THE SIGNIFICANCE OF ELLIPTIC DIFFERENTIAL OPERATORS IN ARTIFICIAL INTELLIGENCE SYSTEMS.

Authors

  • Jurayev Shaxzod Shuxratjonvich Asia International University

Keywords:

Elliptic Differential Operators; Artificial Intelligence; Partial Differential Equations; Laplace Operator; Poisson Equation; Machine Learning; Regularization; Image Processing; Physics-Informed Neural Networks (PINNs); Fourier Neural Operator (FNO); DeepONet; Explainable AI.

Abstract

Elliptic differential operators play a crucial role in modeling complex physical and mathematical processes within artificial intelligence systems. They are employed in image processing, data smoothing, regularization, and the construction of physics-informed neural networks (PINNs). This article analyzes the theoretical foundations of elliptic operators, their role in artificial intelligence architectures, and their practical domains of application.

Downloads

Download data is not yet available.

References

Evans, L. C. Partial Differential Equations. American Mathematical Society, 2010.

Tikhonov, A. N., & Samarskii, A. A. Equations of Mathematical Physics. Dover Publications, 1990.

Hornik, K., Stinchcombe, M., & White, H. “Multilayer Feedforward Networks are Universal Approximators.” Neural Networks, 1989.

LeCun, Y., Bengio, Y., & Hinton, G. “Deep Learning.” Nature, 2015.

Chen, R. T. Q. et al. “Neural Ordinary Differential Equations.” NeurIPS, 2018.

Bertalmio, M. Image Processing and PDEs. SIAM, 2001.

Downloads

Published

2025-10-14

How to Cite

Jurayev Shaxzod Shuxratjonvich. (2025). THE SIGNIFICANCE OF ELLIPTIC DIFFERENTIAL OPERATORS IN ARTIFICIAL INTELLIGENCE SYSTEMS. Journal of Applied Science and Social Science, 15(10), 650–654. Retrieved from https://www.internationaljournal.co.in/index.php/jasass/article/view/2090

Issue

Vol. 15 No. 10 (2025): Volume 15 Issue 10

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

All content published in the Journal of Applied Science and Social Science (JASSS) is protected by copyright. Authors retain the copyright to their work, and grant JASSS the right to publish the work under a Creative Commons Attribution License (CC BY). This license allows others to distribute, remix, adapt, and build upon the work, even commercially, as long as they credit the author(s) for the original creation.