https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Wassing_et_al_2022a Wassing et al 2022a - Revision history 2026-04-10T09:53:36Z Revision history for this page on the wiki MediaWiki 1.27.0-wmf.10 https://www.scipedia.com/wd/index.php?title=Wassing_et_al_2022a&diff=259841&oldid=prev JSanchez: JSanchez moved page Draft Sanchez Pinedo 560492550 to Wassing et al 2022a 2022-11-22T12:49:34Z <p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_560492550" class="mw-redirect" title="Draft Sanchez Pinedo 560492550">Draft Sanchez Pinedo 560492550</a> to <a href="/public/Wassing_et_al_2022a" title="Wassing et al 2022a">Wassing et al 2022a</a></p> <table class="diff diff-contentalign-left" data-mw="interface"> <tr style='vertical-align: top;' lang='en'> <td colspan='1' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='1' style="background-color: white; color:black; text-align: center;">Revision as of 12:49, 22 November 2022</td> </tr><tr><td colspan='2' style='text-align: center;' lang='en'><div class="mw-diff-empty">(No difference)</div> </td></tr></table> JSanchez https://www.scipedia.com/wd/index.php?title=Wassing_et_al_2022a&diff=259809&oldid=prev JSanchez at 12:26, 22 November 2022 2022-11-22T12:26:28Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 12:26, 22 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6" >Line 6:</td> <td colspan="2" class="diff-lineno">Line 6:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Abstract ==</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Abstract ==</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;pdf&gt;Media:Draft_Sanchez Pinedo_560492550384_abstract.pdf&lt;/pdf&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>&lt;pdf&gt;Media:Draft_Sanchez Pinedo_560492550384_abstract.pdf&lt;/pdf&gt;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Full Paper ==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;pdf&gt;Media:Draft_Sanchez Pinedo_560492550384_paper.pdf&lt;/pdf&gt;</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:259807:newid:259809 --> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Wassing_et_al_2022a&diff=259807&oldid=prev JSanchez at 12:26, 22 November 2022 2022-11-22T12:26:25Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 12:26, 22 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The numerical approximation of solutions to the compressible Euler and Navierstokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been successfully employed for solving partial differential equations by incorporating the equations into a loss function that is minimized during the training of a neural network. This approach yields a so-called physics-informed neural network which does not rely on a classical discretization and can address parametric problems in a straightforward manner. Therefore, it avoids characteristic difficulties of traditional approaches, such as finite volume methods. This has raised the question, whether physics-informed neural networks may be a viable alternative to conventional methods for computational fluid dynamics. Here, we show a new physics-informed neural network training procedure to approximately solve the two-dimensional compressible Euler equations, which makes use of artificial dissipation during the training process. We demonstrate how additional dissipative terms help to avoid unphysical results and how the additional numerical viscosity can be reduced during training while iterating towards a solution. Furthermore, we showcase how this approach can be combined with parametric boundary conditions. Our results highlight the appearance of unphysical results when solving compressible flows with physics-informed neural networks and offer a new approach to overcome this problem. We therefore expect that the presented methods enable the application of physics-informed neural networks for previously difficult to solve problems.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The numerical approximation of solutions to the compressible Euler and Navierstokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been successfully employed for solving partial differential equations by incorporating the equations into a loss function that is minimized during the training of a neural network. This approach yields a so-called physics-informed neural network which does not rely on a classical discretization and can address parametric problems in a straightforward manner. Therefore, it avoids characteristic difficulties of traditional approaches, such as finite volume methods. This has raised the question, whether physics-informed neural networks may be a viable alternative to conventional methods for computational fluid dynamics. Here, we show a new physics-informed neural network training procedure to approximately solve the two-dimensional compressible Euler equations, which makes use of artificial dissipation during the training process. We demonstrate how additional dissipative terms help to avoid unphysical results and how the additional numerical viscosity can be reduced during training while iterating towards a solution. Furthermore, we showcase how this approach can be combined with parametric boundary conditions. Our results highlight the appearance of unphysical results when solving compressible flows with physics-informed neural networks and offer a new approach to overcome this problem. We therefore expect that the presented methods enable the application of physics-informed neural networks for previously difficult to solve problems.</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Abstract ==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;pdf&gt;Media:Draft_Sanchez Pinedo_560492550384_abstract.pdf&lt;/pdf&gt;</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:259805:newid:259807 --> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Wassing_et_al_2022a&diff=259805&oldid=prev JSanchez at 12:26, 22 November 2022 2022-11-22T12:26:23Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 12:26, 22 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Summary==</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The numerical approximation of solutions to the compressible Euler and Navierstokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been successfully employed for solving partial differential equations by incorporating the equations into a loss function that is minimized during the training of a neural network. This approach yields a so-called physics-informed neural network which does not rely on a classical discretization and can address parametric problems in a straightforward manner. Therefore, it avoids characteristic difficulties of traditional approaches, such as finite volume methods. This has raised the question, whether physics-informed neural networks may be a viable alternative to conventional methods for computational fluid dynamics. Here, we show a new physics-informed neural network training procedure to approximately solve the two-dimensional compressible Euler equations, which makes use of artificial dissipation during the training process. We demonstrate how additional dissipative terms help to avoid unphysical results and how the additional numerical viscosity can be reduced during training while iterating towards a solution. Furthermore, we showcase how this approach can be combined with parametric boundary conditions. Our results highlight the appearance of unphysical results when solving compressible flows with physics-informed neural networks and offer a new approach to overcome this problem. We therefore expect that the presented methods enable the application of physics-informed neural networks for previously difficult to solve problems.</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:259804:newid:259805 --> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Wassing_et_al_2022a&diff=259804&oldid=prev JSanchez: Created blank page 2022-11-22T12:26:21Z <p>Created blank page</p> <p><b>New page</b></p><div></div> JSanchez