Towards discovery of the differential equations
DOI10.1134/s1064562423701156arXiv2308.04901OpenAlexW4392646820MaRDI QIDQ6204271
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
multiobjective optimizationevolutionary optimizationphysics-informed neural networkdifferential equation discovery
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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