Towards discovery of the differential equations

DOI10.1134/s1064562423701156arXiv2308.04901OpenAlexW4392646820MaRDI QIDQ6204271

R. V. Titov, A. A. Hvatov

Publication date: 27 March 2024

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2308.04901

zbMATH Keywords

multiobjective optimizationevolutionary optimizationphysics-informed neural networkdifferential equation discovery

Mathematics Subject Classification ID

Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Bayesian inference (62F15) Symbolic computation and algebraic computation (68W30) Bayesian problems; characterization of Bayes procedures (62C10) Multi-objective and goal programming (90C29) Smoothness and regularity of solutions to PDEs (35B65) Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) (68N19) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Cites Work

• Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• DLGA-PDE: discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm
• Weak SINDy for partial differential equations
• PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
• DeepXDE: A Deep Learning Library for Solving Differential Equations

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