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Resolving the Dual-Timescale Forecasting Dilemma in High-Frequency Cyber-Physical Telemetry via Physics-Grounded Dynamic Asymptotic Decomposition

Avik Kumar Das

arXiv:2609.31361v1eess.SP

TL;DR

High-frequency telemetry forecasting over hours must balance short-term kinetic behavior against long-term diurnal equilibrium. The paper proposes Dynamic Asymptotic Decomposition, which transitions forecast authority toward the diurnal baseline. Across 16 walk-forward windows, it reports an overall MAE of 0.1764 and lower error than three named baselines.

  • Problem

    At 5-second sampling, forecasting 2,160 steps ahead spans kinetic and diurnal regimes, while existing approaches face noise amplification, variance growth, or physical-constraint issues.

    Source: §1 · p. 2

  • Method

    Dynamic Asymptotic Decomposition combines a continuous sigmoidal authority transition with monotonically increasing L2 regularization and a non-negativity constraint.

    Source: §1 · p. 3, §2.1 · p. 4, §2.2 · p. 5

  • Results

    MAE of 0.1764 was 78.3% lower than Deep LSTM (0.8143), 60.2% lower than PatchTST (0.4431), and 20.8% lower than DLinear (0.2227).

    Source: §6 · p. 27

  • Takeaways & Limitations

    The theoretical analysis provides an analytical basis for multi-step prediction by showing that the minimum-variance estimator converges to the diurnal baseline as autoregressive mutual information decays over extended horizons.

    Source: §6 · p. 27

    The framework assumes a stable periodic thermodynamic equilibrium and a stationary 5.0-second sampling interval after clock-jitter correction.

    Source: §5.2 · p. 27

Abstract

from arXiv · show

High-frequency industrial cyber-physical systems (CPS) stream continuous sensor telemetry at sub-10-second intervals. Multi-horizon forecasting over hours is required for predictive maintenance and operational control. However, deploying machine learning models over extended horizons (H = 2,160 steps at dt = 5 s) encounters the Dual-Timescale Forecasting Dilemma: the trade-off between short-horizon kinetic momentum and long-horizon diurnal thermodynamic equilibrium. Autoregressive rollouts suffer from compounding error drift, while direct multi-output projectors exhibit variance explosion and noise extrapolation. In this work, we prove that autoregressive mutual information decays exponentially toward zero over extended lead times, and that the optimal minimum-variance estimator converges asymptotically to the periodic diurnal baseline (Lemma 1 and Theorem 1). Guided by these bounds, we propose the Dynamic Asymptotic Decomposition (DAD) framework. The architecture couples a continuous sigmoidal authority transition schedule \(\alpha(h)\) with monotonic L2 regularization scaling \(\lambda(h)\), transferring prediction authority from kinetic autoregression to diurnal equilibrium while enforcing physical non-negativity. Evaluated across a 30-day industrial telemetry stream (N = 518,400 steps) over 16 walk-forward test windows, DAD achieves an overall Mean Absolute Error (MAE) of 0.1764, representing a 78.3% error reduction over Deep LSTM (0.8143), 60.2% over PatchTST (0.4431), and 20.8% over DLinear (0.2227). Computational profiling demonstrates edge execution in 0.72 ms with 0.203 MFLOPs and 72k parameters on a single CPU core (over 3400x faster than Transformer baselines), validated by an automated dual-stage CI/CD quality assurance harness and physical fail-safe architecture.

1. Introduction

High-frequency industrial telemetry requires forecasts across thousands of steps, where short-term kinetic dynamics and long-term diurnal behavior create competing demands. The paper introduces a physics-grounded framework to address this dilemma and reports its benchmark and edge-computing results.

