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	<title>Math Martin Hernandez</title>
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		<title>PINNs Introductory Code for the Heat Equation</title>
		<link>https://dcn.nat.fau.eu/pinns-introductory-code-for-the-heat-equation/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Fri, 01 Dec 2023 14:54:19 +0000</pubDate>
				<category><![CDATA[Hub]]></category>
		<category><![CDATA[Hub Martín Hernández]]></category>
		<category><![CDATA[Hub Ziqi Wang]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Martin Hernandez]]></category>
		<category><![CDATA[Math Ziqi Wang]]></category>
		<category><![CDATA[controlling physical systems]]></category>
		<category><![CDATA[Reinforcement learning]]></category>
		<category><![CDATA[RL]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=27768</guid>

					<description><![CDATA[PINNs Introductory Code for the Heat Equation This repository provides some basic insights on Physics Informed Neural Networks (PINNs) and their implementation. PINNs are numerical methods based on the universal approximation capacity of neural networks, aiming to approximate solutions of partial differential equations. Recently, extensive focus has been on approximating solutions of various equations, leading [&#8230;]]]></description>
		
		
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		<title>Lloyd&#8217;s Algorithm</title>
		<link>https://dcn.nat.fau.eu/lloyds-algorithm/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Sat, 23 Jul 2022 07:26:56 +0000</pubDate>
				<category><![CDATA[Hub]]></category>
		<category><![CDATA[Hub Martín Hernández]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Martin Hernandez]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=21476</guid>

					<description><![CDATA[Author: Martín Hernández, FAU DCN-AvH Code: In this repository, we show a code for Lloyd&#8217;s algorithm. Also called Voronoid iteration, this is an iterative algorithm finding for equispaced convex cells in euclidean space. Lloyd&#8217;s algorithm finds the distribution of the cells computing their center of mass and iteratively applying the Voronoid tessellation. Like the closely [&#8230;]]]></description>
		
		
		
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		<title>Uniform Turnpike Property</title>
		<link>https://dcn.nat.fau.eu/uniform-turnpike-property/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Mon, 09 May 2022 05:31:20 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Martin Hernandez]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=16828</guid>

					<description><![CDATA[Uniform Turnpike Property 1 Introduction In this post, we analyze a heat equation with rapidly oscillating coefficients dependent on a parameter , with a distributed control. We show that the uniform null controllability implies the uniform turnpike property, i.e., the turnpike property with constants independent of the -parameter. The main conclusions of this post are [&#8230;]]]></description>
		
		
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