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<font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Dear Colleagues</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">,</span></font><font face="wf_segoe-ui_normal,Segoe UI,Segoe WP,Tahoma,Arial,sans-serif,serif,EmojiFont" size="3" color="#212121"><br>
</font><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="3" color="#BF5AF2"><br>
</font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">This is a kind reminder that the </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">last</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"> </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">International </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Bayes </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Club </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">(</span></font><a href="https://www.math.vu.nl/thebayesclub/" target="_blank" rel="noopener noreferrer" id="LPlnk987560" previewremoved="true"><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span id="LPlnk987560" style="font-size: 16px;"><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span id="LPlnk987560" style="font-size: 16px;"><font face="wf_segoe-ui_normal,Segoe UI,Segoe WP,Tahoma,Arial,sans-serif,serif,EmojiFont" size="2"><span id="LPlnk987560" style="font-size: 15px;"><font face="Arial,Helvetica,sans-serif,serif,EmojiFont" size="3"><span id="LPlnk987560"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">https://www.math.vu.nl/thebayesclub/</span></font></span></font></span></font></span></font></span></font></a><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">) </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">meeting of this academic year </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">will take place tomorrow, on the </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><b>11th</b></span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><b> of </b></span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><b>June</b></span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><b> </b></span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><b>(</b></span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><b>Friday</b></span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><b>)</b></span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"> from </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">4</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"> pm
(CEST)</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">. This time we have only one speaker: Andrew Stuart (Caltech</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">)</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">. </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">P</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">lease
find below the title and abstract of his talk</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">. </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">After </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">the
talks we will open up our </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"> virtual </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">meeting
place at gather.town so if you want to hang out and perhaps have a beer virtually with your colleagues then </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">you </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">are
invited to join. Since this is the last seminar of the semester it would be great if many of you could join even just for a short while. </span></font></span></font></div>
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<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2" color="#212121"><span style="font-size: 16px;"><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">T</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">he
seminar will be on zoom:</span></font></span></font></div>
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<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"> </span></font></div>
<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Topic: International Bayes club</span></font></span></font></div>
<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Time: Jun 11, 2021 04:00 PM Amsterdam, Berlin,
Rome, Stockholm, Vienna</span></font></span></font></div>
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<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Join Zoom Meeting</span></font></span></font></div>
<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">https://vu-live.zoom.us/j/96986415015?pwd=bnpjZDJhRkl2VkloYkN6TlVjd3VyUT09</span></font></span></font></div>
<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><br>
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<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Meeting ID: 969 8641 5015</span></font></span></font></div>
<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Passcode: 982915</span></font></span></font></div>
<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"> </span></font></div>
<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"> </span></font></span></font></div>
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<font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Link to the meeting place at gather
town:</span></font></span></font></div>
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<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><a href="https://gather.town/app/4lK8Zj28Ys0WtutP/IBC" target="_blank" rel="noopener noreferrer" id="LPlnk32836" previewremoved="true"><span id="LPlnk32836"><font face="Helvetica,serif,EmojiFont" size="3"><span id="LPlnk32836" style="font-size: 20px;"><font color="#1155CC"><span id="LPlnk32836"><font size="2" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">https://gather.town/app/4lK8Zj28Ys0WtutP/IBC</span></font></span></font></span></font></span></a></span></font></div>
<div><font face="Calibri,Helvetica,sans-serif,serif,EmojiFont" size="2"><span style="font-size: 16px;"><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Password: bayesbayesbayes</span></font></span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Speaker: </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Andrew
Stuart (</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Computing and Mathematical Sciences</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">, </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Caltech</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">)</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Title: </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Solving
PDEs With Gaussian Processes</span></font><br>
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<div style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">
<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Coauthors: </span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Yifan
Chen, Bamdad Hosseini and Houman Owhadi</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Abstract:</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><br>
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<div style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">
<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">We describe an approach to solving PDEs in which the solution</span></font></div>
<div style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">
<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">is found by minimizing a squared RKHS norm subject to a penalty,</span></font></div>
<div style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">
<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">or constraint, defined via the PDE. This links to the subject of</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Gaussian processes subject to pointwise nonlinear constraints.</span></font></div>
<div style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">
<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">We introduce a framework for the methodology, establish convergence</span></font></div>
<div style="font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">
<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">of the resulting numerical method, and describe numerical results.</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Forward problems for a nonlinear elliptic PDE, Burgers' equation</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">and a regularized Eikonal equation are presented; and the method</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">is extended to inverse problems and applied to the problem of</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">permeability identification in the Darcy model of flow in a porous medium.</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Best wishes,</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">Botond</span></font></div>
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<font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;">(on behalf of the organisers)</span></font><font size="2" color="#212121" style="font-family: Tahoma, Geneva, sans-serif, serif, EmojiFont;"><span style="font-size: 11pt;"><br>
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