1. Introduction

  • At a 5-second cadence, forecasting three hours ahead requires 2,160 steps, spanning short-term kinetic and extended-horizon thermodynamic regimes.Autoregressive rollouts amplify noise, while fixed-weight direct projectors can exhibit variance growth and extrapolation drift.Source: §1 · p. 2
  • Industrial telemetry streams can contain timestamp reversals, packet loss, clock drift, and shutdown flatlines that naive resampling or imputation may distort.The passage also identifies historian padding and multi-scale missing data as acquisition challenges.Source: §1 · p. 3
  • MAE of 0.1764 reduced error by 78.3% versus Deep LSTM (0.8143) and 60.2% versus PatchTST (0.4431).The evaluation used a 30-day stream of 518,400 steps across 16 walk-forward windows.Source: §1 · p. 3
  • The proposed framework combines a continuous sigmoidal authority transition with increasing L2 regularization to hand off prediction authority from kinetic autoregression to diurnal equilibrium.The paper states that its theoretical results establish exponentially decaying autoregressive mutual information and convergence of the minimum-variance estimator to the periodic diurnal baseline.Source: §1 · p. 3

2. Proposed methodology: Dynamic asymptotic decomposition framework

This section presents the DAD methodology, which conditions telemetry, blends candidate models with authority shifting from kinetic autoregression to a diurnal baseline as lead time grows, and enforces non-negativity. It also describes Bayesian hyperparameter optimization of the transition center and L2 penalty to identify a stable convex basin supporting reliable parameter convergence.

2.1. Mathematical telemetry formulation, information bounds, and error dynamics

  • At 5-second cadence over 30 days, the framework targets 2,160-step forecasts; its theory says mutual information decays exponentially and autoregression beyond H_cohere amplifies noise-driven variance.The setup uses a 2,160-observation historical lookback, while the theory states that localized feature correlations fall below the measurement noise floor beyond the kinetic coherence length.Source: §2.1 · p. 4

2.2. Dynamic asymptotic decomposition formulation

  • DAD uses a continuous sigmoid to shift authority from kinetic features at h ≤ 30 min to diurnal equilibrium at h ≥ 90 min, while λ(h) rises with horizon.The diurnal baseline is a conditional expectation across historical days, with T_day = 17,280 steps; the framework bounds asymptotic variance by σ_diurnal^2.Source: §2.2 · pp. 5–6

2.3. System architecture and pipeline topology

  • The operational pipeline has four layers: telemetry conditioning, a 45-feature store, evaluation of 10 model paradigms, and top-model blending with a non-negativity bound.The ingestion layer corrects timestamp non-monotonicities, mitigates packet collisions, aligns clock drift, and segments operational hurdle states.Source: §2.3 · p. 6

2.4. Telemetry invariants, error pathologies, and multi-scale conditioning

  • Conditioning addresses telemetry pathologies through chronological sorting, interval-mean collision aggregation, shape-preserving interpolation, and operational hurdle segmentation.The hurdle state is defined as s_t = 1_{y_t > 0.05}.Source: §2.4 · p. 7
  • Diagnostics show diurnal and semi-diurnal spectral peaks, rapid autocorrelation decay over the first 30 minutes followed by 24-hour re-emergence, and clock offsets bounded within [-2.5 s, +2.5 s].The clock drift was realigned to the regular 5-second observation lattice.Source: §2.4 · pp. 7–8, Figure 3 · p. 8

2.5. Candidate architecture selection and benchmark criteria

  • The benchmark spans 10 architectures, while the proposed system is a top-four convex ensemble of regularized models with 72k parameters and a non-negativity bound.The candidate set covers classical, direct linear, deep sequential, dilated convolutional, transformer, and pre-trained foundation models.Source: §2.5 · pp. 8–9

2.6. Bayesian hyperparameter optimization and convergence dynamics

  • Optuna TPE minimized validation MAE across 16 consecutive 3-hour windows; selected settings include a 540-step (45m) transition inflection, 180-step (15m) bandwidth, and 2,160-step (3.0h) lookback.The selected base L2 penalty was 10.0 and the regularization scaling multiplier was 32.0.Source: §2.6 · pp. 10–11
  • The Bayesian objective surface has a convex basin near H_trans = 540 steps (45 minutes) and λ_0 = 10.0, supporting numerical stability and reliable parameter convergence.The joint response surface evaluates the L2 regularization penalty λ and transition inflection center H_trans.Source: §2.6 · p. 11, Figure 5 · p. 12

3. Experimental evaluation, benchmarking, and ablation dynamics

Across 16 walk-forward windows, the benchmark comparison shows the proposed framework maintaining bounded error as Deep LSTM diverges at longer leads. The ablation results track improvement from an unregularized baseline to the final ensemble, while training dynamics distinguish fast direct projections from slower, unstable deep models.

