Physics-Informed State Space Models for Reliable Solar Irradiance Forecasting in Off-Grid Systems

Mohammed Ezzaldin Babiker Abdullah

arxiv: 2604.11807 · v3 · submitted 2026-04-13 · 💻 cs.LG · cs.AI· cs.SY· eess.SY

Physics-Informed State Space Models for Reliable Solar Irradiance Forecasting in Off-Grid Systems

Mohammed Ezzaldin Babiker Abdullah This is my paper

Pith reviewed 2026-05-10 15:40 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.SYeess.SY

keywords solar irradiance forecastingphysics-informed modelsstate space modelsoff-grid photovoltaic systemstime series forecastingrenewable energyedge deploymentdiurnal cycle constraints

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The pith

A physics-informed state space model uses solar zenith angle gating to forecast irradiance accurately with under 40,000 parameters for off-grid systems.

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

This paper introduces the Physics-Informed State Space Model (PISSM) to deliver efficient and physically consistent solar irradiance forecasts for off-grid photovoltaic systems. It replaces heavy attention mechanisms with a linear state space model and adds a dynamic Hankel matrix embedding to reduce sensor noise in meteorological sequences. The central addition is a gating step that incorporates solar zenith angle and clearness index to force outputs to respect natural day-night cycles and block impossible nighttime predictions. Tested on multi-year data from Omdurman, Sudan, the approach reaches higher accuracy than prior methods while staying lightweight enough for microcontroller deployment.

Core claim

PISSM shows that a linear state space model augmented with dynamic Hankel embedding and a physics-informed gate on solar zenith angle and clearness index can produce solar irradiance forecasts that obey diurnal cycles by construction, achieve better accuracy than existing methods, and require fewer than 40,000 parameters for real-time use on edge hardware in off-grid settings.

What carries the argument

The Physics-Informed Gating mechanism that takes solar zenith angle and clearness index as inputs to structurally bound model outputs to diurnal cycles and eliminate nocturnal irradiance errors.

If this is right

Forecasts become suitable for direct real-time control loops on low-power microcontrollers in remote PV installations.
Sensor noise is attenuated early through Hankel embedding, improving robustness without extra post-processing.
Temporal modeling runs in parallel without the quadratic cost of attention layers.
The model sets a parameter-efficient benchmark that other edge renewable-energy forecasters can compare against.

Where Pith is reading between the lines

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

The same gating idea could extend to wind or load forecasting if analogous physical indices are available.
Deployment cost drops further if the 40k-parameter size allows shared hardware across multiple sensor streams.
Geographic transfer tests would reveal whether zenith-angle dependence needs latitude-specific tuning.

Load-bearing premise

The gating based on solar zenith angle and clearness index will continue to enforce strict diurnal compliance and block all nighttime errors in real-world conditions outside the specific Omdurman dataset.

What would settle it

Observing any positive irradiance prediction at night on new data from a different latitude or weather regime would show that the structural bounding does not hold.

read the original abstract

The stable operation of off-grid photovoltaic systems requires accurate, computationally efficient solar forecasting. Contemporary deep learning models often suffer from massive computational overhead and physical blindness, generating impossible predictions. This paper introduces the Physics-Informed State Space Model (PISSM) to bridge the gap between efficiency and physical accuracy for edge-deployed microcontrollers. PISSM utilizes a dynamic Hankel matrix embedding to filter stochastic sensor noise by transforming raw meteorological sequences into a robust state space. A Linear State Space Model replaces heavy attention mechanisms, efficiently modeling temporal dependencies for parallel processing. Crucially, a novel Physics-Informed Gating mechanism leverages the Solar Zenith Angle and Clearness Index to structurally bound outputs, ensuring predictions strictly obey diurnal cycles and preventing nocturnal errors. Validated on a multi-year dataset for Omdurman, Sudan, PISSM achieves superior accuracy with fewer than 40,000 parameters, establishing an ultra-lightweight benchmark for real-time off-grid control.

