A Mesh-Free Algorithm to Solve an Inverse Source Problem for Degenerate Two-Dimensional Parabolic Equation from Final Observations

DOI10.52737/18291163-2023.15.8-1-11MaRDI QIDQ6159341

Khalid Atifi

Publication date: 1 June 2023

Published in: Armenian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

optimizationheat equationinverse problemdeep learningdegenerate two-dimensional equation

Mathematics Subject Classification ID

Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Sampling theory, sample surveys (62D05) Heat equation (35K05) Degenerate parabolic equations (35K65) Optimization of shapes other than minimal surfaces (49Q10) PDEs with randomness, stochastic partial differential equations (35R60) Weak solutions to PDEs (35D30) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Cites Work

• DGM: a deep learning algorithm for solving partial differential equations
• Solving inverse problems in stochastic models using deep neural networks and adversarial training
• An inverse backward problem for degenerate two-dimensional parabolic equation
• La différentiation automatique et son utilisation en optimisation

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