DSPR: Dual-Stream Physics-Residual Networks for Trustworthy Industrial Time Series Forecasting

Yeran Zhang; Pengwei Yang; Guoqing Wang; Tianyu Li

cs.LGApr 8, 2026

DSPR: Dual-Stream Physics-Residual Networks for Trustworthy Industrial Time Series Forecasting

Authors: Yeran Zhang, Pengwei Yang, Guoqing Wang, Tianyu Li

Organizations: School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China · Research Center, East Hope Group Co., Ltd, Shanghai, China

Abstract

Accurate forecasting of industrial time series requires balancing predictive accuracy with physical plausibility under non-stationary operating conditions. Existing data-driven models often achieve strong statistical performance but struggle to respect regime-dependent interaction structures and transport delays inherent in real-world systems. To address this challenge, we propose DSPR (Dual-Stream Physics-Residual Networks), a forecasting framework that explicitly decouples stable temporal patterns from regime-dependent residual dynamics. The first stream models the statistical temporal evolution of individual variables. The second stream focuses on residual dynamics through two key mechanisms: an Adaptive Window module that estimates flow-dependent transport delays, and a Physics-Guided Dynamic Graph that incorporates physical priors to learn time-varying interaction structures while suppressing spurious correlations. Experiments on four industrial benchmarks spanning heterogeneous regimes demonstrate that DSPR consistently improves forecasting accuracy and robustness under regime shifts while maintaining strong physical plausibility. It achieves state-of-the-art predictive performance, with Mean Conservation Accuracy exceeding 99% and Total Variation Ratio reaching up to 97.2%. Beyond forecasting, the learned interaction structures and adaptive lags provide interpretable insights that are consistent with known domain mechanisms, such as flow-dependent transport delays and wind-to-power scaling behaviors. These results suggest that architectural decoupling with physics-consistent inductive biases offers an effective path toward trustworthy industrial time-series forecasting. Furthermore, DSPR's demonstrated robust performance in long-term industrial deployment bridges the gap between advanced forecasting models and trustworthy autonomous control systems.

Figures & tables

Figure 1. Fidelity collapse in state-of-the-art industrial forecasting. (a) MCA Failure : SOTA models fail to capture abrupt step responses, violating local mass conservation (shaded areas). (b) TVR Failure : Statistical averaging over-smooths high-frequency transients, suppressing critical physical dynamics. (c) TDA Failure : Predictive lags at regime transitions yield incorrect causal directions (directional mismatch).

Figure 2. Overview of the proposed DSPR framework. a) Overall Architecture: Decouples dynamics into statistical patterns and physical residuals. b) Statistical Base Stream: Extracts dominant temporal patterns via multi-scale decomposition. c) Static Branch: Models invariant spatial dependencies using physical priors. d) Dynamic Branch: Captures transient fluctuations via Adaptive Windows and dynamic graphs.

Dataset	Metric	DSPR	TimeMixer	PG-NN	TimeFilter	MSGNet	iTransformer	PatchTST	TimesNet	Informer	L-MPC
Dataset	Metric	(Ours)	2024	(Loss-based)	2025	2024	2023	2023	2023	2021	Classic
SCR	MAE $\downarrow$	0.265	0.286	0.292	0.297	0.302	0.307	0.287	0.297	0.448	0.675
	RMSE $\downarrow$	0.415	0.435	0.448	0.451	0.454	0.475	0.442	0.485	0.720	1.050
	MCA $\uparrow$	99.8%	99.1%	99.5%	98.4%	98.2%	98.2%	97.9%	98.5%	96.5%	95.0%
	TVR (Ideal 100%)	97.2%	88.5%	82.0%	86.5%	85.2%	85.0%	91.2%	65.4%	55.4%	48.5%
	TDA $\uparrow$	83.5%	74.9%	76.5%	73.0%	71.5%	72.5%	78.6%	68.5%	62.0%	55.0%

Table 1. Full evaluation results. Performance metrics are averaged across all prediction horizons (

H

) in normalized space. PG-NN represents the loss-penalty baseline. Best results are in bold , second best are underlined .Full results are in Appendix F .

Model Variant	MAE	RMSE
DSPR (Full Model)	0.291	0.436
No-prior (No $\mathbf{A}^{\text{prior}}$ )	0.332 (+14.09%)	0.495 (+13.53%)
Shuffled-prior (Randomized $\mathbf{A}^{\text{prior}}$ )	0.328 (+12.71%)	0.490 (+12.38%)
w/o Adaptive Window ( $\tau_{\text{lag}}$ )	0.306 (+5.15%)	0.455 (+4.36%)
Statistical Trend Only (No Residual)	0.308 (+5.84%)	0.465 (+6.65%)

Table 2. Ablation study on Kiln dataset. Values in parentheses indicate the relative performance degradation (MAE/RMSE increase) compared to the full DSPR model.

Base Architecture	Original	+ Physics-Residual	Gain
TimesNet ( Wu et al., 2023 )	0.340	0.320	$+5.9\%$
iTransformer ( Liu et al., 2023 )	0.327	0.310	$+5.2\%$
PatchTST ( Nie et al., 2023 )	0.315	0.302	$+4.1\%$
Statistical Trend (TimeMixer)	0.308	0.291	$+5.5\%$

Table 3. Generality analysis (Kiln dataset). Equipping diverse base architectures with the Physics-Aware Residual Stream consistently yields performance gains (Normalized MAE).

Panel of Figure 3 — Figure 3. Regime adaptation visualization ( $L=24,H=24$ ). Under High-Load transients (c) , statistical baselines (TimeMixer, PatchTST) exhibit significant phase lag. DSPR (red) aligns tightly with ground truth, demonstrating that the Physics-Residual stream successfully adapts effective transport delays.

