“…We use the same set of mixed boundary conditions on both equations u(0, y) = 0 (32) u(1, y) = 0 (33) u(x, 0) = 0 (34) ∂ ∂y u(x, 1) = 2 sin(πx) (35) and both PDEs have the same analytic solution u(x, y) = y 2 sin(πx). ( 36)…”
Section: Pde 521 2d Linear and Non-linear Pdementioning
confidence: 99%
“…The Kovasznay flow solution shown in Fig. 17 is often used to benchmark traditional [35,36] as well as neural network-based [37,38] numerical solvers. Compared to these methods, in this subsection we show that using L-BFGS + GNE we are able to achieve orders of magnitude more accurate numerical solutions in a fraction of the time.…”
“…We use the same set of mixed boundary conditions on both equations u(0, y) = 0 (32) u(1, y) = 0 (33) u(x, 0) = 0 (34) ∂ ∂y u(x, 1) = 2 sin(πx) (35) and both PDEs have the same analytic solution u(x, y) = y 2 sin(πx). ( 36)…”
Section: Pde 521 2d Linear and Non-linear Pdementioning
confidence: 99%
“…The Kovasznay flow solution shown in Fig. 17 is often used to benchmark traditional [35,36] as well as neural network-based [37,38] numerical solvers. Compared to these methods, in this subsection we show that using L-BFGS + GNE we are able to achieve orders of magnitude more accurate numerical solutions in a fraction of the time.…”
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