Cea’s Lemma, pseudotime XNODE, Numerical optimization and variational techniques, Systems of nonlinear higher-order PDEs, Pseudo-time XNODE, Cea's lemma, Stability and convergence of numerical methods for boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, PDEs on manifolds, weak adversarial network, Numerical PDE, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Weak solutions to PDEs, Weak Adversarial Network, Artificial neural networks and deep learning