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<header id="title-block-header" class="quarto-title-block default">
<div class="quarto-title">
<h1 class="title">FNOs for Surrogate Modeling</h1>
</div>
<div class="quarto-title-meta">
</div>
</header>
<!-- quarto render updates.qmd --to html -->
<section id="motivational-example" class="level2">
<h2 class="anchored" data-anchor-id="motivational-example">Motivational Example</h2>
<p>Given seismic observations of a CO2 plume, can we invert for the underlying permeability distribution?</p>
<p><span class="math inline">\(p(K|d) \propto p(d|K)\cdot p(K)\)</span><br>
<br>
<span class="math inline">\(K\)</span> is our permeability<br>
<span class="math inline">\(d\)</span> is our seismic observation</p>
<p>Since <span class="math inline">\(p(d|K)\)</span> is expensive to compute, we train a FNO as a surrogate to offload some of the computation.</p>
</section>
<section id="background-of-fourier-neural-operators-fnos" class="level2">
<h2 class="anchored" data-anchor-id="background-of-fourier-neural-operators-fnos">Background of Fourier Neural Operators (FNOs)</h2>
<p>Learns approximations to the solution operator to parametric PDEs</p>
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="assets/fno_arch.png" class="img-fluid figure-img" style="width:80.0%"></p>
<figcaption class="figure-caption">FNO Architechture</figcaption>
</figure>
</div>
<ul>
<li>Acts on functions in lifted space</li>
<li>Spectral convolution (i.e learned weighting on low-frequency modes)</li>
</ul>
</section>
<section id="problem" class="level2">
<h2 class="anchored" data-anchor-id="problem">Problem</h2>
<p>Mapping permeability to time-varying CO2 concentration governed by two-phase flow equations.</p>
<table class="table">
<caption>Dataset details</caption>
<thead>
<tr class="header">
<th style="text-align: left;"><span class="math inline">\(n_x \cdot n_y \cdot n_t \cdot n_c\)</span></th>
<th style="text-align: left;">samples</th>
<th style="text-align: left;">modes</th>
<th style="text-align: left;">sconv blocks</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">64 x 64 x 51 x 4</td>
<td style="text-align: left;">1000</td>
<td style="text-align: left;">8</td>
<td style="text-align: left;">4</td>
</tr>
</tbody>
</table>
</section>
<section id="section" class="level2">
<h2 class="anchored" data-anchor-id="section">10/4/23</h2>
<p>- Trained for 300/500 epochs on the GPU<br>
- The model seems to have stop learning around ~150 epochs<br>
- Objective is <span class="math inline">\(\frac{norm(y - fno(x))}{norm(y)}\)</span><br>
- Using AdamW as optimizer<br>
- The weight application is on CPU (using third party library for einsum)</p>
<p><strong>Currently working on</strong><br>
- Debugging Kronecker Distribution<br>
- Moving Einsum Computation to GPU (Currently ~ 4.5 days projected for 500 epochs)</p>
<section id="evaluation" class="level4">
<h4 class="anchored" data-anchor-id="evaluation">Evaluation</h4>
<div class="quarto-layout-panel">
<div class="quarto-layout-row quarto-layout-valign-top">
<div class="quarto-layout-cell" style="flex-basis: 50.0%;justify-content: center;">
<p><img src="assets/10.4.23/300_eval.png" class="img-fluid"></p>
</div>
<div class="quarto-layout-cell" style="flex-basis: 50.0%;justify-content: center;">
<p><img src="assets/10.4.23/300_loss.png" class="img-fluid"></p>
</div>
</div>
</div>
</section>
</section>
<section id="section-1" class="level2">
<h2 class="anchored" data-anchor-id="section-1">10/13/23</h2>
<p>- Fixed Kronecker Distribution Bug<br>
- Made custom operators for Distrbuted Batch Norm, Distributed Weights Application<br>
- Trained serial FNO for 85 epochs<br>
- Mapped the weights to a distributed FNO. Working <code>v1</code> forward pass</p>
<p><strong>Currently working on</strong><br>
- Gradient for the network</p>
<p><strong>Roadblocks</strong><br>
- No stable Einsum Package for Einsum on GPU<br>
- <code>Einsum</code> : No GPU support<br>
- <code>Tullio.jl</code> : GPU support but last release > 1 year, lots of errors setting up and no runtime contraction order support<br>
