Deploying to gh-pages from @ da44882 🚀

Author: naveenguptaiitr

assets/jupyter/blog.ipynb.html

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-<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en"><generator uri="https://jekyllrb.com/" version="4.3.3">Jekyll</generator><link href="https://kgml-lab.github.io/feed.xml" rel="self" type="application/atom+xml"/><link href="https://kgml-lab.github.io/" rel="alternate" type="text/html" hreflang="en"/><updated>2025-04-20T20:03:01+00:00</updated><id>https://kgml-lab.github.io/feed.xml</id><title type="html">KGML Lab</title><subtitle>Group website of Knowledge-guided Machine Learning (KGML) Lab at Virginia Tech </subtitle><entry><title type="html">Google Gemini updates: Flash 1.5, Gemma 2 and Project Astra</title><link href="https://kgml-lab.github.io/blog/2024/google-gemini-updates-flash-15-gemma-2-and-project-astra/" rel="alternate" type="text/html" title="Google Gemini updates: Flash 1.5, Gemma 2 and Project Astra"/><published>2024-05-14T00:00:00+00:00</published><updated>2024-05-14T00:00:00+00:00</updated><id>https://kgml-lab.github.io/blog/2024/google-gemini-updates-flash-15-gemma-2-and-project-astra</id><content type="html" xml:base="https://kgml-lab.github.io/blog/2024/google-gemini-updates-flash-15-gemma-2-and-project-astra/"><![CDATA[]]></content><author><name></name></author><summary type="html"><![CDATA[We’re sharing updates across our Gemini family of models and a glimpse of Project Astra, our vision for the future of AI assistants.]]></summary></entry><entry><title type="html">Displaying External Posts on Your al-folio Blog</title><link href="https://kgml-lab.github.io/blog/2022/displaying-external-posts-on-your-al-folio-blog/" rel="alternate" type="text/html" title="Displaying External Posts on Your al-folio Blog"/><published>2022-04-23T23:20:09+00:00</published><updated>2022-04-23T23:20:09+00:00</updated><id>https://kgml-lab.github.io/blog/2022/displaying-external-posts-on-your-al-folio-blog</id><content type="html" xml:base="https://kgml-lab.github.io/blog/2022/displaying-external-posts-on-your-al-folio-blog/"><![CDATA[]]></content><author><name></name></author></entry></feed>
+<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en"><generator uri="https://jekyllrb.com/" version="4.3.3">Jekyll</generator><link href="https://kgml-lab.github.io/feed.xml" rel="self" type="application/atom+xml"/><link href="https://kgml-lab.github.io/" rel="alternate" type="text/html" hreflang="en"/><updated>2025-04-20T20:13:08+00:00</updated><id>https://kgml-lab.github.io/feed.xml</id><title type="html">KGML Lab</title><subtitle>Group website of Knowledge-guided Machine Learning (KGML) Lab at Virginia Tech </subtitle><entry><title type="html">Google Gemini updates: Flash 1.5, Gemma 2 and Project Astra</title><link href="https://kgml-lab.github.io/blog/2024/google-gemini-updates-flash-15-gemma-2-and-project-astra/" rel="alternate" type="text/html" title="Google Gemini updates: Flash 1.5, Gemma 2 and Project Astra"/><published>2024-05-14T00:00:00+00:00</published><updated>2024-05-14T00:00:00+00:00</updated><id>https://kgml-lab.github.io/blog/2024/google-gemini-updates-flash-15-gemma-2-and-project-astra</id><content type="html" xml:base="https://kgml-lab.github.io/blog/2024/google-gemini-updates-flash-15-gemma-2-and-project-astra/"><![CDATA[]]></content><author><name></name></author><summary type="html"><![CDATA[We’re sharing updates across our Gemini family of models and a glimpse of Project Astra, our vision for the future of AI assistants.]]></summary></entry><entry><title type="html">Displaying External Posts on Your al-folio Blog</title><link href="https://kgml-lab.github.io/blog/2022/displaying-external-posts-on-your-al-folio-blog/" rel="alternate" type="text/html" title="Displaying External Posts on Your al-folio Blog"/><published>2022-04-23T23:20:09+00:00</published><updated>2022-04-23T23:20:09+00:00</updated><id>https://kgml-lab.github.io/blog/2022/displaying-external-posts-on-your-al-folio-blog</id><content type="html" xml:base="https://kgml-lab.github.io/blog/2022/displaying-external-posts-on-your-al-folio-blog/"><![CDATA[]]></content><author><name></name></author></entry></feed>

feed.xml

@@ -103,9 +103,9 @@ <h2 class="title is-3"> Abstract </h2>
   <div class="container is-max-desktop has-text-justified">
     <h2 class="title is-3">Method Overview</h2>
     <p>
-    We propose Generalized Forward-Inverse (GFI) framework based on two assumptions. First, according to the manifold assumption, we assume that the velocity maps v ∈ V and seismic
-    waveforms p ∈ P can be projected to their corresponding latent space representations, v˜ and p˜, respectively, which can be mapped back to their reconstructions in the original space, vˆ and pˆ. 
-    Note that the sizes of the latent spaces can be smaller or larger than the original spaces. Further, the size of v˜ may not match with the size of p˜. Second, according to the latent space
+    We propose Generalized Forward-Inverse (GFI) framework based on two assumptions. First, according to the manifold assumption, we assume that the velocity maps v ∈ \(\mathcal{V}\) and seismic
+    waveforms p ∈ \(\mathcal{P}\) can be projected to their corresponding latent space representations, \(\tilde{v}\) and \(\tilde{p}\), respectively, which can be mapped back to their reconstructions in the original space, \(\hat{v}\) and \(\hat{p}\). 
+    Note that the sizes of the latent spaces can be smaller or larger than the original spaces. Further, the size of \(\tilde{v}\) may not match with the size of \(\tilde{p}\). Second, according to the latent space
     translation assumption, we assume that the problem of learning forward and inverse mappings in the original spaces of velocity and waveforms can be reformulated as learning translations in their
     latent spaces. 
     </p>

projects/GFI-framework/index.html

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