Expand ms_thesis.md with objectives and background

Added sections detailing the objective and background of the work on reactive flow simulations, including the development of a machine learning surrogate framework and its integration with PeleLMeX.

Author: sachdevakunal

_projects/ms_thesis.md

@@ -5,4 +5,22 @@ tools: "Python (JAX, NumPy), MATLAB, Cantera, PeleLMeX, High-Performance Computi
 link: /projects/ms-thesis/
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+### Objective of This Work
+
+- **Reactive flow simulations** are limited by the high computational cost of chemistry integration.  
+- Developed a **machine learning–based surrogate framework** to accelerate this step in **PeleLMeX**, an open-source, high-fidelity CFD solver for reactive flows.  
+- Implemented a **Deep Operator Network (DeepONet)** to learn the temporal evolution of reduced thermochemical states, bypassing conventional numerical integration.  
+- Established a **C–Python interface** enabling seamless integration of the trained model with PeleLMeX.  
+- Validated the framework on a **2D reacting flow case**, demonstrating strong accuracy and significant computational savings.  
+
+### Background: Reaction Integration in PeleLMeX
+
+- **PeleLMeX** is an **open-source, high-fidelity CFD solver** for **low-Mach reactive flow simulations**, built on the **AMReX** framework.  
+- The solver employs an **operator-splitting approach**, separating **transport (advection + diffusion)** from **reaction** during each time advance.  
+- In the **reaction step**, every grid cell solves a **system of stiff, nonlinear ODEs** representing detailed chemical kinetics.  
+- These ODEs are integrated using **SUNDIALS CVODE**, an implicit solver designed for stiff reaction systems.  
+- Although robust, this step dominates computational cost — typically **over 70% of total runtime**, especially for detailed fuel mechanisms.  
+- Each cell evolves independently, enabling parallel execution but resulting in **high cumulative computational overhead**.  
+- This motivates the development of a **faster surrogate** capable of predicting the **temporal evolution of thermochemical states** directly, without iterative ODE integration.  
+