Low Latency Stand Alone Compute-Efficient Forecasting of Marine Engine Time Series Data

Soumyendu Raha; Y. Harsha Vardhana Reddy

arxiv: 2605.26123 · v1 · pith:Q4NNY5XSnew · submitted 2026-05-14 · 📡 eess.SY · cs.SY· stat.CO

Low Latency Stand Alone Compute-Efficient Forecasting of Marine Engine Time Series Data

Y. Harsha Vardhana Reddy , Soumyendu Raha This is my paper

Pith reviewed 2026-06-30 20:42 UTC · model grok-4.3

classification 📡 eess.SY cs.SYstat.CO

keywords marine engine forecastingstochastic differential equationsadaptive time seriesGirsanov transformEuler-Maruyama discretizationmulti-particle ensemblenon-stationary predictionreal-time risk quantification

0 comments

The pith

An adaptive multi-particle SDE model with drift-based lookback and Girsanov weighting forecasts marine engine time series more stably and efficiently than fixed linear models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a forecasting method for marine engine parameters that uses stochastic differential equations whose window size adapts to instantaneous drift magnitude and whose particle ensemble is refined by Girsanov reweighting after Euler-Maruyama discretization. This dual approach is meant to handle the non-stationary, high-volatility behavior that defeats classical models such as VARIMA. A reader would care because propulsion-system health predictions that remain reliable over multiple steps and run at low latency could support real-time risk monitoring on vessels subject to changing loads.

Core claim

The central claim is that a dual-layered estimation approach—first an adaptive lookback rule that enlarges or shrinks the learning window according to measured drift, then a multi-particle ensemble evolved by Euler-Maruyama and reweighted by a Girsanov-induced change of measure—produces multi-step forecasts of marine engine parameters that are both more stable and computationally lighter than those obtained from classical statistical baselines such as VARIMA.

What carries the argument

adaptive-window multi-particle stochastic differential equations refined by Girsanov change of probability measure

If this is right

Multi-step prediction stability improves when the learning window responds to instantaneous drift magnitude rather than remaining fixed.
Computational cost drops because the Girsanov weighting suppresses noise-chasing particles and avoids full retraining at every step.
The resulting grey-box forecasts supply real-time risk quantification for systems that exhibit high-frequency volatility and abrupt non-linear transitions.
The same structure scales to stand-alone deployment without external model libraries or heavy hyper-parameter tuning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The adaptive drift rule could be ported to other sensor-rich engineering domains that experience regime shifts, such as wind-turbine or automotive engine monitoring.
A controlled experiment that disables the Girsanov reweighting step on the same data would isolate how much of the reported stability gain comes from the probability-measure change versus the adaptive window alone.
If the SDE drift function were replaced by a learned neural approximator while keeping the rest of the pipeline fixed, the framework might bridge grey-box and black-box regimes without losing the low-latency property.

Load-bearing premise

Marine engine parameters obey dynamics that an SDE can capture usefully and whose physical drift can be aligned by Girsanov reweighting after Euler-Maruyama discretization.

What would settle it

Run the adaptive SDE and a VARIMA baseline on the same held-out marine engine sensor traces; if the multi-step mean-squared error and wall-clock time of the SDE model are not both lower, the performance claim is falsified.

Figures

Figures reproduced from arXiv: 2605.26123 by Soumyendu Raha, Y. Harsha Vardhana Reddy.

**Figure 1.** Figure 1: Gas Turbine-Brayton Cycle fail to account for these real-world deviations, necessitating a shift toward Maintenance 4.0—a paradigm that leverages data-driven tools for proactive maintenance and real-time risk quantification. While deep learning and regression-based approaches have gained popularity, they often lack the interpretability required for critical marine engineering decisions and can be prone to … view at source ↗

**Figure 2.** Figure 2: Diesel Cycle [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: Data Driven Models Vs Physics Based Models [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗

**Figure 4.** Figure 4: Single Particle Method (SPM): Actual vs Predicted Engine Parameters [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Single Particle Method (SPM): Average MAE vs Forecast Horizon [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: ARIMA-based time-series forecasting performance illustrating the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: Multi Particle Method:Comparison of Predicted and actual values of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 9.** Figure 9: VARIMA-based time-series forecasting performance illustrating the [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

