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Physics-Informed State Space Models for Day-Ahead Photovoltaic Power Forecasting

Phil Aupke, Muhammad Hassan, Khalid Ali, Seema, Andreas Kassler, Andreas Theocharis

arXiv:2610.14014v1cs.LGcs.AI

TL;DR

Day-ahead PV forecasting must capture temporal patterns while respecting physical system constraints, but existing approaches leave system-level PV conversion physics underexplored with selective state space models. This paper combines a differentiable PV model with PowerMamba, reducing RMSE by 38.5% and MAE by 45.8% relative to a physics-only model. System-level physics provides the dominant gain, and the embedded physics improves robustness under measurement corruption.

  • Problem

    Existing physics-informed approaches capture limited PV behavior, while integrating system-level conversion physics with selective SSMs for NWP-driven day-ahead forecasting remains largely unexplored.

    Source: §I · p. 1

  • Method

    A differentiable PV conversion module provides a structured baseline, while PowerMamba learns residual corrections from NWP inputs over a 24-hour horizon.

    Source: §I · p. 1, §III · p. 2

  • Results

    38.5% RMSE reduction and 45.8% MAE reduction versus the physics-only model; the proposed model also outperforms the data-driven baseline.

    Source: B. Physics-Informed State Space… · p. 4

  • Takeaways & Limitations

    Ablations identify core system-level PV physics as the dominant accuracy contributor, while atmospheric refinements add only marginal improvement.

    Source: C. Assessment of Embedded Physical… · p. 4, §V · p. 5

    The relative importance of physics components may not generalize across climates, array configurations, or inverter architectures, and variant comparisons lacked repeated-seed runs.

    Source: §V · p. 5

Abstract

from arXiv · show

Accurate day-ahead photovoltaic (PV) power forecasting requires both strong temporal modeling and adherence to physical PV system constraints. Purely data-driven models often ignore the underlying PV conversion process and may produce predictions that are outside the operational range of a PV system. In this paper, we propose a physics-informed state space framework that combines a differentiable PV conversion model with a selective state space backbone (PowerMamba). Our approach follows a physics-residual decomposition. The physics module provides a structured baseline based on solar geometry, irradiance, temperature effects, and inverter limits, while the state space model learns residual corrections from numerical weather prediction (NWP) inputs over a 24-hour horizon. Experiments on one year of utility-scale PV data show that the proposed method significantly improves forecasting accuracy, reducing RMSE by 38.5% and MAE by 45.8% compared to a physics-only baseline, and outperforming a purely data-driven model. Results further show that incorporating system-level physics provides the largest performance gains, while additional refinements offer only marginal improvements. Beyond accuracy, the model improves robustness by constraining predictions toward physical feasibility, reducing unrealistic predictions under corrupted measurements.

I. INTRODUCTION

Day-ahead PV forecasts matter for power-system operations, but data-driven models may violate PV system limits and existing physics-informed approaches leave system-level conversion physics underexplored. The paper proposes combining that physics with a selective state space model for NWP-driven forecasting.

I. INTRODUCTION

  • Forecast errors translate into balancing costs and reduced grid reliability, making accurate day-ahead PV forecasting important for unit commitment, reserve allocation, and market scheduling.Source: §I · p. 1
  • Data-driven forecasts may violate inverter limits and degrade under sensor drift, measurement corruption, or distribution shifts.Prior hybrid approaches combine physical PV models with data-driven corrections, but typically incorporate limited aspects of PV behavior.Source: §I · p. 1
  • System-level PV conversion physics—including solar geometry, irradiance transposition, and inverter constraints—remains largely unexplored with selective SSMs for NWP-driven operational day-ahead forecasting.Source: §I · p. 1
  • The proposed physics–residual decomposition pairs a structured PV physics baseline with a selective state space model that learns residual corrections from NWP inputs.The sequence model operates over a 24-hour horizon.Source: §I · p. 1
  • Progressive ablation identifies core PV conversion physics as the dominant accuracy contributor, with higher-order refinements yielding diminishing returns.Source: §I · p. 1
  • The embedded physics module constrains predictions toward inverter capacity, reducing unrealistic outputs under measurement corruption.Source: §I · p. 2

II. BACKGROUND AND RELATED WORK

Prior sequence models offer efficient temporal modeling but do not encode PV conversion constraints, while existing physics-informed PV approaches generally capture isolated effects. This work combines system-level PV physics with a selective state space backbone for NWP-driven day-ahead forecasting.

