A HYBRID INTEGRATION MODEL BASED ON ARTIFICIAL INTELLIGENCE ELEMENTS FOR SOLVING BOUNDARY VALUE PROBLEMS
Keywords:
boundary value problems, artificial intelligence, hybrid integration, Physics-Informed Neural Network, differential equation, integration, neural network, optimization, computational complexity, convergence, nonlinear model, software, parallel computing, Python, TensorFlow.Abstract
This article presents a hybrid integration model based on artificial intelligence elements for solving boundary value problems. Traditional numerical methods (Finite Element, Finite Difference, Spectral Methods) require significant time and computational resources to solve complex nonlinear and high-dimensional boundary value problems. To address this, the article proposes a new hybrid model based on the concept of Physics-Informed Neural Networks (PINN). This model combines traditional mathematical algorithms with the self-learning capabilities of artificial intelligence to integrate boundary conditions of differential equations. The study analyzes metrics such as computational complexity, error rates, and convergence speed, demonstrating their applicability for automating scientific and technical computing software in the context of Uzbekistan. The results show that the hybrid AI-integration model is effective in solving differential equations quickly, accurately, and reliably. The model’s software implementation was tested using Python-based TensorFlow and NumPy libraries.
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