Model	High Load	Med Load	Low Load	Avg
Informer	0.585	0.420	0.355	0.453
iTransformer	0.485	0.310	0.265	0.353
PG-NN (Loss)	0.385	0.265	0.205	0.285
PatchTST	0.365	0.245	0.195	0.268
TimeMixer	0.315	0.240	0.210	0.255
DSPR (Ours)	0.265	0.225	0.195	0.228

Table 4. Regime-specific performance (MAE) on SCR dataset (Horizon H=24). The test set is partitioned by volatility. DSPR demonstrates superior adaptation, particularly in the High-Load regime where rapid transients cause significant phase lag in baselines.

Figure 4. Fidelity validation on SCR dataset. DSPR (red) maintains physical conservation (MCA) and dynamic variance (TVR) across long horizons, avoiding structural collapse observed in baselines.

Figure 5. Mechanism recovery in SCR. Distributions of learned transport delays

\tau_{t,c}

across High, Medium, and Low-load regimes. (a) DSPR resolves distinct, physics-consistent lag shifts (

\approx

105s–115s) by dynamically adapting receptive fields. (b) PG-NN fails to distinguish these regime-dependent delays, exhibiting fidelity collapse despite soft loss constraints.

Figure 6. Mechanism identification map. In the SDWPF turbine, DSPR recovers key physical loops: the dominant yaw control alignment from Ndir to Wdir and the aerodynamic energy path between Wspd and Patv, validating architecture-level physics discovery.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	SCR (Ours)	Kiln (Ours)	TEP	SDWPF
Domain	Chemical	Thermal	Chemical	Energy
Time Steps	259,200	298,790	250,000	35,280
Variables	9	7	10	7
Sampling Rate	10 s	10 s	3 min	10 min
Physical Prior	Mass Balance	Thermodynamics	Reaction	Fluid Dyn.

Appendix

Table 5. Statistics of the four real-world industrial datasets.

Dataset	TimeMixer (SOTA Baseline)		DSPR (Ours)
Dataset	MAE	RMSE	MAE	RMSE
SCR (Chemical)	$0.286\pm 0.003$	$0.435\pm 0.004$	$\mathbf{0.265}\pm\mathbf{0.001}$	$\mathbf{0.415}\pm\mathbf{0.002}$
Kiln (Thermal)	$0.308\pm 0.004$	$0.465\pm 0.005$	$\mathbf{0.291}\pm\mathbf{0.002}$	$\mathbf{0.436}\pm\mathbf{0.002}$
TEP (Control)	$0.456\pm 0.005$	$0.592\pm 0.003$	$\mathbf{0.436}\pm\mathbf{0.001}$	$\mathbf{0.564}\pm\mathbf{0.001}$
SDWPF (Wind)	$0.338\pm 0.005$	$0.537\pm 0.006$	$\mathbf{0.335}\pm\mathbf{0.002}$	$\mathbf{0.522}\pm\mathbf{0.003}$

Appendix

Table 6. Robustness evaluation with Error Bars. We report the

\text{Mean}\pm\text{Std}

of MAE and RMSE across 3 independent runs. Lower mean and lower standard deviation indicate better stability and reproducibility.

Condition	Jaccard (Top-5)	Rank Correlation
Random Seed 1	0.87	0.90
Random Seed 2	0.89	0.92
Time Split 1	0.85	0.90
Time Split 2	0.88	0.91
Average	0.87	0.91

Appendix

Table 7. Stability of discovered mechanisms. High correlation across seeds confirms that learned dependencies represent robust physical relationships rather than random noise.

Figure 7. Closed-loop response comparison over 4-hour window. The traditional PID controller exhibits significant overshoot and oscillation due to transport delay mismatch. In contrast, the DSPR-based controller anticipates emission peaks and adjusts ammonia injection preemptively, achieving tighter setpoint tracking and reducing reagent waste.

Dataset	H	DSPR (Ours)					TimeMixer ’24					PG-NN (Loss)					PatchTST ’23					MSGNet ’24
Dataset	H	MAE	RMSE	MCA	TVR	TDA	MAE	RMSE	MCA	TVR	TDA	MAE	RMSE	MCA	TVR	TDA	MAE	RMSE	MCA	TVR	TDA	MAE	RMSE	MCA	TVR	TDA
SCR	24	0.215	0.352	99.9	98.5	86.5	0.235	0.390	99.3	91.0	78.5	0.245	0.395	99.7	84.5	79.0	0.230	0.385	98.5	93.5	81.5	0.252	0.402	98.5	88.0	74.0
	48	0.242	0.385	99.9	97.8	84.5	0.268	0.415	99.2	89.5	76.0	0.275	0.430	99.6	83.0	77.5	0.272	0.428	98.2	92.0	79.5	0.285	0.435	98.3	86.5	72.5
	96	0.275	0.420	99.8	96.5	82.0	0.295	0.450	99.0	87.5	73.5	0.305	0.465	99.4	81.5	75.5	0.302	0.460	97.8	90.5	77.0	0.315	0.470	98.1	84.2	70.5
	192	0.328	0.503	99.6	96.0	81.0	0.346	0.485	98.9	86.0	71.6	0.343	0.502	99.3	79.0	74.0	0.344	0.495	97.1	88.8	76.4	0.356	0.509	97.9	82.1	69.0
	Avg.	0.265	0.415	99.8	97.2	83.5	0.286	0.435	99.1	88.5	74.9	0.292	0.448	99.5	82.0	76.5	0.287	0.442	97.9	91.2	78.6	0.302	0.454	98.2	85.2	71.5

Appendix

Table 8. Granular breakdown of Accuracy vs. Physical Fidelity. We report detailed performance metrics across increasing prediction horizons (

H

) to analyze model stability. Best results are in bold ; second best are underlined .

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