II. BACKGROUND AND RELATED WORK

  • Selective SSMs such as Mamba offer linear-complexity sequence modeling, but remain data-driven and do not encode PV conversion constraints.Prior PV hybrids typically include isolated physical effects rather than the full system-level conversion chain.Source: §II · p. 2
  • The proposed approach integrates a system-level PV conversion pipeline with a selective state space backbone through a physics-residual decomposition.It targets NWP-driven day-ahead forecasting.Source: §II · p. 2

III. METHODOLOGY

The methodology combines a differentiable PV physics layer with PowerMamba, which models systematic deviations, then sums their outputs and enforces non-negative forecasts. The task uses historical observations and future NWP inputs to predict a 24-hour sequence, with a selective state space backbone for temporal dependencies.

III. METHODOLOGY

  • The architecture combines a physical PV baseline with a PowerMamba residual layer, sums their outputs, and applies ReLU to enforce non-negative predictions.The physical layer models solar geometry, irradiance transposition, temperature-dependent efficiency, and inverter capacity constraints.Source: §III · p. 2

A. Problem Formulation

  • The model predicts the next 96 steps—24 hours at 15-minute resolution—from 288 historical steps, using future NWP inputs.Static plant parameters are configuration inputs to the physics module rather than time-varying model features.Source: A. Problem Formulation · p. 2

B. State Space Backbone

  • PowerMamba uses input-dependent state-space recurrences to model long-range temporal dependencies with linear complexity.Its input-dependent matrices enable selective propagation and forgetting.Source: B. State Space Backbone · pp. 2–3

C. Differentiable Photovoltaic Physics Module

The differentiable physics module models the PV conversion chain from irradiance transposition through inverter-constrained power generation. It focuses on dominant deterministic processes and uses bounded, learnable thermal and efficiency parameters for site-specific adaptation.

C. Differentiable Photovoltaic Physics Module

  • The differentiable physics module embeds a learnable PV conversion chain from irradiance transposition through DC power generation to inverter capacity enforcement.It captures dominant deterministic processes while supporting end-to-end training.Source: C. Differentiable Photovoltaic Physics… · p. 3
  • The module omits inter-row shading, soiling, spectral mismatch, and detailed inverter efficiency curves because they fall below the noise floor of 15-minute, 4 km NWP inputs.Source: C. Differentiable Photovoltaic Physics… · p. 3
  • Thermal and efficiency parameters are learnable but bounded to physically plausible ranges, enabling site-specific adaptation while preserving consistency.Source: C. Differentiable Photovoltaic Physics… · p. 3

D. Physics–Residual Decomposition

The decomposition assigns irradiance-to-power conversion to first-principles modeling and unresolved forecast errors and site effects to data-driven learning. The final prediction combines both components, with non-negativity enforced by ReLU.

D. Physics–Residual Decomposition

  • The decomposition separates first-principles irradiance-to-power conversion from NWP errors, site-specific effects, and unresolved atmospheric variability learned from data.The paper intends this separation to keep the backbone from relearning known physics and to preserve a physical baseline when training data quality degrades.Source: D. Physics–Residual Decomposition · p. 3
  • The final prediction combines the physical baseline and backbone output, while ReLU enforces non-negativity.The inverter capacity limit is enforced only within the physical prediction through smooth saturation.Source: D. Physics–Residual Decomposition · p. 3

E. Training Objective and Optimization

Training balances predictive accuracy with physical consistency, then uses a staged schedule to fit the physics module before joint training with the residual backbone.

E. Training Objective and Optimization

  • The composite training objective balances predictive accuracy and physical consistency using a weighted sum of mean squared error and a physics penalty.The physics penalty discourages learned physics parameters from leaving plausible bounds, with λphys = 0.01.Source: E. Training Objective and Optimization · p. 3
  • During 10 warm-up epochs, the residual backbone stays frozen while the physics module is fitted, followed by joint training through 30 epochs.This schedule is intended to prevent the data-driven component from dominating the physical baseline.Source: E. Training Objective and Optimization · p. 3
  • The residual backbone uses two Mamba blocks with dmodel = 128, dstate = 64, dconv = 2, expansion factor 2, and dropout p = 0.2.Training uses batch size 64, Adam, learning rate 10^-3, and RevIN feature normalization.Source: E. Training Objective and Optimization · p. 3

IV. EVALUATION

The evaluation uses real-world operational data to assess forecasting accuracy, physical-component ablations, and robustness to measurement corruption.

