0.055	0.158	0.057	0.163	0.057	0.160	0.064	0.168
Solar-Energy	0.354	0.365	0.376	0.359	0.403	0.361	0.517	0.492
IEAC	0.750	0.439	0.754	0.441	0.767	0.479	0.930	0.562

Appendix

Table 7: Multivariate forecasting on additional datasets with forecasting horizons

\in\{24,36,48,60\}

for Exchange and

\in\{96,192,336,720\}

for others. Averaged results are reported here with the best in bold .

Dataset	Patch Size P
Dataset	32	64	96	128	Avg
ETTh1	0.0134	0.0116	0.0598	0.0105	0.0238
ETTh2	0.0087	0.0080	0.1094	0.0075	0.0334
ETTm1	0.0306	0.0179	0.0624	0.0148	0.0314
ETTm2	0.0143	0.0101	0.1347	0.0090	0.0420
Weather	0.0007	0.0011	0.0009	0.0002	0.0007

Appendix

Table 8: Cross-Time Cross-Variate Correlation Coefficients

Noise	Patch Size P
Channels	32	64	96	128	Avg
0	0.0134	0.0116	0.0598	0.0105	0.0238
1	0.0105	0.0087	0.0461	0.0080	0.0183
2	0.0078	0.0073	0.0364	0.0065	0.0145
3	0.0068	0.0057	0.0294	0.0052	0.0118
4	0.0055	0.0049	0.0246	0.0044	0.0098

Appendix

Table 9: Cross-variable correlation decay under synthetic noise injection.

Panel of Figure 9 — Figure 9: Heatmap for Cross-Time Cross-Variate Correlation Coefficient of ETTm2 and Weather. The color intensity (brightness) within the heatmaps directly maps to the absolute magnitude of the Cross-Time Cross-Variate Correlation Coefficient. Bright regions (represented by lighter yellow) indicate “correlation hotspots” where the coefficient approaches 0.8, signifying potent synchronous or asynchronous dependencies between the specific variable patches. Conversely, dark regions (represented by deep purple) denote “null zones” where the correlation is near zero, indicating that the variables evolve independently without identifiable inter-series relationships in those temporal windows.

Figure 10: Comparison of gradient dynamics and training stability. We visualize the

L_{2}

norm of weight gradient differences between consecutive steps (

\nabla\mathbf{W}_{t+1}-\nabla\mathbf{W}_{t}

) for the fully-connected layers of the feature-fusion module. DualWeaver maintains a remarkably smooth, consistent gradient transition, underscoring the superior numerical stability of our dual-surrogate optimization framework.

Methods			DualWeaver		AdaPTS		SFT		Vanilla		TimePro		SimpleTM		TimeMixer		iTrans.
Methods			(Ours)		(2025)		SFT		Vanilla		(2025)		(2025)		(2024)		(2024)
Metirc			MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
	ETTh1	96	0.352	0.380	0.351	0.387	0.360	0.384	0.366	0.392	0.375	0.398	0.366	0.392	0.381	0.401	0.386	0.405
		192	0.401	0.410	0.401	0.421	0.411	0.415	0.415	0.419	0.427	0.429	0.422	0.421	0.440	0.433	0.441	0.436
		336	0.434	0.431	0.437	0.445	0.452	0.438	0.450	0.439	0.472	0.450	0.440	0.438	0.501	0.462	0.487	0.458
		720	0.437	0.456	0.456	0.479	0.486	0.474	0.446	0.457	0.476	0.474	0.463	0.462	0.501	0.482	0.503	0.491

Appendix

Table 10: Multivariate forecasting results on public datasets with forecasting horizons

\in\{96,192,336,720\}

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