THE ROLE OF THE LAPLACE OPERATOR IN ARTIFICIAL INTELLIGENCE
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The Laplace operator, a second-order differential operator, plays a critical role in modern computational systems, especially within Artificial Intelligence (AI) and machine learning frameworks. Originally formulated in mathematical physics, it has become an essential analytical tool for processing multidimensional data, understanding spatial structures, and optimizing algorithms. This paper explores the theoretical foundations of the Laplace operator, its integration into AI models, and its practical applications in image processing, neural networks, and optimization. The study also discusses its physical interpretations and the future prospects of its use in AI-related fields
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1.Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017). Geometric deep learning: Going beyond Euclidean data. IEEE Signal Processing Magazine, 34(4), 18–42.
2.Chung, F. R. K. (1997). Spectral Graph Theory. American Mathematical Society.
3.Grigoryan, A. (2009). Heat Kernel and Analysis on Manifolds. American Mathematical Society.
4.Hammond, D. K., Vandergheynst, P., & Gribonval, R. (2011). Wavelets on graphs via spectral graph theory. Applied and Computational Harmonic Analysis, 30(2), 129–150.
5.Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707.
6.Belkin, M., & Niyogi, P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6), 1373–1396.