<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
h1
{mso-style-priority:9;
mso-style-link:"Heading 1 Char";
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
font-size:24.0pt;
font-family:"Calibri",sans-serif;
font-weight:bold;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:#0563C1;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri",sans-serif;
color:windowtext;}
span.Heading1Char
{mso-style-name:"Heading 1 Char";
mso-style-priority:9;
mso-style-link:"Heading 1";
font-family:"Calibri",sans-serif;
font-weight:bold;}
span.odd
{mso-style-name:odd;}
span.date-display-single
{mso-style-name:date-display-single;}
span.date-display-range
{mso-style-name:date-display-range;}
span.date-display-start
{mso-style-name:date-display-start;}
span.date-display-end
{mso-style-name:date-display-end;}
span.fn
{mso-style-name:fn;}
span.map-icon
{mso-style-name:map-icon;}
span.locality
{mso-style-name:locality;}
span.region
{mso-style-name:region;}
span.postal-code
{mso-style-name:postal-code;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri",sans-serif;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1027" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal style='background:white'><span style='color:black'><a href="https://statistics.yale.edu/" title="Department of Statistics and Data Science
"><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0;text-decoration:none'><img border=0 width=150 height=49 style='width:1.5625in;height:.5069in' id=logo src="cid:image001.jpg@01D94823.1A1B6B00" alt="Department of Statistics and Data Science
"></span></a></span><span style='font-family:"Arial",sans-serif;color:black'> <a href="https://statistics.yale.edu/" title=Home><b><span style='font-size:22.0pt;color:#286DC0'>Department of Statistics and Data Science </span></b></a></span><b><i><u><span style='font-size:22.0pt;font-family:"Arial",sans-serif;color:#286DC0'> <o:p></o:p></span></u></i></b></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif'>In-Person seminars will be held at Mason Lab 211, 9 Hillhouse Avenue with the option of virtual participation (<a href="https://yale.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=f8b73c34-a27b-42a7-a073-af2d00f90ffa"><span style='color:windowtext;text-decoration:none'>https://yale.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=f8b73c34-a27b-42a7-a073-af2d00f90ffa</span></a>)<o:p></o:p></span></p><p class=MsoNormal><b><span style='font-family:"Arial",sans-serif'><a href="https://0.0.0.10/"><span style='color:windowtext;text-decoration:none'>3:30pm</span></a> - Pre-talk meet and greet teatime - Dana House, 24 Hillhouse Avenue </span></b><b><o:p></o:p></b></p><h1 style='mso-margin-top-alt:.1in;margin-right:0in;margin-bottom:0in;margin-left:0in;background:white'><span style='font-size:14.0pt;font-family:"Arial",sans-serif;color:black'>Lu Lu, </span><span class=odd><span style='font-size:14.0pt;font-family:"Arial",sans-serif;color:black'>University of Pennsylvania</span></span><span style='font-size:14.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></h1><p class=MsoNormal style='background:white'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter" />
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0" />
<v:f eqn="sum @0 1 0" />
<v:f eqn="sum 0 0 @1" />
<v:f eqn="prod @2 1 2" />
<v:f eqn="prod @3 21600 pixelWidth" />
<v:f eqn="prod @3 21600 pixelHeight" />
<v:f eqn="sum @0 0 1" />
<v:f eqn="prod @6 1 2" />
<v:f eqn="prod @7 21600 pixelWidth" />
<v:f eqn="sum @8 21600 0" />
<v:f eqn="prod @7 21600 pixelHeight" />
<v:f eqn="sum @10 21600 0" />
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect" />
<o:lock v:ext="edit" aspectratio="t" />
</v:shapetype><v:shape id="Picture_x0020_2" o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;margin-left:0;margin-top:.15pt;width:103.35pt;height:124pt;z-index:251658240;visibility:visible;mso-wrap-style:square;mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;mso-wrap-distance-bottom:0;mso-position-horizontal:absolute;mso-position-horizontal-relative:text;mso-position-vertical:absolute;mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'>
<v:imagedata src="cid:image002.jpg@01D94823.1A1B6B00" o:title="" />
<w:wrap type="square"/>
</v:shape><![endif]--><![if !vml]><img width=138 height=165 style='width:1.4375in;height:1.7222in' src="cid:image004.jpg@01D94823.36CEFB90" align=left hspace=12 v:shapes="Picture_x0020_2"><![endif]><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Date: Monday, February 27, 2023</span></span><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></span></p><p class=MsoNormal style='background:white'><span class=date-display-single><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Time: </span></span><span class=date-display-start><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>4:00PM</span></span><span class=date-display-range><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> to </span></span><span class=date-display-end><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>5:00PM</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=fn><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>Mason Lab 211</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'> </span><span class=map-icon><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222;letter-spacing:.6pt'><a href="http://maps.google.com/?q=9+Hillhouse+Ave%2C+New+Haven%2C+CT%2C+06511%2C+us"><span style='color:#286DC0'>see map</span></a> </span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>9 Hillhouse Ave<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span class=locality><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>New Haven</span></span><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>, <span class=region>CT</span> <span class=postal-code>06511</span><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><a href="https://directory.seas.upenn.edu/lu-lu/"><span style='color:#003C76'>Website</span></a><o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>Title: Physics-informed deep learning: Blending data and physics for learning functions and operators<o:p></o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'><o:p> </o:p></span></b></p><p class=MsoNormal style='background:white'><b><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>Information and Abstract: <o:p></o:p></span></b></p><p style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:0in;background:white;box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:#222222'>Deep learning has achieved remarkable success in diverse applications; however, its use in scientific applications has emerged only recently. In this talk, I will first review physics-informed neural networks (PINNs) and available extensions for solving forward and inverse problems of partial differential equations (PDEs). I will then introduce a less known but powerful result that a NN can accurately approximate any nonlinear operator. This universal approximation theorem of operators is suggestive of the potential of NNs in learning operators of complex systems. I will present the deep operator network (DeepONet) to learn various operators that represent deterministic and stochastic differential equations. I will demonstrate the effectiveness of DeepONet and its extensions to diverse multiphysics and multiscale problems, such as nanoscale heat transport, bubble growth dynamics, high-speed boundary layers, electroconvection, hypersonics, and geological carbon sequestration. Deep learning models are usually limited to interpolation scenarios, and I will quantify the extrapolation complexity and develop a complete workflow to address the challenge of extrapolation for deep neural operators.<o:p></o:p></span></p><p class=MsoNormal style='box-sizing: inherit'><span style='font-size:12.0pt;font-family:"Arial",sans-serif;color:black'>For more details and upcoming events visit our website at <a href="http://statistics.yale.edu/"><span style='color:black'>http://statistics.yale.edu/</span></a></span><o:p></o:p></p><p class=MsoNormal><span style='font-family:"Arial",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:18.0pt;font-family:"Arial",sans-serif'>Department of Statistics and Data Science<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'>Yale University<br>24 Hillhouse Avenue<br>New Haven, CT 06511<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Arial",sans-serif;color:black'>t 203.432.0666<br>f 203.432.0633<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>