⚡ electrical engineering

Physics-Informed Neural Network Framework for Predicting Compressive Strength of Coconut Fiber Reinforced Concrete

This study proposes a Physics-Informed Neural Network (PINN) framework that integrates fundamental concrete material laws with experimental data to accurately and reliably predict the compressive strength of coconut fiber reinforced concrete while ensuring physical consistency and interpretability.

Original authors: Ishwor Thapa, Bishwash Poudel, Rojan Subedi, Sundar Adhikari, Garima Shrestha, Pratik Rana Magar

Published 2026-10-05

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CC BY 4.0

Original authors: Ishwor Thapa, Bishwash Poudel, Rojan Subedi, Sundar Adhikari, Garima Shrestha, Pratik Rana Magar

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Concrete is the most widely used building material on Earth, a substance so fundamental that it shapes the skyline of every modern city. Yet, the very process that makes it strong also harms the planet, as the production of its key ingredient, cement, generates a massive amount of carbon dioxide. In the search for a greener future, engineers have turned to nature, mixing coconut fibers into the concrete to create a composite that is both sustainable and tough. These fibers, derived from coconut husks, act like tiny reinforcements that help the material resist cracking and absorb energy. However, predicting exactly how strong this new material will be is a difficult puzzle. The strength depends on a complex dance of factors: how much water is mixed in, how long the concrete cures, how much fiber is added, and even how much recycled rubble is used instead of fresh stone. If the mix is wrong, the building could be unsafe; if it is too conservative, the material is wasted.

For years, scientists have tried to solve this puzzle using computer models that learn from past experiments. These models are good at finding patterns in data, but they often fail when asked to predict something they haven't seen before. They might suggest that a concrete mix cured for a year is weaker than one cured for a month, or that adding more water makes the concrete stronger. These errors happen because the computer is just memorizing numbers without understanding the physical laws that govern how concrete actually hardens. To fix this, a team of researchers from Nepal has developed a new kind of computer model that forces the computer to obey the laws of physics. They call this a Physics-Informed Neural Network. Instead of letting the computer guess freely, they built the rules of cement chemistry directly into the model's brain, ensuring that every prediction it makes respects the reality of how materials behave.

The researchers began by gathering a massive collection of data, pulling together 586 records from 30 different scientific studies. These records contained details about every aspect of the concrete mixes, from the amount of cement and water to the length and amount of coconut fiber used. They then fed this information into their new model, but with a crucial twist. Before the model could make a prediction, it had to pass a series of tests based on known physical truths. For instance, the model was programmed to know that concrete always gets stronger as it gets older, never weaker. It was also taught that adding more water generally makes the concrete weaker, and that replacing natural stone with recycled concrete rubble usually reduces the strength. If the model tried to predict a result that broke these rules, it was corrected immediately. This process ensured that the model didn't just learn from the data, but learned with the data, guided by the fundamental principles of material science.

The results showed that this new approach was highly effective. The model predicted the strength of the coconut fiber concrete with remarkable accuracy, matching the performance of the best traditional computer models. However, the real victory was in its reliability. When the researchers tested the model on scenarios it had never seen before, such as concrete that had been curing for a very long time or mixes with unusual amounts of fiber, the new model behaved sensibly. It correctly predicted that strength would continue to rise slowly over time and eventually level off, whereas older models sometimes made wild, impossible guesses, suggesting the concrete would suddenly lose strength or become impossibly strong. The new model also correctly identified the "sweet spot" for adding coconut fibers. It learned that adding a small amount of fiber strengthens the concrete, but adding too much actually weakens it because the fibers start to clump together and create air pockets. The model pinpointed this optimal range to be between 1.5 and 2.0 percent of the total mix, a finding that aligns perfectly with what engineers have observed in the real world.

By combining the power of modern artificial intelligence with the timeless rules of physics, the researchers have created a tool that engineers can trust. This tool does not just spit out numbers; it offers a clear, logical explanation for why a mix will be strong or weak. It respects the fact that concrete is a living material that changes over time and reacts to its ingredients in specific ways. This work suggests a new path forward for sustainable construction, where engineers can design buildings with coconut fiber concrete with confidence, knowing that their designs are grounded in both data and the laws of nature. The study demonstrates that when we teach computers to understand the physical world, rather than just memorize it, we can solve complex engineering problems with greater safety and precision, paving the way for a more sustainable built environment.