- <code>OMEinsum.jl</code> : GPU support and runtime contraction support, failing for our use case on specific GPUs<br>
- Mathias has suggested to open an issue with <code>OMEinsum.jl</code> Devs</p>
<section id="forward-pass-dfno-on-a-2x2-using-cpu" class="level4">
<h4 class="anchored" data-anchor-id="forward-pass-dfno-on-a-2x2-using-cpu">Forward Pass DFNO on a 2x2 using CPU</h4>
<p><img src="assets/10.13.23/85_DFNO.png" class="img-fluid"></p>
</section>
</section>
<section id="section-2" class="level2">
<h2 class="anchored" data-anchor-id="section-2">10/18/23</h2>
<p>- Added Operators and AD rules for gradient<br>
- Trained DFNO for 2 epochs</p>
<p><strong>Currently working on</strong><br>
- Code Cleanup<br>
- Distributed IO<br>
- GPU support</p>
<section id="trained-dfno-on-a-2x2-using-cpu-for-1-epoch" class="level4">
<h4 class="anchored" data-anchor-id="trained-dfno-on-a-2x2-using-cpu-for-1-epoch">Trained DFNO on a 2x2 using CPU for 1 epoch</h4>
<div class="quarto-layout-panel">
<div class="quarto-layout-row quarto-layout-valign-top">
<div class="quarto-layout-cell" style="flex-basis: 72.5%;justify-content: center;">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="assets/10.18.23/2_eval.png" class="img-fluid figure-img"></p>
<figcaption class="figure-caption">Serial</figcaption>
</figure>
</div>
</div>
<div class="quarto-layout-cell" style="flex-basis: 27.5%;justify-content: center;">
<p><img src="assets/10.18.23/2_loss.png" class="img-fluid"></p>
</div>
</div>
</div>
<div class="quarto-layout-panel">
<div class="quarto-layout-row quarto-layout-valign-top">
<div class="quarto-layout-cell" style="flex-basis: 72.5%;justify-content: center;">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="assets/10.18.23/dfno_2_eval.png" class="img-fluid figure-img"></p>
<figcaption class="figure-caption">Parallel</figcaption>
</figure>
</div>
</div>
<div class="quarto-layout-cell" style="flex-basis: 27.5%;justify-content: center;">
<p><img src="assets/10.18.23/dfno_2_loss.png" class="img-fluid"></p>
</div>
</div>
</div>
</section>
</section>
<section id="section-3" class="level2">
<h2 class="anchored" data-anchor-id="section-3">10/30/23</h2>
<p>- Added Hacks for GPU Training of DFNO<br>
- Trained DFNO on 4 workers using GPU for 200 epochs<br>
- Ported 2D to 3D FNO<br>
- Checkpoints for training</p>
<p><strong>Currently working on</strong><br>
- Gradient Tests<br>
- Running on Perlmutter<br>
- Scaling Tests on 3D for ML4Seismic</p>
<section id="trained-2d-dfno-on-a-2x2-using-gpu-for-200-epochs" class="level4">
<h4 class="anchored" data-anchor-id="trained-2d-dfno-on-a-2x2-using-gpu-for-200-epochs">Trained 2D DFNO on a 2x2 using GPU for 200 epochs</h4>
<div class="quarto-layout-panel">
<div class="quarto-layout-row quarto-layout-valign-top">
<div class="quarto-layout-cell" style="flex-basis: 50.0%;justify-content: center;">
<p><img src="assets/10.30.23/ep%3D200_p%3D4_gpu%3D1_eval.png" class="img-fluid"></p>
</div>
<div class="quarto-layout-cell" style="flex-basis: 50.0%;justify-content: center;">
<p><img src="assets/10.30.23/ep%3D200_p%3D4_gpu%3D1_loss.png" class="img-fluid"></p>
</div>
</div>
</div>
</section>
<section id="modular-codebase-35-lines-to-train-custom-2d-or-3d-dfno" class="level4">
<h4 class="anchored" data-anchor-id="modular-codebase-35-lines-to-train-custom-2d-or-3d-dfno">Modular Codebase (~35 lines to train custom 2D or 3D DFNO)</h4>
<div class="sourceCode" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">Pkg</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="bu">Pkg</span>.<span class="fu">activate</span>(<span class="st">"./"</span>)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">include</span>(<span class="st">"src/models/DFNO_2D/DFNO_2D.jl"</span>)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">.DFNO_2D</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">MPI</span></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a>MPI.<span class="fu">Init</span>()</span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a>partition <span class="op">=</span> [<span class="fl">1</span>,<span class="fl">2</span>,<span class="fl">2</span>,<span class="fl">1</span>]</span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a>comm <span class="op">=</span> MPI.COMM_WORLD</span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="pp">@assert</span> MPI.