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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Nicholas Mueller</title>
<meta name="description" content="Applied mathematician and engineer building simulation, forecasting, and scientific software systems for environmental and energy applications.">
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<link rel="stylesheet" href="site.css">
<link rel="icon" href="assets/favicon.svg">
</head>
<body>
<div class="site-shell">
<header class="site-header">
<a class="brand" href="index.html">
<span class="brand__name">Nicholas Mueller</span>
<span class="brand__tag">Applied mathematician, engineer, and scientific software developer</span>
</a>
<nav class="nav" aria-label="Primary">
<a class="active" href="index.html">Home</a>
<a href="cv/">CV</a>
<a href="achievements/">Achievements</a>
<a href="software/">Software</a>
<a href="publications/">Publications</a>
<a href="notes/">Notes</a>
<a href="contact/">Contact</a>
</nav>
</header>
<div class="layout">
<aside class="sidebar">
<img class="sidebar__avatar" src="assets/avatar.jpeg" alt="Nicholas Mueller">
<p class="eyebrow" style="margin-top:16px;">Currently</p>
<p>Research Fellow at TU Delft, working on digital-twin simulation and forecasting for offshore floating solar.</p>
<div class="chip-row">
<span class="chip">Simulation</span>
<span class="chip">Forecasting</span>
<span class="chip">HPC</span>
<span class="chip">Scientific ML</span>
</div>
<div class="sidebar__links">
<a href="https://github.com/nichomueller">GitHub</a>
<a href="https://scholar.google.com/citations?user=PXLbDdYAAAAJ&hl=en">Scholar</a>
<a href="https://www.linkedin.com/in/nicholas-mueller-braden">LinkedIn</a>
</div>
</aside>
<main class="panel">
<div class="panel__inner">
<section class="hero">
<div class="hero__copy">
<p class="eyebrow">About</p>
<p class="hero__lead">I'm an applied mathematician and engineer working on data-driven simulation of physical systems, combining reduced-order modeling, data assimilation, and machine learning with physics-based solvers across diverse engineering and scientific applications. Ultimately, I want to develop technologies that help us understand and address the challenges of climate change and contribute to a more sustainable future for everyone.</p>
<div class="cta-row">
<a class="button" href="cv/">View CV</a>
<a class="button--ghost" href="software/">Explore Software</a>
<a class="button--ghost" href="contact/">Get in touch</a>
</div>
</div>
</section>
<section class="section">
<div class="section-head">
<div>
<p class="eyebrow">What I do</p>
</div>
</div>
<div class="card-grid">
<article class="feature-card">
<p class="card-kicker">Simulation Systems</p>
<h3 class="card-title">Reduced-order models for PDE workflows that are otherwise too slow to iterate on</h3>
<p>I build simulation pipelines that go from a full finite element solver down to a low-dimensional approximation, without throwing away the physics, so calibration and design loops that used to take hours run in seconds.</p>
</article>
<article class="feature-card">
<p class="card-kicker">Forecasting Pipelines</p>
<h3 class="card-title">Data assimilation and uncertainty quantification for operational settings</h3>
<p>I mostly work with Kalman-type filters, variational methods, and multi-fidelity algorithms. They all do roughly the same job: combine sparse, noisy observations with a physical model so the resulting prediction comes with a confidence interval you can trust.</p>
</article>
<article class="feature-card">
<p class="card-kicker">Scientific Software</p>
<h3 class="card-title">Research code that behaves like engineering software</h3>
<p>I develop performant scientific software grounded in mathematical rigor and designed to deliver meaningful results across a range of engineering and scientific applications. I build with reproducibility, testing, and documentation in mind from the outset, and I make my work open source so that it can be used, extended, and built upon by anyone interested.</p>
</article>
<article class="feature-card">
<p class="card-kicker">Compute Strategy</p>
<h3 class="card-title">HPC-aware implementations for large-scale models</h3>
<p>My day-to-day toolkit includes MPI, GPU-aware computing, and Slurm-based workflows. I use these tools to develop scalable methods that can move from small proof-of-concept problems to demanding scientific and engineering applications.</p>
</article>
</div>
</section>
<section class="section">
<article class="current-work-sticker">
<p class="card-kicker">Current work</p>
<h2 class="section-title">Digital twins for offshore renewable energy</h2>
<p class="section-intro">Right now that's DigiOcean4Solar, an NWO Vidi project that's building a digital framework to simulate how waves, wind, and floating solar platforms interact at the scale of a whole farm. One island's wake changes the conditions the next island downstream has to be designed for, and modeling the whole farm as a system is what makes that visible ahead of time. My part is the forecasting and uncertainty quantification layer that sits on top of that.</p>
