Variational principles for nonpotential operators

By V. Filippov, B. M. OHJIHnilOB, Baphaijhohhme IIPHHIJHn, Ben Silve. 1994

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Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data (2019, background): “For problems where such potentials cannot be found [46], one can consider V as the square of the residual norm of the PDE evaluated at different trial solutions, e.”
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks (2019, background): “Our goal is to expand on the work in [3] in which PDE solutions were represented as an optimization problem by either minimizing an energy functional or alternatively the square of the PDE residual [25].”
Some developments in general variational inequalities (2004, background): “It has been shown that this theory provides the most natural, direct, simple, unified and efficient framework for a general treatment of a wide class of unrelated linear and nonlinear problems, see, for example, [1–150] and the references therein.”