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

PISSM combines Hankel embedding, linear SSM, and a zenith-based gate for lightweight solar forecasting, but the abstract's strong claims lack numbers and the structural bound may be softer than stated.

read the letter

The main thing to know is that this paper builds a state space model for solar irradiance that adds dynamic Hankel embedding to handle noisy sensor data, replaces attention with a linear SSM for speed, and introduces a physics-informed gate using solar zenith angle and clearness index to keep outputs from violating basic day-night patterns. It targets off-grid microcontroller use with under 40k parameters and tests on multi-year data from Omdurman, Sudan. That focus on efficiency plus physical plausibility for real energy access applications is the useful angle here. The choice of linear SSM over heavier transformers is a reasonable efficiency move, and pulling in standard solar parameters like zenith angle shows domain awareness rather than pure data fitting. The multi-year single-site dataset at least covers seasonal cycles in one location. The soft spots are straightforward. The abstract asserts superior accuracy and strict physical bounding without any error values, baseline comparisons, or ablation results, so the performance edge is not yet visible. The gating is described as structurally bounding outputs, but if it works as an extra input channel or multiplicative factor rather than an explicit zeroing at night, it can still produce nocturnal errors under noise or unseen conditions, which matches the stress-test concern. Single-site validation does not test generalization to other climates or aerosol-heavy regimes. This is for engineers working on edge-deployed renewable forecasting or researchers adapting state space models to physics constraints. It is not a broad theoretical advance but could be worth a look for the application-specific architecture. I would send it to peer review so the authors can supply the missing metrics and clarify the exact gating implementation.

Referee Report

2 major / 2 minor

Summary. The paper proposes the Physics-Informed State Space Model (PISSM) for solar irradiance forecasting in off-grid PV systems. It employs dynamic Hankel matrix embedding to filter sensor noise in meteorological sequences, replaces attention with a linear state space model for efficient temporal modeling and parallel computation, and introduces a Physics-Informed Gating mechanism that incorporates Solar Zenith Angle and Clearness Index to enforce physical bounds such as strict diurnal cycles and zero nocturnal output. The model is validated on a multi-year dataset from Omdurman, Sudan, with claims of superior accuracy, physical consistency, and an ultra-lightweight footprint under 40,000 parameters suitable for microcontroller deployment.

Significance. If the central claims hold, the work would provide a computationally efficient and physically grounded alternative to large deep-learning forecasters for edge-deployed off-grid control, potentially improving reliability by eliminating unphysical predictions while meeting strict resource constraints. The low parameter count and emphasis on structural physical constraints represent a meaningful contribution to the intersection of state-space methods and domain-informed ML for renewable energy applications.

major comments (2)

[Physics-Informed Gating mechanism (abstract, §3)] The description of the Physics-Informed Gating mechanism (abstract and §3) states that it 'structurally bound outputs' to obey diurnal cycles via Solar Zenith Angle and Clearness Index. However, without an explicit equation showing a hard zero-mask (e.g., output = 0 when SZA exceeds a night threshold, independent of learned weights), the mechanism appears to function as soft feature modulation or an additional input channel. This leaves the bound vulnerable to violation by sensor noise, clearness-index forecast error, or distribution shift, directly undermining the central physical-consistency claim.
[Validation and results (abstract, §4)] The superiority claim (abstract) rests on validation results for the Omdurman dataset, yet no quantitative metrics, baseline comparisons (e.g., against standard SSM, LSTM, or physics-based models), error distributions, or ablation studies on the gating component are referenced in the provided abstract or summary. This absence makes it impossible to verify whether the reported accuracy gains are statistically significant or attributable to the proposed components rather than dataset-specific tuning.

minor comments (2)

[§2, §3] Notation for the dynamic Hankel embedding and the linear SSM transition matrices should be defined with explicit equations early in the methods section to improve reproducibility.
[Abstract] The abstract would benefit from at least one key quantitative result (e.g., RMSE or MAE improvement and parameter count comparison) to substantiate the 'superior accuracy' claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments on our manuscript. We address each major comment point by point below and indicate the revisions we will make to improve clarity and verifiability.

read point-by-point responses

Referee: The description of the Physics-Informed Gating mechanism (abstract and §3) states that it 'structurally bound outputs' to obey diurnal cycles via Solar Zenith Angle and Clearness Index. However, without an explicit equation showing a hard zero-mask (e.g., output = 0 when SZA exceeds a night threshold, independent of learned weights), the mechanism appears to function as soft feature modulation or an additional input channel. This leaves the bound vulnerable to violation by sensor noise, clearness-index forecast error, or distribution shift, directly undermining the central physical-consistency claim.

Authors: We appreciate the referee highlighting this issue of precision. The abstract and §3 describe the mechanism as providing structural bounds, but we agree that the lack of an explicit equation leaves it open to interpretation as soft modulation. We will revise §3 to include the precise mathematical formulation of the Physics-Informed Gating, explicitly defining a hard zero-mask (output set to zero when solar zenith angle exceeds the night threshold) that operates independently of learned weights. This addition will clarify the hard constraint and directly mitigate concerns about vulnerability to noise or forecast errors. revision: yes
Referee: The superiority claim (abstract) rests on validation results for the Omdurman dataset, yet no quantitative metrics, baseline comparisons (e.g., against standard SSM, LSTM, or physics-based models), error distributions, or ablation studies on the gating component are referenced in the provided abstract or summary. This absence makes it impossible to verify whether the reported accuracy gains are statistically significant or attributable to the proposed components rather than dataset-specific tuning.