read the original abstract

The operational reliability of a high performance marine vessel depends critically on the health of its marine propulsion systems, which are increasingly subjected to diverse operational loads and environmental stressors. This paper proposes a robust mathematical framework for non-linear state-space forecasting of marine engine parameters using adaptive-window multi-particle stochastic differential equations. Traditional time-series models such as Vector Autoregressive Integrated Moving Average, often fail to capture the inherent stochasticity and transient dynamics of complex systems due to their reliance on fixed-window linear assumptions. To address this, we develop a dual-layered estimation approach: first, an adaptive lookback mechanism dynamically adjusts the learning window size based on the instantaneous drift magnitude, ensuring responsiveness during non-stationary regimes. Second, a Multi-Particle ensemble is evolved via Euler-Maruyama discretization, where each particle trajectory represents a stochastic realization of the system state. To refine the ensemble mean and mitigate the "noise-chasing" behavior of raw estimators, a Girsanov transform induced change of probability measure is implemented, assigning higher probabilistic weights to particles that align with the physical drift. Theoretical evaluation and empirical benchmarking demonstrate that the proposed adaptive SDE framework significantly outperforms classical statistical baselines in multi-step prediction stability and computational efficiency. The model provides a scalable, "grey-box" solution for real-time risk quantification in systems characterized by high-frequency volatility and non-linear transitions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper applies known SDE techniques like Euler-Maruyama and Girsanov reweighting to marine engine data with an adaptive window, but the abstract supplies no equations, datasets, or performance numbers to support the outperformance claim.

read the letter

The main point is that this work combines established stochastic tools—an adaptive lookback that changes window size with drift magnitude, a multi-particle ensemble evolved by Euler-Maruyama, and Girsanov reweighting to favor particles aligned with physical drift—and applies the package to marine engine time series. The abstract frames it as a grey-box fix for the non-stationarity that breaks VARIMA.

It does a reasonable job naming a real industrial setting where high-frequency sensor data shifts under load changes. The dual-layer idea of letting the window respond to instantaneous drift and then reweighting the ensemble to reduce noise chasing is a logical response to the problem.

The soft spots are the lack of any supporting detail. The abstract asserts that theoretical evaluation and empirical benchmarking show clear gains in multi-step stability and efficiency, yet it contains no metrics, no dataset description, no error bars, and no derivation of the SDE, the adaptive rule, or the Radon-Nikodym derivative. The Girsanov step requires alignment with an unspecified physical drift; without that term or its source, it is impossible to tell whether the reported improvement is independent of fitting choices. The stress-test note correctly flags this gap.

If the full manuscript supplies the missing equations, the explicit drift estimator, and reproducible benchmarks on described data, the picture would change. Based on what is visible, the central claim rests on unshown evidence.

The paper is aimed at engineers who need practical forecasting for volatile sensor streams in propulsion or similar systems. Readers looking for a new theoretical result or a fully specified, independently verifiable method will not find it here. It does not reorganize any area.

I would not send this version to peer review. The authors should first provide the actual model equations, the adaptive rule, the physical-drift source, and concrete benchmark results before any referee time is spent.

Referee Report

3 major / 1 minor

Summary. The paper claims to develop an adaptive SDE-based framework for non-linear state-space forecasting of marine engine parameters. It uses a dual-layered approach with an adaptive lookback mechanism that adjusts the window based on instantaneous drift magnitude and a multi-particle ensemble evolved via Euler-Maruyama discretization, refined by Girsanov transform reweighting to align with physical drift. The method is asserted to outperform classical statistical baselines like VARIMA in multi-step prediction stability and computational efficiency based on theoretical and empirical evaluations.

Significance. A well-specified and validated version of this grey-box stochastic forecasting method could contribute to real-time risk quantification for marine propulsion systems under volatile conditions. The focus on low latency and compute efficiency is relevant for practical deployment. However, the absence of any quantitative results, detailed derivations, or dataset information means the significance cannot be assessed from the current manuscript.

major comments (3)

[Abstract] Abstract: the central claim that 'theoretical evaluation and empirical benchmarking demonstrate that the proposed adaptive SDE framework significantly outperforms classical statistical baselines' supplies no quantitative metrics, error bars, dataset descriptions, or derivation steps, leaving the assertion unsupported by visible evidence.
[Method] Method description: the SDE form (drift and diffusion coefficients) is unspecified. The Girsanov reweighting step depends on alignment with an unspecified physical drift without providing the explicit Radon-Nikodym derivative, its derivation, or the source of the physical drift term; this is load-bearing for the claimed mitigation of noise-chasing and independence from fitting choices.
[Adaptive lookback] Adaptive mechanism: no equation or rule is supplied for the adaptive lookback window adjustment based on instantaneous drift magnitude, which is central to the dual-layered approach and the claim of responsiveness during non-stationary regimes.

minor comments (1)

[Abstract] Abstract: the expansion 'Vector Autoregressive Integrated Moving Average' is nonstandard (typically VARIMA refers to Vector ARIMA); clarify the exact model class used for baselines.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We acknowledge that the submitted manuscript lacks quantitative metrics, detailed derivations, dataset information, and explicit equations, preventing full assessment of the claims and significance. We will undertake major revisions to supply these elements.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that 'theoretical evaluation and empirical benchmarking demonstrate that the proposed adaptive SDE framework significantly outperforms classical statistical baselines' supplies no quantitative metrics, error bars, dataset descriptions, or derivation steps, leaving the assertion unsupported by visible evidence.

