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physics.comp-ph2024★ 9 cited
Multi-soliton solutions and data-driven discovery of higher-order Burgers' hierarchy equations with physics informed neural networks
D. A. Kaltsas, L. Magafas, P. Papadopoulou +1
The Burgers hierarchy consists of nonlinear evolutionary partial differential equations (PDEs) with progressively higher-order dispersive and nonlinear terms. Notable members of th…
physics.comp-ph2024★ 17 cited
Constrained Hamiltonian Systems and Physics-Informed Neural Networks: Hamilton-Dirac Neural Networks
Dimitrios A. Kaltsas
The effectiveness of the Physics Informed Neural Networks (PINNs) for learning the dynamics of constrained Hamiltonian systems is demonstrated using the Dirac theory of constraints…