IV. EVALUATION

  • The experiments assess overall day-ahead photovoltaic forecasting accuracy using real-world operational data.The data are described as real-world operational data; this passage does not specify dataset duration or location.Source: §IV · p. 3
  • Progressive ablation experiments assess the impact of embedding physical components in the model.Source: §IV · p. 3
  • The evaluation also tests robustness under measurement corruption.Source: §IV · p. 3

A. Experimental Setup

The study evaluates day-ahead forecasts on one year of utility-scale PV data using seasonal chronological folds. The reported Fold 2 validation curve drops below both baselines after the residual backbone activates.

A. Experimental Setup

  • The dataset covers July 2018–June 2019 at 15-minute resolution, with an approximately 13.2 MW inverter limit and a 24-hour, 96-step forecast horizon.The annual data span summer, winter, and transitional seasons; NWP forecasts have approximately 4 km spatial resolution.Source: A. Experimental Setup · pp. 3–4
  • Four chronological expanding-window folds train on 20%, 40%, 60%, and 80% of the data, with each test set covering approximately one season.RMSE and nRMSE are computed over daylight hours to avoid bias from nighttime zero production.Source: A. Experimental Setup · p. 4

B. Physics-Informed State Space Architecture

  • Table II summarizes day-ahead forecasting performance across validation folds, while Table III covers progressively embedded physical components.Source: Table II · p. 4, Table III · p. 4
  • σRMSE = ±0.02 MW across Folds 1–3, while Fold 4 error is elevated and attributed to measurement corruption.Fold 2 validation MSE tracks the physics-only curve during the 0–10 epoch warm-up, then falls below both baselines after residual activation.Source: B. Physics-Informed State Space… · p. 4, Figure 2 · p. 4

C. Assessment of Embedded Physical Components

Progressive ablations show that core PV physics accounts for most accuracy gains, while higher-order atmospheric refinements add little at the available input resolution. Under corrupted measurements, the physics module keeps predictions within inverter constraints, although fixed calibration cannot distinguish a genuine capacity change without periodic recalibration.

C. Assessment of Embedded Physical Components

  • A 7.1% RMSE reduction from solar geometry rose to 13.3% cumulatively with temperature-dependent and system-level effects, while atmospheric refinements added 0.6%.At 15-minute temporal and 4 km NWP spatial resolution, aerosol optical depth and spectral corrections are poorly resolved, limiting what the residual branch can learn.Source: C. Assessment of Embedded Physical… · p. 4

D. Robustness and Physical Consistency

  • After March 2019, measured peaks reached 17.28 MW—30.9% above the 13.2 MW inverter limit—while physics-informed predictions remained within the constraint.The period is described as apparent measurement corruption; the measurements also exceeded the plant’s realistic operating ceiling of approximately 15.8 MW by 9.4%.Source: D. Robustness and Physical Consistency · p. 4, Figure 3 · p. 5
  • Because inverter capacity is calibrated once and held fixed, the model cannot distinguish a genuine capacity change without periodic recalibration on updated operating data.Before March 2019, isolated above-limit readings had a median of 13.5 MW and represented less than 0.3% of pre-corruption samples.Source: D. Robustness and Physical Consistency · p. 4
  • 26.9% of Fold 4 daylight steps had above-limit predictions from data-driven PowerMamba, while the physics-informed model remained within the inverter constraint.Fold 4 RMSE was 2.02 MW versus 1.60 ± 0.02 MW for Folds 1–3; excluding Fold 4, the physics-informed model achieved 1.50 MW mean RMSE (7.50% nRMSE).Source: D. Robustness and Physical Consistency · pp. 4–5

V. CONCLUSION AND FUTURE WORK

The proposed physics-informed state space framework combines a differentiable PV conversion module with PowerMamba and improves accuracy over a physics-only benchmark. The reported gains come primarily from system-level physics, but their magnitude and component ranking may not generalize beyond the single studied installation.

V. CONCLUSION AND FUTURE WORK

  • 38.5% RMSE and 45.8% MAE reductions over a physics-only benchmark were achieved by the proposed framework on utility-scale PV data.The conclusion attributes the dominant gain to system-level physics, with atmospheric refinements offering only marginal improvements.Source: §V · p. 5
  • The framework combines a differentiable PV conversion module with PowerMamba through a physics–residual decomposition.The physics module adds 141 parameters to the 517k-parameter backbone, and full 24-hour inference completes in seconds on a single GPU.Source: §V · p. 5
  • Because the results come from one utility-scale installation, improvement magnitudes and the relative importance of physics components may not generalize across sites.The conclusion specifically identifies differences in climate, array configuration, and inverter architecture as potential boundaries.Source: §V · p. 5
  • Variant comparisons were not verified with repeated-seed runs.Source: §V · p. 5

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