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Refine research page into publication-aligned research subsections #176

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46 changes: 34 additions & 12 deletions 5-research.md
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layout: page
title: Research
image: assets/images/ideas.webp
description: 'Past, Present, and Planned Projects'
description: 'Core Areas and Representative Directions'
nav-menu: true
banner_color: style5
---
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<h2>Research Overview</h2>
</header>
<p>
Our research at SECQUOIA (Systems Engineering, Computation, and Quantum Optimization for AI) spans multiple areas at the intersection of optimization, artificial intelligence, and emerging computation paradigms. We develop theory, algorithms, and software for large-scale optimization, with applications in process systems engineering, data-driven decision-making, and quantum-enhanced computation. Our work is problem-driven and interdisciplinary, with active collaborations in chemical engineering, quantum information, and computer science.
Our research at SECQUOIA spans a set of connected themes that recur throughout Prof. David
Bernal's publication record: mathematical optimization, process systems engineering, quantum
algorithms, data-driven learning, and open scientific software. Across these areas, we
develop models, algorithms, and benchmark problems that connect rigorous theory with
deployable tools for chemical, energy, biomedical, and other industrial applications.
</p>
</div>
</section>
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<div class="content">
<div class="inner">
<header class="major">
<h3>Generalized Disjunctive Programming and Mixed-Integer Nonlinear Optimization</h3>
<h3>Mathematical Optimization, GDP, and MINLP</h3>
</header>
<p>
We develop exact and approximation algorithms for solving generalized disjunctive programming (GDP) models arising in process network synthesis, scheduling, and design under uncertainty. Current work explores tight reformulations, surrogate-based relaxations, and scalable solution strategies for nonlinear and dynamic systems with discrete decisions.
We develop theory and algorithms for generalized disjunctive programming, mixed-integer
nonlinear programming, and other nonlinear discrete optimization models. Representative
directions include outer-approximation methods, convexification, regularization,
decomposition, and logic-based search strategies for planning, scheduling, design, and
dynamic optimization problems.
</p>
</div>
</div>
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<div class="content">
<div class="inner">
<header class="major">
<h3>Quantum Optimization and Quantum-Inspired Algorithms</h3>
<h3>Process Systems Engineering and Sustainable Operations</h3>
</header>
<p>
We study how quantum computing can accelerate optimization by designing and benchmarking hybrid quantum-classical algorithms. This includes variational quantum algorithms for discrete-continuous problems, quantum-enhanced surrogate modeling, and tensor network simulations to evaluate algorithmic performance under realistic noise models.
Our optimization methods are motivated by applications in process systems engineering,
including process synthesis, design and control, refinery planning and scheduling,
manufacturing networks, water systems, and supply chains. Many of these projects target
sustainability by improving resource efficiency, renewable electricity generation, and the
operation of complex chemical and energy systems.
</p>
</div>
</div>
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<div class="content">
<div class="inner">
<header class="major">
<h3>Federated Learning for Process and Biomedical Applications</h3>
<h3>Quantum Optimization, Simulation, and Benchmarking</h3>
</header>
<p>
Our group explores federated learning in settings where data privacy, heterogeneity, and limited communication are key constraints. Applications include predictive modeling in pharmaceutical manufacturing and multimodal learning from DNA and MRI data for disease classification. We also investigate secure federated learning using fully homomorphic encryption.
We study how emerging quantum and quantum-inspired methods can help solve hard
optimization and simulation problems. Current work spans hybrid quantum-classical
optimization, QUBO formulations, routing and network problems, variational algorithms,
performance benchmarking, and practical assessments of quantum hardware and heuristic
solvers on scientifically meaningful test cases.
</p>
</div>
</div>
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<div class="content">
<div class="inner">
<header class="major">
<h3>AI-Augmented Process Engineering</h3>
<h3>Federated Learning and AI for Engineering and Healthcare</h3>
</header>
<p>
We integrate machine learning into process simulation and control workflows by leveraging domain knowledge and physical models. Projects include developing digital twins, interpretable surrogate models, and adaptive model-predictive control for chemical and energy systems.
We investigate machine learning methods that respect privacy, distribution, and scientific
structure in the data. Recent efforts include federated learning for chemical engineering
and healthcare, tensor-network-based learning architectures, fully homomorphic encryption
for privacy-preserving collaboration, and learning-enhanced optimization workflows.
</p>
</div>
</div>
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<div class="content">
<div class="inner">
<header class="major">
<h3>Open-Source Software for Optimization and AI</h3>
<h3>Open-Source Software, Libraries, and Reproducibility</h3>
</header>
<p>
We contribute to the development of open-source tools to advance reproducibility and usability of optimization and learning methods. Ongoing efforts include software for mixed-integer optimization, simulation-based optimization, federated learning, and quantum algorithm simulation.
Reproducible software is a core part of our research. We contribute to and help develop
open-source tools and benchmark libraries for optimization and quantum computing,
including modeling ecosystems, solver toolkits, curated problem libraries, and reusable
datasets that make new methods easier to compare, extend, and deploy.
</p>
</div>
</div>
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