Dynamic correlation modeling between training load and sports performance is central to scientific training. The traditional Banister impulse-response (IR) model, constrained by a linear assumption and one-dimensional load input, cannot characterize multi-time-scale coupling or individual heterogeneity. This paper proposes a multi-scale temporal attention network (MS-TANet) with three collaborative modules: a multi-scale dilated causal convolution (MS-DCC) module that extracts day-, week- and month-scale load features in parallel and fuses them by learnable gating; a sparse decay self-attention (SD-SA) module that embeds a learnable exponential decay bias to identify training-effect lag windows, reducing asymptotic complexity to <InlineEquation ID="IEq1"><EquationSource Format="TEX">$O(L(\text{l}\text{o}\text{g}L+k{D}_{k}))$</EquationSource><EquationSource Format="MATHML"><math><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>L</mi><mrow><mo stretchy="false">(</mo><mtext>log</mtext><mi>L</mi><mo>+</mo><mi>k</mi><msub><mi>D</mi><mi>k</mi></msub><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo></mrow></math></EquationSource></InlineEquation> via top-k sparsification with locality-sensitive hashing; and an individual embedding and feature modulation (IE-FM) module that conditions temporal features on static attributes and monthly-refreshed physiological covariates. A physics-constrained regularization loss and a three-stage curriculum strategy embed physiological priors and mitigate small-sample overfitting. Unlike TFT, which treats attention as purely data-driven, MS-TANet elevates the physiological time constant to an interpretable learnable parameter; unlike physics-informed networks with hard residual constraints, it embeds fatigue decay and adaptation boundedness as soft regularization, forming a “local–long-range–individual” complementary structure. On three datasets, MS-TANet attains R2 of 0.889, 0.871 and 0.853—4.0 percentage points (4.8% relative) above the best baseline TFT and 21.7 points (33.4% relative) above Banister IR. Shapley decomposition attributes 26.7%, 23.4% and 11.2% of the gain to SD-SA, IE-FM and their interaction. The learned half-lives (16.9–21.0 days) match physiological ranges, though this partly reflects the built-in decay bias rather than a free discovery. Attention heatmaps pass window-removal, perturbation and randomization checks, and 95% prediction intervals reach 93.7% empirical coverage.

Dynamic correlation modeling and algorithm optimization of athletes' training load and performance based on deep time series network

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2026年7月9日

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Na Li,
Lijian Zhang,
Le Cheng,
Dongdong Xu,
Xiuling Zhang,
Yan Xu

摘要

Dynamic correlation modeling between training load and sports performance is central to scientific training. The traditional Banister impulse-response (IR) model, constrained by a linear assumption and one-dimensional load input, cannot characterize multi-time-scale coupling or individual heterogeneity. This paper proposes a multi-scale temporal attention network (MS-TANet) with three collaborative modules: a multi-scale dilated causal convolution (MS-DCC) module that extracts day-, week- and month-scale load features in parallel and fuses them by learnable gating; a sparse decay self-attention (SD-SA) module that embeds a learnable exponential decay bias to identify training-effect lag windows, reducing asymptotic complexity to $O(L(\text{l}\text{o}\text{g}L+k{D}_{k}))$ $O (L (log L + k D_{k}))$ via top-k sparsification with locality-sensitive hashing; and an individual embedding and feature modulation (IE-FM) module that conditions temporal features on static attributes and monthly-refreshed physiological covariates. A physics-constrained regularization loss and a three-stage curriculum strategy embed physiological priors and mitigate small-sample overfitting. Unlike TFT, which treats attention as purely data-driven, MS-TANet elevates the physiological time constant to an interpretable learnable parameter; unlike physics-informed networks with hard residual constraints, it embeds fatigue decay and adaptation boundedness as soft regularization, forming a “local–long-range–individual” complementary structure. On three datasets, MS-TANet attains R² of 0.889, 0.871 and 0.853—4.0 percentage points (4.8% relative) above the best baseline TFT and 21.7 points (33.4% relative) above Banister IR. Shapley decomposition attributes 26.7%, 23.4% and 11.2% of the gain to SD-SA, IE-FM and their interaction. The learned half-lives (16.9–21.0 days) match physiological ranges, though this partly reflects the built-in decay bias rather than a free discovery. Attention heatmaps pass window-removal, perturbation and randomization checks, and 95% prediction intervals reach 93.7% empirical coverage.