3.1. Model training dynamics, optimization convergence, and empirical benchmarks

  • Direct linear and closed-form ridge projection heads converge in under 4 seconds, while deep recurrent and self-attention backbones take 5–15 minutes and exhibit optimization instability.Figure 6 tracks loss, gradient norms, matrix condition number, and computational complexity across training epochs.Source: §3.1 · p. 13, Figure 6 · p. 14

3.2. Multi-horizon lead-time degradation and benchmark comparison

  • The proposed framework maintains a sub-0.27 error profile while Deep LSTM diverges exponentially after 30 minutes across horizons up to 2,160 steps.Figure 7 also compares test-window performance and accuracy-latency trade-offs.Source: §3.2 · p. 15, Figure 7 · p. 16

3.3. Component ablation study and sensitivity analysis

  • 0.1764 MAE marks the final ensemble, down from the unregularized baseline of 0.3002 across the five-stage ablation.The five milestones’ explanatory R² rises from 0.6214 to 0.8842; the 0.8520 stage still has partial drift at bounds.Source: §3.3 · p. 19, Figure 10 · p. 19, Figure 11 · p. 20
  • Across 16 walk-forward windows, the ablation dashboard examines horizon-specific error changes, feature importance, transition-center sensitivity, and bias-variance decomposition.Figure 13 additionally covers hyperparameter sensitivity, bandwidth robustness, and noise-floor analysis across operational regimes.Source: §3.3 · pp. 18, 20, 21, Table 6 · p. 18, Figure 12 · p. 21

4. Industrial edge feasibility, computational profiling, and automated MLOps infrastructure

The framework’s inference cost is reported alongside edge-device execution timings, including a sub-millisecond result on a single CPU core. Its deployment pipeline also specifies pre-deployment checks and runtime fallbacks for data and prediction faults.

4.1. Computational complexity, theoretical FLOPs, and execution profiling

  • 0.72 ms single-core inference on an Intel Xeon vCPU and 3.24 ms on an embedded ARM Cortex-A72 are both below the 5.0-second real-time latency budget.The framework uses 0.203 MFLOPs; Figure 14 profiles complexity and execution across platforms.Source: §4.1 · pp. 22–23, Table 7 · p. 23, Figure 14 · p. 24

4.2. Automated MLOps quality assurance, contract verification, and fail-safe deployment

  • The dual-stage CI/CD pipeline checks data quality and deployment conditions, while runtime monitoring can revert predictions to the static diurnal baseline after specified sensor faults.The specified fallback triggers include more than 12 consecutive missing steps or clock drift exceeding 2.5 seconds.Source: §4.2 · pp. 24–25, Table 8 · p. 24, Figure 15 · p. 26

5. Discussion, operational generalization, and limitations

The framework is described for horizons ranging from 30 minutes to 24 hours, with transition settings adjusted to asset-specific time constants. Its stated operating assumptions include a stable periodic baseline and stationary sampling, while the discussion connects domain-tailored decomposition to physical signal decorrelation.

5.1. Operational horizon generalization across cyber-physical regimes

  • The framework covers four lookahead regimes from 30 minutes to 24 hours, adjusting transition inflection and bandwidth to match asset-specific time constants.The regimes include kinetic dispatch, reserve ramp tracking, intraday dispatch, and day-ahead planning.Source: §5.1 · p. 26, Figure 16 · p. 27

5.2. Foundational assumptions and physical boundary conditions

  • The framework assumes a stable periodic thermodynamic baseline and stationary 5-second sampling after clock-jitter correction.For seasonal retooling or operating-mode shifts, the baseline can be updated by exponential moving-average filtering; continuous zero-inflated intermittency may instead use compound Poisson or Tweedie heads.Source: §5.2 · p. 27

5.3. Implications for cyber-physical systems and scientific machine learning

  • The discussion argues that larger neural-network parameter scale does not overcome physical signal decorrelation, and that domain-tailored decomposition provides an effective inductive bias for high-frequency telemetry compared with generic sequence transformers.Source: §5.3 · p. 27

6. Conclusions

The conclusion presents theoretical bounds for extended-horizon forecasting and reports the DAD framework’s benchmark and edge-profiling results. It also describes validation and fail-safe features as part of its practical deployment approach.

