<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
</head>
<body>
<div style="font-family: Tahoma, Geneva, sans-serif; font-size: 14pt; color: rgb(0, 0, 0);">
<b><i>"Conservative cell-average-based neural network method for nonlinear conservation laws"</i></b></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; color: rgb(0, 0, 0);">
<span style="font-size: 12pt;"><br>
</span><span style="font-size: 14pt;"><b>Jue Yan</b></span></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Department of Mathematics</div>
<div style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Iowa State University </div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Please feel free to forward/share this invitation with other groups/disciplines that might be interested in this talk/topic. All are welcome to attend. </div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
NOTE: In-person attendance is requested in our 499 Dirac Science Library (DSL) Seminar Room. Zoom access is intended for external (non-departmental) participants only. </div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<b>https://fsu.zoom.us/j/94273595552 </b></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Meeting # <b>942 7359 5552 </b></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
🎦 Colloquium recordings will be made available here, <a href="https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.sc.fsu.edu%2Fcolloquium&data=05%7C02%7Csc-seminar-announce%40lists.fsu.edu%7C0c3f58b9813b41e3654208de8db71c26%7Ca36450ebdb0642a78d1b026719f701e3%7C0%7C0%7C639104014737449293%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=oYM6oMy4brNJogzu2jINB6UNBsfIscb0uoOl4%2FkehG4%3D&reserved=0" originalsrc="https://www.sc.fsu.edu/colloquium">
https://www.sc.fsu.edu/colloquium</a> </div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<b>Wednesday, Apr 1, 2026, Schedule: </b></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
* 3:00 to 3:30 PM Eastern Time (US and Canada) </div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
☕ Nespresso & Teatime - 417 DSL Commons </div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<b>* 3:30 to 4:30 PM Eastern Time (US and Canada) </b></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<b>🕟 Colloquium - 499 DSL Seminar Room </b></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<b><br>
</b></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<b>Abstract: </b></div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
In this talk, we present the recently developed Cell-Average-Based Neural Network (CANN) for time-dependent PDEs. Spatial and temporal discretization in conventional methods is replaced by training a simple feedforward network to obtain an explicit one-step
finite volume method. The well-trained network parameters function as the scheme coefficients. The network method has a minimum number of unknowns, which can be quickly trained on a small training dataset. Unlike conventional numerical methods, the CANN approach
is not limited by the CFL conditions, enabling the use of significantly larger time steps. This leads to a highly efficient computational method for solving PDEs. The conservative version of the CANN method for nonlinear conservation laws will be discussed.
The method, trained on the smooth-solution data from ONE initial-value problem, is verified to solve any initial-value problem involving shocks and rarefaction waves. The network can accurately learn a numerical flux, such as the Lax-Friedrichs flux, thereby
guaranteeing convergence to the physically relevant entropy solutions. The extension of the method to non-uniform meshes will be considered. A bound-preserving version of the network method is presented for linear Advection equations.</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
<br>
</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Additional colloquium details can be found here.</div>
<div class="elementToProof" style="font-family: Tahoma, Geneva, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<a href="https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.sc.fsu.edu%2Fnews-and-events%2Fcolloquium%2F1915-colloquium-with-jue-yan-2026-04-01&data=05%7C02%7Csc-seminar-announce%40lists.fsu.edu%7C0c3f58b9813b41e3654208de8db71c26%7Ca36450ebdb0642a78d1b026719f701e3%7C0%7C0%7C639104014737469887%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=NZu29stigp0Dnb37m2%2BCcFCesj%2BrrHVFt2FKKnj2AjE%3D&reserved=0" originalsrc="https://www.sc.fsu.edu/news-and-events/colloquium/1915-colloquium-with-jue-yan-2026-04-01">https://www.sc.fsu.edu/news-and-events/colloquium/1915-colloquium-with-jue-yan-2026-04-01</a></div>
</body>
</html>