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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>2025-04-20T20:13:08+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>
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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>2025-04-20T20:20:59+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>
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
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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 \(\hat{p}\).
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waveforms p ∈ \(\mathcal{P}\) can be projected to their corresponding latent space representations, ṽ and p̃, respectively, which can be mapped back to their reconstructions in the original space, \(\hat{v}\) and \(\hat{p}\).
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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
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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
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latent spaces.
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</p>
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<b>Latent U-Net Architecture: </b>
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<b>Latent U-Net Architecture: </b> We propose a novel architecture to solve forward and inverse problems using two latent space translation models implemented using U-Nets, termed Latent U-Net. As shown in Figure below, Latent
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U-Net uses ConvNet backbones for both encoder-decoder pairs: (Ev, Dv) and (Ep, Dp), to project
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v and p to lower-dimensional representations. We also constrain the sizes of the latent spaces of
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\(\tilde{v}\) and \(\tilde{p}\) to be identical, i.e., dim(\(\tilde{v}\)) = dim(\(\tilde{p}\)), so that we can train two separate U-Net models to implement the latent space mappings L<sub>ṽ → p̃</sub> and L<sub>p̃ → ṽ</sub>.
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