AI-SOLVE: Accelerating Computational Science with a Machine Learning-Enhanced Linear Algebra Library
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In this work, we present AI-Solve, an innovative software library that combines advanced linear algebra solvers with machine learning algorithms to expedite solutions for large-scale, parametrized problems in engineering and computational sciences. AI-Solve introduces two key methodologies aimed at different classes of computational challenges. The first, POD-2G, integrates reduced-order modeling with neural networks to accelerate the solution of parametrized linear systems, significantly reducing computational time for high-dimensional, linear systems [1]. This approach leverages Proper Orthogonal Decomposition (POD) for dimensionality reduction, coupled with neural network-based surrogates, achieving remarkable speed-ups without compromising solution accuracy. The second methodology employs the transformer neural network architecture to address transient, nonlinear problems characterized by complex parameter dependencies [2]. By incorporating transformers' efficient sequence modeling capabilities, this approach enhances the performance and scalability of solving nonlinear transient equations. Together, these methodologies provide a robust framework for tackling a wide range of parametrized, large-scale problems with improved computational efficiency, potentially transforming applications in fields from structural análisis to real-time simulation and control.