<span class="fu">Comm_size</span>(comm) <span class="op">==</span> <span class="fu">prod</span>(partition)</span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a>modelConfig <span class="op">=</span> DFNO_2D.<span class="fu">ModelConfig</span>(nx<span class="op">=</span><span class="fl">64</span>, ny<span class="op">=</span><span class="fl">64</span>, nt<span class="op">=</span><span class="fl">51</span>, nblocks<span class="op">=</span><span class="fl">4</span>, partition<span class="op">=</span>partition)</span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a>dataConfig <span class="op">=</span> DFNO_2D.<span class="fu">DataConfig</span>(modelConfig<span class="op">=</span>modelConfig)</span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-19"><a href="#cb1-19" aria-hidden="true" tabindex="-1"></a>model <span class="op">=</span> DFNO_2D.<span class="fu">Model</span>(modelConfig)</span>
<span id="cb1-20"><a href="#cb1-20" aria-hidden="true" tabindex="-1"></a>θ <span class="op">=</span> DFNO_2D.<span class="fu">initModel</span>(model)</span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-22"><a href="#cb1-22" aria-hidden="true" tabindex="-1"></a>x_train, y_train, x_valid, y_valid <span class="op">=</span> DFNO_2D.<span class="fu">loadDistData</span>(dataConfig)</span>
<span id="cb1-23"><a href="#cb1-23" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-24"><a href="#cb1-24" aria-hidden="true" tabindex="-1"></a>trainConfig <span class="op">=</span> DFNO_2D.<span class="fu">TrainConfig</span>(</span>
<span id="cb1-25"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a> epochs<span class="op">=</span><span class="fl">200</span>,</span>
<span id="cb1-26"><a href="#cb1-26" aria-hidden="true" tabindex="-1"></a> x_train<span class="op">=</span>x_train,</span>
<span id="cb1-27"><a href="#cb1-27" aria-hidden="true" tabindex="-1"></a> y_train<span class="op">=</span>y_train,</span>
<span id="cb1-28"><a href="#cb1-28" aria-hidden="true" tabindex="-1"></a> x_valid<span class="op">=</span>x_valid,</span>
<span id="cb1-29"><a href="#cb1-29" aria-hidden="true" tabindex="-1"></a> y_valid<span class="op">=</span>y_valid,</span>
<span id="cb1-30"><a href="#cb1-30" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb1-31"><a href="#cb1-31" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-32"><a href="#cb1-32" aria-hidden="true" tabindex="-1"></a>DFNO_2D.<span class="fu">train!</span>(trainConfig, model, θ)</span>
<span id="cb1-33"><a href="#cb1-33" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-34"><a href="#cb1-34" aria-hidden="true" tabindex="-1"></a>MPI.<span class="fu">Finalize</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
</section>
</main>
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// don't keep focus
button.blur();
// flash "checked"
button.classList.add('code-copy-button-checked');
var currentTitle = button.getAttribute("title");
button.setAttribute("title", "Copied!");
let tooltip;
if (window.bootstrap) {
button.setAttribute("data-bs-toggle", "tooltip");
button.setAttribute("data-bs-placement", "left");
button.setAttribute("data-bs-title", "Copied!");
tooltip = new bootstrap.Tooltip(button,
{ trigger: "manual",
customClass: "code-copy-button-tooltip",
offset: [0, -8]});
tooltip.show();
}
setTimeout(function() {
if (tooltip) {
tooltip.hide();
button.removeAttribute("data-bs-title");
button.removeAttribute("data-bs-toggle");
button.removeAttribute("data-bs-placement");
}
button.setAttribute("title", currentTitle);
button.classList.remove('code-copy-button-checked');
}, 1000);
// clear code selection
e.clearSelection();
});
function tippyHover(el, contentFn) {
const config = {
allowHTML: true,
content: contentFn,
maxWidth: 500,
delay: 100,
arrow: false,
appendTo: function(el) {
return el.parentElement;
},
interactive: true,
interactiveBorder: 10,
theme: 'quarto',
placement: 'bottom-start'
};
window.tippy(el, config);
}
