Horn et al 2022a - Revision history

https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Horn_et_al_2022a Horn et al 2022a - Revision history 2026-04-25T13:58:08Z Revision history for this page on the wiki MediaWiki 1.27.0-wmf.10 https://www.scipedia.com/wd/index.php?title=Horn_et_al_2022a&diff=259845&oldid=prev JSanchez: JSanchez moved page Draft Sanchez Pinedo 465137278 to Horn et al 2022a 2022-11-22T12:52:16Z

<p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_465137278" class="mw-redirect" title="Draft Sanchez Pinedo 465137278">Draft Sanchez Pinedo 465137278</a> to <a href="/public/Horn_et_al_2022a" title="Horn et al 2022a">Horn 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 12:52, 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=Horn_et_al_2022a&diff=259797&oldid=prev JSanchez at 12:25, 22 November 2022 2022-11-22T12:25:50Z

<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 12:25, 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'> </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'> </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'> </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><pdf>Media:Draft_Sanchez Pinedo_465137278902_abstract.pdf</pdf></div></td><td class='diff-marker'> </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><pdf>Media:Draft_Sanchez Pinedo_465137278902_abstract.pdf</pdf></div></td></tr> <tr><td colspan="2"> </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"> </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"> </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;"><pdf>Media:Draft_Sanchez Pinedo_465137278902_paper.pdf</pdf></ins></div></td></tr> </table>

JSanchez https://www.scipedia.com/wd/index.php?title=Horn_et_al_2022a&diff=259795&oldid=prev JSanchez at 12:25, 22 November 2022 2022-11-22T12:25:49Z

<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 12:25, 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'> </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'> </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'> </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 order to understand when it is useful to build physics constraints into neural networks, we investigate different neural network topologies to solve the N -body problem. Solving the chaotic N -body problem with high accuracy is a challenging task, requiring special numerical integrators that are able to approximate the trajectories with extreme precision. In [1] it is shown that a neural network can be a viable alternative, offering solutions many orders of magnitude faster. Specialized neural network topologies for applications in scientific computing are still rare compared to specialized neural networks for more classical machine learning applications. However, the number of specialized neural networks for Hamiltonian systems has been growing significantly during the last years [3, 5]. We analyze the performance of SympNets introduced in [5], preserving the symplectic structure of the phase space flow map, for the prediction of trajectories in N -body systems. In particular, we compare the accuracy of SympNets against standard multilayer perceptrons, both inside and outside the range of training data. We analyze our findings using a novel view on the topology of SympNets. Additionally, we also compare SympNets against classical symplectic numerical integrators. While the benefits of symplectic integrators for Hamiltonian systems are well understood, this is not the case for SympNets.</div></td><td class='diff-marker'> </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 order to understand when it is useful to build physics constraints into neural networks, we investigate different neural network topologies to solve the N -body problem. Solving the chaotic N -body problem with high accuracy is a challenging task, requiring special numerical integrators that are able to approximate the trajectories with extreme precision. In [1] it is shown that a neural network can be a viable alternative, offering solutions many orders of magnitude faster. Specialized neural network topologies for applications in scientific computing are still rare compared to specialized neural networks for more classical machine learning applications. However, the number of specialized neural networks for Hamiltonian systems has been growing significantly during the last years [3, 5]. We analyze the performance of SympNets introduced in [5], preserving the symplectic structure of the phase space flow map, for the prediction of trajectories in N -body systems. In particular, we compare the accuracy of SympNets against standard multilayer perceptrons, both inside and outside the range of training data. We analyze our findings using a novel view on the topology of SympNets. Additionally, we also compare SympNets against classical symplectic numerical integrators. While the benefits of symplectic integrators for Hamiltonian systems are well understood, this is not the case for SympNets.</div></td></tr> <tr><td colspan="2"> </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"> </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"> </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;"><pdf>Media:Draft_Sanchez Pinedo_465137278902_abstract.pdf</pdf></ins></div></td></tr> </table>

JSanchez https://www.scipedia.com/wd/index.php?title=Horn_et_al_2022a&diff=259793&oldid=prev JSanchez at 12:25, 22 November 2022 2022-11-22T12:25:47Z

<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 12:25, 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"> </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"> </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'> </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'> </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"> </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 order to understand when it is useful to build physics constraints into neural networks, we investigate different neural network topologies to solve the N -body problem. Solving the chaotic N -body problem with high accuracy is a challenging task, requiring special numerical integrators that are able to approximate the trajectories with extreme precision. In [1] it is shown that a neural network can be a viable alternative, offering solutions many orders of magnitude faster. Specialized neural network topologies for applications in scientific computing are still rare compared to specialized neural networks for more classical machine learning applications. However, the number of specialized neural networks for Hamiltonian systems has been growing significantly during the last years [3, 5]. We analyze the performance of SympNets introduced in [5], preserving the symplectic structure of the phase space flow map, for the prediction of trajectories in N -body systems. In particular, we compare the accuracy of SympNets against standard multilayer perceptrons, both inside and outside the range of training data. We analyze our findings using a novel view on the topology of SympNets. Additionally, we also compare SympNets against classical symplectic numerical integrators. While the benefits of symplectic integrators for Hamiltonian systems are well understood, this is not the case for SympNets.</ins></div></td></tr> </table>

JSanchez https://www.scipedia.com/wd/index.php?title=Horn_et_al_2022a&diff=259792&oldid=prev JSanchez: Created blank page 2022-11-22T12:25:45Z

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