6. Conclusions

  • The paper reports that autoregressive mutual information decays exponentially over extended horizons and that the minimum-variance estimator converges to the diurnal baseline.The authors present Lemma 1 and Theorem 1 as an analytical basis for multi-step prediction.Source: §6 · p. 27
  • DAD achieved an overall MAE of 0.1764, reducing error by 78.3% versus Deep LSTM (0.8143), 60.2% versus PatchTST (0.4431), and 20.8% versus DLinear (0.2227).Evaluation covered a 30-day telemetry stream of 518,400 steps across 16 walk-forward windows.Source: §6 · p. 27
  • The framework combines dual-stage CI/CD quality assurance with a physical fail-safe fallback topology for cyber-physical monitoring.The profiling reports 0.72 ms single-core inference, 0.203 MFLOPs, and 72k parameters; it is described as over 3,400× faster than PatchTST.Source: §6 · pp. 27–28

Declaration of competing interests

Declaration of generative AI and AI-assisted technologies in the writing process

The author reports using generative AI to assist with manuscript drafting, language editing, and script structuring, then reviewing and verifying the work.

Declaration of generative AI and AI-assisted technologies in the writing process

  • The author used generative AI for manuscript drafting, language editing, and script structuring, and reviewed and verified the work afterward.The author states they take full responsibility for the published article’s integrity, authenticity, and final contents.Source: Declaration of generative AI and… · p. 28

A.1. Proof of Lemma 1 (Information horizon bound and autoregressive mutual information decay)

The proof models localized kinetic telemetry as a stochastic dynamical system and shows that current-state information about future telemetry decays exponentially with lead time. Beyond a coherence threshold, lagged features have negligible predictive capacity for instantaneous target deviations.

A.1. Proof of Lemma 1 (Information horizon bound and autoregressive mutual information decay)

  • The model represents the causal information state using p historical observations and assumes stochastic dynamics with independent Gaussian disturbances.The disturbance represents measurement turbulence and thermal micro-shocks.Source: §A.1 · p. 32
  • Under linearized stochastic expansion, conditional covariance propagates through a discrete Riccati equation, and conditional entropy approaches the unconditional stationary entropy at long horizons.The resulting mutual information between future state and current state tends to zero.Source: §A.1 · p. 32
  • Mutual information between current state and future telemetry decays exponentially with lead time when the system has a positive maximal Lyapunov exponent.The bound is I(y_{t+h}; x_t) ≤ I_0 exp(-μ h Δt).Source: §A.1 · p. 32
  • Beyond the kinetic coherence length, localized lagged features retain negligible predictive capacity for instantaneous target deviations.The coherence length is defined using the decay rate, sampling interval, initial mutual information, and an information threshold.Source: §A.1 · p. 32

A.2. Proof of Theorem 1 (Asymptotic minimum-variance estimator and periodic convergence)

The proof decomposes telemetry into a deterministic periodic baseline and a zero-mean stochastic residual. As residual memory fades, the forecast converges to the baseline, which minimizes asymptotic forecast variance.

A.2. Proof of Theorem 1 (Asymptotic minimum-variance estimator and periodic convergence)

  • Telemetry is decomposed into a deterministic periodic diurnal baseline and a stochastic residual with zero mean and fading temporal covariance.The baseline represents the asset’s thermodynamic energy equilibrium; the residual satisfies mixing conditions.Source: §A.2 · pp. 32–33
  • The MMSE forecast equals the future baseline plus the conditional expectation of the future residual given the history.As lead time grows, that residual expectation converges to zero, so the forecast converges to the baseline.Source: §A.2 · p. 33
  • At large horizons, nonzero coefficients in an unregularized direct autoregressive head add extraneous forecast variance because current features decorrelate from future telemetry.This contrasts with the asymptotic baseline estimator’s variance-minimizing property.Source: §A.2 · p. 33
  • The asymptotic diurnal estimator minimizes forecast variance, and the sigmoidal blend converges to it as lead time approaches infinity.The theorem compares the baseline forecast error variance with that of any other forecast.Source: §A.2 · p. 33

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