Partial Inverse Design of High-Performance Concrete Using Cooperative Neural Networks for Constraint-Aware Mix Generation

TL;DR

The paper tackles partial inverse design for high-performance concrete under fixed constraints by proposing a Cooperative Neural Network (CoNN) that couples an imputation autoencoder with a surrogate strength predictor. Through cooperative training, CoNN reconstructs missing mix components while ensuring generated designs align with target compressive strength, enabling single-pass inference without retraining for different constraint scenarios. Empirical results show CoNN outperforms standalone autoencoders and Bayesian GP baselines in accuracy and computational efficiency, achieving R^2 around 0.87–0.92 and substantial MSE/MAE reductions. This approach offers a practical, constraint-aware tool for rapid HPC mix proportioning with potential environmental and economic benefits by enabling flexible design under real-world constraints.

Abstract

High-performance concrete requires complex mix design decisions involving interdependent variables and practical constraints. While data-driven methods have improved predictive modeling for forward design in concrete engineering, inverse design remains limited, especially when some variables are fixed and only the remaining ones must be inferred. This study proposes a cooperative neural network framework for the partial inverse design of high-performance concrete. The framework integrates an imputation model with a surrogate strength predictor and learns through cooperative training. Once trained, it generates valid and performance-consistent mix designs in a single forward pass without retraining for different constraint scenarios. Compared with baseline models, including autoencoder models and Bayesian inference with Gaussian process surrogates, the proposed method achieves R-squared values of 0.87 to 0.92 and substantially reduces mean squared error by approximately 50% and 70%, respectively. The results show that the framework provides an accurate and computationally efficient foundation for constraint-aware, data-driven mix proportioning.

Figures (12)

• Figure 1: The DDD paradigm of forward design, inverse design and partial inverse design.
• Figure 2: Cooperative Neural Network (CoNN) (adopted from nugraha_cooperative_2025). Schematic illustration of the CoNN framework for partial inverse design of HPC. The upper (green) region shows the surrogate model predicting compressive strength from complete mix designs, while the lower (purple) region shows the autoencoder-based imputation model reconstructing masked variables. CoNN is optimized cooperatively through reconstruction ($\mathcal{L}_{1}$) and performance ($\mathcal{L}_{2}$) objectives, combined into a unified loss ($\mathcal{L}_{\mathrm{AE}}$). Red arrows indicate the backpropagation flow connecting both models, forming a feedback loop that aligns reconstructed compositions with desired performance targets.
• Figure 3: Data distribution of the five-split experiment setup (original scale).
• Figure 4: Inference process of Cooperative Neural Network (CoNN) (adopted from nugraha_cooperative_2025).
• Figure 5: Performance comparison of standalone DAE and CoNN-DAE for (a) MAE, (b) MSE, and (c) $R^2$ across varying proportions of undetermined variables. Average results over five runs ($n = 5$) are shown with $\pm 1$ standard deviation.