https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Carniello_et_al_2022a Carniello et al 2022a - Revision history 2026-04-25T13:56:37Z Revision history for this page on the wiki MediaWiki 1.27.0-wmf.10 https://www.scipedia.com/wd/index.php?title=Carniello_et_al_2022a&diff=259832&oldid=prev JSanchez: JSanchez moved page Draft Sanchez Pinedo 885075734 to Carniello et al 2022a 2022-11-22T12:44:32Z <p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_885075734" class="mw-redirect" title="Draft Sanchez Pinedo 885075734">Draft Sanchez Pinedo 885075734</a> to <a href="/public/Carniello_et_al_2022a" title="Carniello et al 2022a">Carniello 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 12:44, 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=Carniello_et_al_2022a&diff=259821&oldid=prev JSanchez at 12:27, 22 November 2022 2022-11-22T12:27:08Z <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 12:27, 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_8850757341364_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_8850757341364_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_8850757341364_paper.pdf&lt;/pdf&gt;</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:259819:newid:259821 --> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Carniello_et_al_2022a&diff=259819&oldid=prev JSanchez at 12:27, 22 November 2022 2022-11-22T12:27:06Z <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 12:27, 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>In this work, we present an application of modern deep learning methodologies to the numerical solution of two dimensional hyperbolic partial differential equations in transport models. More specifically, we employ a supervised deep neural network that takes into account of initial-boundary value problems for a scalar, 2D inviscid Burgers model including the case with Riemann data, whose solutions develop discontinuity, containing both shock wave and rarefaction wave. We also apply the proposed PINN approach to the linear advection equation with periodic sinusoidal initial condition. Our results suggest that a relatively simple deep learning model was capable of achieving promising results in the linear advection and inviscid Burgers equation with rarefaction, providing numerical evidence of good approximation of weakentropy solutions to the case of nonlinear 2D inviscid Burgers model. For the Riemann problems, the neural network performed better when rarefaction wave is predominant. The premises underlying these preliminary results as an integrated physics-informed deep learning approach are promising. However, there are hints of evidence suggesting specific fine tuning on the PINN methodology for solving hyperbolic-transport problems in the presence of shock formation in the solutions.</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>In this work, we present an application of modern deep learning methodologies to the numerical solution of two dimensional hyperbolic partial differential equations in transport models. More specifically, we employ a supervised deep neural network that takes into account of initial-boundary value problems for a scalar, 2D inviscid Burgers model including the case with Riemann data, whose solutions develop discontinuity, containing both shock wave and rarefaction wave. We also apply the proposed PINN approach to the linear advection equation with periodic sinusoidal initial condition. Our results suggest that a relatively simple deep learning model was capable of achieving promising results in the linear advection and inviscid Burgers equation with rarefaction, providing numerical evidence of good approximation of weakentropy solutions to the case of nonlinear 2D inviscid Burgers model. For the Riemann problems, the neural network performed better when rarefaction wave is predominant. The premises underlying these preliminary results as an integrated physics-informed deep learning approach are promising. However, there are hints of evidence suggesting specific fine tuning on the PINN methodology for solving hyperbolic-transport problems in the presence of shock formation in the solutions.</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_8850757341364_abstract.pdf&lt;/pdf&gt;</ins></div></td></tr> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Carniello_et_al_2022a&diff=259817&oldid=prev JSanchez at 12:27, 22 November 2022 2022-11-22T12:27:05Z <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 12:27, 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;">In this work, we present an application of modern deep learning methodologies to the numerical solution of two dimensional hyperbolic partial differential equations in transport models. More specifically, we employ a supervised deep neural network that takes into account of initial-boundary value problems for a scalar, 2D inviscid Burgers model including the case with Riemann data, whose solutions develop discontinuity, containing both shock wave and rarefaction wave. We also apply the proposed PINN approach to the linear advection equation with periodic sinusoidal initial condition. Our results suggest that a relatively simple deep learning model was capable of achieving promising results in the linear advection and inviscid Burgers equation with rarefaction, providing numerical evidence of good approximation of weakentropy solutions to the case of nonlinear 2D inviscid Burgers model. For the Riemann problems, the neural network performed better when rarefaction wave is predominant. The premises underlying these preliminary results as an integrated physics-informed deep learning approach are promising. However, there are hints of evidence suggesting specific fine tuning on the PINN methodology for solving hyperbolic-transport problems in the presence of shock formation in the solutions.</ins></div></td></tr> </table> JSanchez https://www.scipedia.com/wd/index.php?title=Carniello_et_al_2022a&diff=259816&oldid=prev JSanchez: Created blank page 2022-11-22T12:27:03Z <p>Created blank page</p> <p><b>New page</b></p><div></div> JSanchez