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
for (var i=0; i<noterefs.length; i++) {
const ref = noterefs[i];
tippyHover(ref, function() {
// use id or data attribute instead here
let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href');
try { href = new URL(href).hash; } catch {}
const id = href.replace(/^#\/?/, "");
const note = window.document.getElementById(id);
return note.innerHTML;
});
}
let selectedAnnoteEl;
const selectorForAnnotation = ( cell, annotation) => {
let cellAttr = 'data-code-cell="' + cell + '"';
let lineAttr = 'data-code-annotation="' + annotation + '"';
const selector = 'span[' + cellAttr + '][' + lineAttr + ']';
return selector;
}
const selectCodeLines = (annoteEl) => {
const doc = window.document;
const targetCell = annoteEl.getAttribute("data-target-cell");
const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation));
const lines = annoteSpan.getAttribute("data-code-lines").split(",");
const lineIds = lines.map((line) => {
return targetCell + "-" + line;
})
let top = null;
let height = null;
let parent = null;
if (lineIds.length > 0) {
//compute the position of the single el (top and bottom and make a div)
const el = window.document.getElementById(lineIds[0]);
top = el.offsetTop;
height = el.offsetHeight;
parent = el.parentElement.parentElement;
if (lineIds.length > 1) {
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
const bottom = lastEl.offsetTop + lastEl.offsetHeight;
height = bottom - top;
}
if (top !== null && height !== null && parent !== null) {
// cook up a div (if necessary) and position it
let div = window.document.getElementById("code-annotation-line-highlight");
if (div === null) {
div = window.document.createElement("div");
div.setAttribute("id", "code-annotation-line-highlight");
div.style.position = 'absolute';
parent.appendChild(div);
}
div.style.top = top - 2 + "px";
div.style.height = height + 4 + "px";
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
if (gutterDiv === null) {
gutterDiv = window.document.createElement("div");
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
gutterDiv.style.position = 'absolute';
const codeCell = window.document.getElementById(targetCell);
const gutter = codeCell.querySelector('.code-annotation-gutter');
gutter.appendChild(gutterDiv);
}
gutterDiv.style.top = top - 2 + "px";
gutterDiv.style.height = height + 4 + "px";
}
selectedAnnoteEl = annoteEl;
}
};
const unselectCodeLines = () => {
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
elementsIds.forEach((elId) => {
const div = window.document.getElementById(elId);
if (div) {
div.remove();
}
});
selectedAnnoteEl = undefined;
};
// Attach click handler to the DT
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
for (const annoteDlNode of annoteDls) {
annoteDlNode.addEventListener('click', (event) => {
const clickedEl = event.target;
if (clickedEl !== selectedAnnoteEl) {
unselectCodeLines();
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
if (activeEl) {
activeEl.classList.remove('code-annotation-active');
}
selectCodeLines(clickedEl);
clickedEl.classList.add('code-annotation-active');
} else {
// Unselect the line
unselectCodeLines();
clickedEl.classList.remove('code-annotation-active');
}
});
}
const findCites = (el) => {
const parentEl = el.parentElement;
if (parentEl) {
const cites = parentEl.dataset.cites;
if (cites) {
return {
el,
cites: cites.split(' ')
};
} else {
return findCites(el.parentElement)
}
} else {
return undefined;
}
};
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
for (var i=0; i<bibliorefs.length; i++) {
const ref = bibliorefs[i];
const citeInfo = findCites(ref);
if (citeInfo) {
tippyHover(citeInfo.el, function() {
var popup = window.document.createElement('div');
citeInfo.cites.forEach(function(cite) {
var citeDiv = window.document.createElement('div');
citeDiv.classList.add('hanging-indent');
citeDiv.classList.add('csl-entry');
var biblioDiv = window.document.getElementById('ref-' + cite);
if (biblioDiv) {
citeDiv.innerHTML = biblioDiv.innerHTML;
}
popup.appendChild(citeDiv);
});
return popup.innerHTML;
});
}
}
});
</script>
</div> <!-- /content -->
</body></html>