An enhanced neural network algorithm and its applications for numerical optimization and parameter extraction of photovoltaic models

Smarter Solar Power for Everyday Life

Solar panels are becoming fixtures on rooftops and in fields around the world, but getting the most electricity out of every ray of sunlight is still a challenge. This article introduces a new computer technique that helps engineers build more accurate virtual models of solar panels. With better models, they can design and control photovoltaic (PV) systems that are cheaper, more reliable, and more efficient—benefits that ultimately reach homeowners, businesses, and the power grid.

Why Solar Panels Need a “Digital Twin”

Behind every physical PV module there is a mathematical stand‑in—a model—that predicts how much current and voltage the panel will deliver under different conditions, such as temperature and sunlight. These models are vital for planning solar farms, tracking the best operating point, and diagnosing faults without constantly probing the hardware. But the models have several hidden parameters, such as internal resistances and diode currents, that cannot be measured directly. Instead, they must be inferred from real current–voltage measurements. Because the relationships inside the model are highly nonlinear and contain many local traps, finding the right parameter values is a difficult search problem, especially for more detailed models like the double‑diode model or full PV module models.

From Nature-Inspired Search to Brain-Inspired Search

Over the last decade, engineers have turned to so‑called metaheuristic algorithms—search methods inspired by animal behavior, physics, or other natural processes—to estimate PV parameters. Techniques based on whales, bats, marine predators, teaching–learning in classrooms, and many others have shown promise because they balance exploration of the search space with fine‑tuning around good solutions. In parallel, artificial neural networks have transformed fields like image recognition and robotics. Their structure and learning behavior have also inspired new optimization methods. One such method is the Neural Network Algorithm (NNA), a metaheuristic that mimics feedback neural networks and has strong global search ability, but tends to get stuck in local optima when the problem is very complex.

An Enhanced Neural Network Algorithm

The authors propose an Enhanced Neural Network Algorithm, or ENNA, designed specifically to overcome NNA’s weaknesses. ENNA adds two key ingredients. First, a perturbation operator injects controlled randomness based on the normal (bell‑shaped) distribution and on differences between several candidate solutions; this shakes the search out of dead ends without losing what has already been learned. Second, an elite operator lets each candidate learn from both the best solution found so far and the average position of the entire population, using a crossover matrix to mix these influences. On top of this, ENNA uses three different movement strategies that alternate between following the current best, revisiting historical populations, and jumping toward the elite mix. Unlike the original NNA, ENNA keeps the chances of global moves and local tweaking in better balance throughout the run.

Putting ENNA to the Test

To show that ENNA is not just clever in theory, the researchers first challenged it with 52 demanding benchmark functions drawn from international optimization test suites. These functions are widely used to compare algorithms and include simple, rugged, and composite landscapes with many local traps. Across these tests, ENNA consistently ranked at or near the top when compared against ten strong competitors, including differential evolution, equilibrium optimizer, whale optimization, and advanced NNA variants. ENNA either achieved the best average solution or tied for best on roughly 80 percent of the functions, and statistical tests confirmed that these improvements were not due to chance.

Sharper Models for Real Solar Hardware

The real payoff comes when ENNA is applied to practical PV parameter extraction. The team used measured current–voltage data from a commercial silicon solar cell and from a 36‑cell PV module. They fitted three model types: the widely used single‑diode model, the more detailed double‑diode model, and a full module model that accounts for series and parallel connections of cells. In every case, ENNA achieved extremely low root‑mean‑square errors between the measured and simulated curves—about 0.00099 for the single‑diode and double‑diode models and 0.00243 for the module—beating or matching leading state‑of‑the‑art algorithms from previous studies. The fitted curves almost overlap the experimental data, indicating that the internal parameters found by ENNA provide a very faithful “digital twin” of the real devices.

What This Means for Future Solar Systems

For non‑specialists, the takeaway is that ENNA offers a more reliable and repeatable way to tune the mathematical models that underpin solar power design and control. When those models are more accurate, engineers can better predict how panels will behave, locate the point of maximum power more precisely, and evaluate new layouts or materials with greater confidence. While ENNA is computationally heavier than some simpler methods, its strong search capabilities and lack of extra tuning knobs make it an attractive general tool for complex engineering problems, from smarter solar farms today to other energy and optimization challenges in the future.

Citation: Chi, A., Mirjalili, S. & Zhang, Y. An enhanced neural network algorithm and its applications for numerical optimization and parameter extraction of photovoltaic models. Sci Rep 16, 7306 (2026). https://doi.org/10.1038/s41598-026-37918-9

Keywords: solar energy, photovoltaic models, optimization algorithms, neural network methods, parameter estimation