</article>
</section>
<section class="section split-grid">
<div>
<div class="section-head">
<div>
<p class="eyebrow">Selected Work</p>
<h2 class="section-title">Software I actually use</h2>
</div>
</div>
<div class="media-grid">
<article class="project-card">
<img src="assets/gridaproms.png" alt="GridapROMs.jl">
<p class="card-kicker">GridapROMs.jl</p>
<h3 class="card-title">Reduced-order modeling toolkit for parameterised PDEs</h3>
<p>Handles nonlinear, transient, and multi-field problems, with reduced-order algorithms that have achieved up to 100,000x speedups over full-order simulations.</p>
<div class="project-links">
<a href="software/">Details</a>
<a href="https://github.com/gridap/GridapROMs.jl">Repository</a>
</div>
</article>
<article class="project-card">
<img src="assets/opal.png" alt="Opal.jl">
<p class="card-kicker">Opal.jl</p>
<h3 class="card-title">Data assimilation across ODEs, PDEs, and reduced-order surrogates</h3>
<p>Kalman, particle, and variational filters behind one interface, with add-ons for localisation, inflation, bias correction, and integration with ROM pipelines for efficiency.</p>
<div class="project-links">
<a href="software/">Details</a>
<a href="https://github.com/nichomueller/Opal.jl">Repository</a>
</div>
</article>
</div>
</div>
<aside class="quote-card">
<p class="card-kicker">Working Style</p>
<blockquote>
I care about turning mathematically sound ideas into scientific software that is reliable, scalable, and useful beyond the problem it was originally designed to solve
</blockquote>
<div class="meta-list">
<div>
<strong>Current domain</strong>
Offshore renewable energy and environmental risk
</div>
<div>
<strong>Core methods</strong>
Reduced-order modelling, filtering, UQ, scientific ML
</div>
<div>
<strong>Main languages</strong>
Julia, Python, C++, MATLAB
</div>
<div>
<strong>Output style</strong>
Open-source libraries, papers, reproducible workflows
</div>
</div>
</aside>
</section>
<section class="section">
<div class="section-head">
<div>
<p class="eyebrow">Highlights</p>
<h2 class="section-title">Recent trajectory</h2>
</div>
</div>
<div class="timeline">
<article class="timeline-card">
<div class="timeline-meta">2026 - present</div>
<h3 class="card-title">TU Delft, DigiOcean4Solar</h3>
<p>Developing digital-twin and large-scale multiphysics frameworks for offshore floating solar farms, with a forecasting and uncertainty quantification layer that feeds into how a farm's layout and structures get designed.</p>
</article>
<article class="timeline-card">
<div class="timeline-meta">2022 - 2025</div>
<h3 class="card-title">PhD in Applied Mathematics, Monash University</h3>
<p>Built reduced-order methods, novel tensor-based compression workflows, unfitted finite element techniques, and scientific software for parameterised PDEs and computational fluid dynamics.</p>
</article>
<article class="timeline-card">
<div class="timeline-meta">2020 - 2021</div>
<h3 class="card-title">R&D internship at CSEM</h3>
<p>Worked on topology optimisation for compliant aerospace mechanisms under manufacturing and stress constraints, connecting numerical methods to engineering requirements.</p>
</article>
</div>
</section>
<section class="section">
<div class="section-head">
<div>
<p class="eyebrow">Notes</p>
<h2 class="section-title">Short writing on methods, software, and modeling practice</h2>
</div>
<a class="button--ghost" href="notes/">See all notes</a>
</div>
<div class="card-grid">
<article class="info-card note-card">
<p class="card-kicker">Project note</p>
<h3 class="card-title">Building scientific software that lasts</h3>
<p>A short piece on how thoughtful interfaces, testing, and benchmarking help turn research ideas into reliable tools for the wider scientific community.</p>
</article>
<article class="info-card note-card">
<p class="card-kicker">Performance note</p>
<h3 class="card-title">The optimization behind GridapROMs.jl that isn't parallelism</h3>
<p>A specific implementation trick from the GridapROMs.jl paper: reordering a loop, not parallelizing it, is what drives the memory savings.</p>
</article>
<article class="info-card note-card">
<p class="card-kicker">Data assimilation note</p>
<h3 class="card-title">Why reservoir computing fits naturally inside a bias-aware Kalman filter</h3>
<p>Only the linear readout of an echo state network needs training, which is what makes it cheap enough to retrain repeatedly inside a filtering loop. From the Opals.jl paper.</p>
</article>
<article class="info-card note-card">
<p class="card-kicker">Orientation</p>
<h3 class="card-title">The whole pipeline, start to finish</h3>
<p>My work spans mathematical modelling, numerical methods, and software engineering, from formulating a method on paper through to a package other people install and use.</p>
</article>
</div>
</section>
</div>
</main>
</div>
<footer class="site-footer">
Nicholas Mueller. Applied mathematics, forecasting systems, and scientific software.
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