Technical Summary: Physics-Informed Neural Network Framework for Predicting Compressive Strength of Coconut Fiber Reinforced Concrete

Problem Statement
Accurate prediction of the compressive strength of Coconut Fiber Reinforced Concrete (CFRC) is critical for sustainable infrastructure design. While data-driven machine learning (ML) models have demonstrated high predictive accuracy, they often function as "black boxes" that lack intrinsic knowledge of the physical laws governing cementitious materials. Consequently, standard ML models frequently produce predictions that violate fundamental principles, such as predicting lower strength for specimens cured longer (violating age-monotonicity) or suggesting that increasing the water-to-cement ratio enhances strength (violating Abrams' law). These physical inconsistencies lead to unreliable extrapolations, posing significant risks in engineering design where mix proportions or curing conditions may fall outside the training data distribution.

Methodology
This study proposes a Physics-Informed Neural Network (PINN) framework specifically tailored for CFRC. The methodology integrates domain-specific physical knowledge at three levels: feature engineering, network architecture, and the loss function.

Dataset: The model was trained on a comprehensive dataset of 586 experimental records compiled from 30 independent peer-reviewed studies (2012–2025). The data covers a broad design space, including cement content, fiber length and dosage, natural and recycled coarse aggregate (RCA) content, water content, and curing ages ranging from 3 to 546 days.
Physics-Engineered Features: To explicitly encode material physics, five derived features were constructed from the raw mix design variables:
- Hydration Factor ( $H$ ): Based on the CEB-FIP Model Code 1990, capturing the sigmoidal strength gain over time.
- Abrams Factor ( $A$ ): Representing the inverse relationship between water-to-cement ratio and strength potential.
- Fiber Efficiency Factor ( $\eta_f$ ): Incorporating aspect ratio and an exponential saturation penalty to model the diminishing returns and eventual strength reduction at excessive fiber dosages.
- RCA Factor ( $R$ ): An exponential decay function modeling strength degradation due to recycled aggregate incorporation.
- Packing Factor ( $P$ ): Normalized total aggregate content.
  These features were concatenated with the original eight mix variables to form a 13-dimensional input vector.
PINN Architecture: The model utilizes a fully connected feedforward network with four hidden layers (128–256–256–128 neurons) using SiLU activation functions and layer normalization to ensure smooth differentiability.
Loss Function: The training objective combines a data fidelity term (Mean Squared Error) with a physics consistency term. The physics loss penalizes violations of established material laws using automatic differentiation:
- Age Monotonicity: Penalizes predictions where strength decreases as curing age increases.
- Abrams Compliance: Penalizes predictions where strength increases with the water-to-cement ratio.
- RCA Degradation: Penalizes predictions where strength increases with higher RCA replacement.
- Cement Benefit: Penalizes predictions where strength decreases with increased cement content.

Key Results
The proposed PINN was evaluated against six baseline models, including Gradient Boosting Regressors (GBR), Random Forests, and standard Deep Neural Networks (DNN).

Predictive Accuracy: The PINN achieved an $R^2$ of 0.9482, an RMSE of 3.89 MPa, and a MAPE of 8.69%. While the GBR model slightly outperformed it in raw accuracy ( $R^2$ = 0.9673), the PINN's performance remained competitive within the top tier of models.
Physics Compliance: The PINN demonstrated superior adherence to physical laws. It achieved a 0.0% violation rate for age-monotonicity (compared to 0.8–1.6% for baselines) and reduced violations of the Abrams' law and RCA degradation constraints by 75–83% compared to unconstrained models.
Interpretability (SHAP Analysis): SHAP values confirmed that the model learned physically meaningful relationships. Curing age (28.3%) and water-to-cement ratio (22.7%) were the dominant predictors. Crucially, the model correctly identified a non-monotonic relationship for fiber content, predicting an optimal dosage window of 1.5–2.0% by volume, beyond which strength declines due to fiber balling and porosity.
Extrapolation: When extrapolating to curing ages beyond the training data (e.g., 730 days), the PINN maintained smooth, asymptotic convergence consistent with hydration kinetics, whereas the unconstrained DNN exhibited non-physical oscillations and overestimations.

Significance and Claims
The paper claims that the proposed framework bridges the gap between data-driven accuracy and physics-based reliability. Its primary significance lies in providing a trustworthy and interpretable tool for CFRC mix design. By embedding physical constraints directly into the learning architecture, the framework ensures that predictions respect fundamental laws of cement hydration and composite mechanics. This "design monotonicity" is essential for safety-critical applications, preventing optimization algorithms from converging on physically impossible solutions (e.g., high-strength mixes with excessive water). The study concludes that while the PINN does not necessarily surpass the raw statistical accuracy of the best black-box models, it offers a critical advantage in reliable extrapolation and scientific validity, making it a viable tool for accelerating the adoption of sustainable coconut fiber reinforced concrete in engineering practice.

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