Physics-Informed Artificial Intelligence for Autonomous Scientific Discovery an Adaptive Framework for Data-Efficient Physical System Modeling

Abstract

The integration of artificial intelligence with physical knowledge has become an important area of scientific machine learning, particularly for modeling physical systems with limited or noisy data. Physics-informed neural networks (PINNs) incorporate governing physical laws into neural-network training. However, conventional PINNs often face challenges such as optimization difficulties, high computational costs, sensitivity to sampling strategies, and limited generalization. This study proposes an adaptive physics-informed artificial intelligence framework that combines deep neural prediction, governing physical equations, residual-based adaptive sampling, automated error assessment, and iterative model refinement. The framework is evaluated using the one-dimensional transient heat equation under different data availability and noise levels. Three models are compared: a conventional data-driven neural network, a standard PINN, and the proposed adaptive PINN. The results show that the proposed model performs significantly better in sparse-data conditions. With only 1% of the available data, it achieves a relative prediction error of 0.00142 compared with 0.185 for the conventional neural network, representing an improvement of more than two orders of magnitude. It also reduces computational collocation overhead by approximately 4.2 times compared with uniform dense sampling. These findings demonstrate the potential of adaptive physics-informed AI for accurate, data-efficient, and computationally efficient modeling of physical systems.