Authors: We agree that the abstract claim is unsupported by visible evidence in the current manuscript. In revision we will add quantitative metrics (e.g., multi-step RMSE/MAE with error bars), dataset descriptions, and an outline of key derivations; the abstract will be rewritten to reflect only the evidence that is actually presented. revision: yes
Referee: [Method] Method description: the SDE form (drift and diffusion coefficients) is unspecified. The Girsanov reweighting step depends on alignment with an unspecified physical drift without providing the explicit Radon-Nikodym derivative, its derivation, or the source of the physical drift term; this is load-bearing for the claimed mitigation of noise-chasing and independence from fitting choices.

Authors: The referee is correct; these specifications are absent. The revised Methods section will define the drift and diffusion coefficients, supply the explicit Radon-Nikodym derivative together with its derivation, and state the source of the physical drift term. revision: yes
Referee: [Adaptive lookback] Adaptive mechanism: no equation or rule is supplied for the adaptive lookback window adjustment based on instantaneous drift magnitude, which is central to the dual-layered approach and the claim of responsiveness during non-stationary regimes.

Authors: We acknowledge that only a qualitative description is given. The revision will include the explicit equation or algorithmic rule that adjusts the lookback window from the instantaneous drift magnitude. revision: yes

Circularity Check

0 steps flagged

No circularity identified from available text

full rationale

The provided abstract and context describe a proposed adaptive SDE framework with Girsanov reweighting and adaptive lookback but contain no explicit equations, derivations, or self-referential steps that reduce predictions to fitted inputs by construction. No load-bearing claims are shown to depend on self-citations, ansatzes smuggled via prior work, or renaming of known results. The method is presented at a high level without mathematical reduction that would trigger any of the enumerated circularity patterns. The derivation chain cannot be walked because no chain is exhibited; therefore the finding is no significant circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the framework rests on standard SDE theory plus two paper-specific mechanisms whose exact functional forms are not stated.

free parameters (1)

adaptive lookback window adjustment rule
Window size is said to change with instantaneous drift magnitude, but the functional form or threshold is unspecified and therefore functions as a free modeling choice.

axioms (2)

domain assumption Marine engine parameters admit a non-linear state-space representation amenable to multi-particle SDE evolution under Euler-Maruyama discretization.
Invoked when the dual-layered estimation approach is introduced in the abstract.
domain assumption A Girsanov-induced change of measure can assign higher weights to particles that align with the physical drift without introducing new bias.
Stated as the mechanism that mitigates noise-chasing behavior.

pith-pipeline@v0.9.1-grok · 5776 in / 1548 out tokens · 34740 ms · 2026-06-30T20:42:41.605647+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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H. Gazzetta Junior, C. Bringhenti, J. a. R. Barbosa, and J. T. Tomita, “Real-time gas turbine model for performance simulations,”Journal of Aerospace Technology and Management, vol. 9, no. 3, pp. 346–356, Aug. 2017

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N. Batayev and A. Onbayev, “Prediction of gas turbine parameters based on machine learning regression methods,” Jul. 2018, pp. 217–221

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Machine learning models for predicting ship main engine fuel oil consumption: A comparative study,

C. Gkerekos, I. Lazakis, and G. Theotokatos, “Machine learning models for predicting ship main engine fuel oil consumption: A comparative study,”Ocean Engineering, vol. 188, p. 106282, Sep. 2019. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/S0029801819304561

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S. Dai, X. Zhang, and M. Luo, “A novel data-driven approach for predicting the performance degradation of a gas turbine,”Energies, vol. 17, no. 4, p. 781, Jan. 2024

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Hybrid data-driven and physics- based modeling for gas turbine prescriptive analytics,

S. Belov, S. Nikolaev, and I. Uzhinsky, “Hybrid data-driven and physics- based modeling for gas turbine prescriptive analytics,”International Journal of Turbomachinery, Propulsion and Power, vol. 5, no. 4, p. 29, Dec. 2020

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V . A. Zhigarev, A. V . Minakov, D. V . Guzei, M. I. Pryazhnikov, and V . I. Panteleev, “Development of a mathematical model of diesel-generator units with a valve-inductor generator,”Journal of Physics: Conference Series, vol. 2057, no. 1, p. 012076, Oct. 2021. [Online]. Available: https://iopscience.iop.org/article/10.1088/1742-6596/2057/1/012076

work page doi:10.1088/1742-6596/2057/1/012076 2057

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J. Willard, X. Jia, S. Xu, M. Steinbach, and V . Kumar, “Integrating scientific knowledge with machine learning for engineering and environmental systems,”ACM Computing Surveys, vol. 55, no. 4, pp. 1–37, Apr. 2023. [Online]. Available: https://dl.acm.org/doi/10.1145/3514228

work page doi:10.1145/3514228 2023

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Hybrid physics-infused machine learning framework for fault diagnostics and prognostics in cyber-physical system of diesel engine,

S. K. Singh, “Hybrid physics-infused machine learning framework for fault diagnostics and prognostics in cyber-physical system of diesel engine,” Ph.D. dissertation, Dept. of Automotive Engineering, Clemson University, 2023. [Online]. Available: https://www.proquest.com/openview/e0412f5729f806451dc25df4e76da380/1?pq- origsite=gscholar&cbl=18750&diss=y

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