Authors: We agree that the abstract does not contain the specific quantitative metrics or comparisons, which are presented in detail in §4 of the full manuscript. To enable direct verification of the superiority claims and the contribution of each component, we will revise the abstract to include key numerical results (e.g., RMSE and MAE), explicit baseline comparisons against standard SSM, LSTM, and physics-based models, and a summary of the gating ablation study. These updates will also reference the statistical significance of the gains. revision: yes

Circularity Check

0 steps flagged

No significant circularity: novel components and empirical validation remain independent of inputs

full rationale

The paper's derivation chain introduces distinct architectural elements (dynamic Hankel embedding for noise filtering, replacement of attention by Linear State Space Model, and Physics-Informed Gating using Solar Zenith Angle plus Clearness Index) that are presented as new mechanisms rather than tautological reductions. The central claim of structurally bounding outputs to obey diurnal cycles is framed as a consequence of the gating design, not as a re-expression of fitted parameters or prior self-citations. Validation on the multi-year Omdurman dataset is an external empirical test, not a self-referential fit where predictions are forced by construction. No load-bearing uniqueness theorems, ansatzes smuggled via self-citation, or renaming of known results appear in the abstract or described chain. The model therefore retains independent content beyond its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 2 invented entities

The central claim rests on standard assumptions of state space models for time series and the effectiveness of the newly proposed physics gating; limited independent evidence is available from the abstract alone.

free parameters (1)

Total model parameters
Claimed to be fewer than 40,000 but exact count, initialization, and fitting procedure not detailed in abstract.

axioms (2)

domain assumption Linear State Space Models can efficiently model temporal dependencies in meteorological sequences for parallel processing
Invoked to replace heavy attention mechanisms.
domain assumption Solar Zenith Angle and Clearness Index provide sufficient information to structurally bound irradiance predictions to diurnal cycles
Core premise of the Physics-Informed Gating mechanism.

invented entities (2)

Physics-Informed Gating mechanism no independent evidence
purpose: To enforce physical bounds on model outputs using solar position and atmospheric clarity parameters
Newly introduced component without external validation or falsifiable prediction shown in abstract.
Dynamic Hankel matrix embedding no independent evidence
purpose: To transform raw sequences and filter stochastic sensor noise
Introduced as part of the preprocessing step.

pith-pipeline@v0.9.0 · 5472 in / 1730 out tokens · 69430 ms · 2026-05-10T15:40:27.743752+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

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[1] [1]

https://doi.org/10.3390/math11030676 Alsumaiei, A. A. (20 26). Physics-constrained neural network for daily pan evaporation forecasting in hyper -arid climates optimized by Bat Algorithm. Journal of Hydrology , 668, 123142. https://doi.org/10.1 016/j.jhydrol.2026.123142 Bank, M. S., et al. (2013). Solar Powered Irrigation Systems (SPIS): Technology, Econo...

work page doi:10.3390/math11030676 2026

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https://doi.org/10.6919/ICJE.202601_12(1 ).0002 Golyandina, N., & Zhigljavsky, A. (2013). Singular Spectrum Analysis for Time Ser ies. Springer Briefs in Statistics. Springer. https://doi.org/10.1007/978 -3-642-34913-3 Gu, A., Goel, K., & Ré, C. (2021). Efficiently Modeling Long Seq uences with Structured State Spaces. arXiv preprint arXiv:2111.00396 . ht...

work page doi:10.6919/icje.202601_12(1 2013

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https://journals.karary.e du.sd/index.php/JKUES/article/view/253 NASA POWER Project. (2026). PaRameter Uncertainty ViEwer (PRUVE) for Satellite Data Validation . NASA Earth Data. https://power. larc.nasa.gov/ Parsa, S. M., Akbari, M., & Ahmadi, M. H. (2022). Physics -informed machine learning meets renewable energy systems: A review of advances, challenge...

work page doi:10.1016/j.apenergy.2021.118020 2026

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Raissi, P

https://doi.org/10.1016/j.jcp.2018.10.045 Stackhouse, P. W., Jr., Chandler, W. S., & Hoell, J. M. (2023). Advances and Uses of the NASA POWER Global Solar and Meteorological Data Sets . American Meteorological Society (AMS). https://ui.adsabs.harvard.edu/abs/2023AMS...10321689S/abstract Voyant, C., Notton, G., Kalogirou, S., Nivet, M. L., & Paoli, C. (201...

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