Related Work: started with equation learning section

thesis/chapters/relwork.tex

@@ -1,12 +1,17 @@
 \chapter{Fundamentals and Related Work}
 \label{cha:relwork}
+The goal of this chapter is to provide an overview of equation learning to establish common knowledge of the topic and problem this thesis is trying to solve. The main part of this chapter is split into two parts. The first part is exploring research that has been done in the field of general purpose computations on the GPU (GPGPU) as well as the fundamentals of it. Focus lies on exploring how graphics processing units (GPUs) are used to achieve substantial speed-ups and when they can be effectively employed. The second part describes the basics of how interpreters and compilers are built and how they can be adapted to the workflow of programming GPUs.
 
 \section{Equation learning}
-Section describing what equation learning is and why it is relevant for the thesis
+% Section describing what equation learning is and why it is relevant for the thesis
+Equation learning is a field of research that aims at understanding and discovering equations from a set of data from various fields like mathematics and physics. Data is usually much more abundant while models often are elusive. Because of this, generating equations with a computer can more easily lead to discovering equations that describe the observed data. \textcite{brunton_discovering_2016} describe an algorithm that leverages equation learning to discover equations for physical systems. A more literal interpretation of equation learning is demonstrated by \textcite{pfahler_semantic_2020}. They use machine learning to learn the form of equations. Their aim was to simplify the discovery of relevant publications by the equations they use and not by technical terms, as they may differ by the field of research. However, this kind of equation learning is not relevant for this thesis.
+
+Symbolic regression is a subset of equation learning, that specialises more towards discovering mathematical equations. 
+% probably transition to symbolic regression and \textcite{werner_informed_2021}. As this seems more fitting and symblic regression probably has more publications/makes it easier to find publications. This is the section where I will also talk about how expressions look (see introduction) and the process of generating and evaluating expressions and therefore how this is a potential performance bottleneck
 
 
 \section[GPGPU]{General Purpose Computation on Graphics Processing Units}
-Describe what GPGPU is and how it differs from classical programming. talk about architecture (SIMD) and some scientific papers on how they use GPUs to accelerate tasks
+Describe what GPGPU is and how it differs from classical programming. talk about architecture (SIMD/SIMT) and some scientific papers on how they use GPUs to accelerate tasks
 
 \subsection[PTX]{Parallel Thread Execution}
 Describe what PTX is to get a common ground for the implementation chapter. Probably a short section

thesis/references.bib

@@ -315,3 +315,19 @@ Publisher: Multidisciplinary Digital Publishing Institute},
 	keywords = {Compute Unify Device Architecture, Element Stiffness Matrice, Global Stiffness Matrix, Iterative Solver, Matrix Solver},
 	file = {Full Text PDF:C\:\\Users\\danwi\\Zotero\\storage\\352VGH3Y\\Georgescu et al. - 2013 - GPU Acceleration for FEM-Based Structural Analysis.pdf:application/pdf},
 }
+
+@article{brunton_discovering_2016,
+	title = {Discovering governing equations from data by sparse identification of nonlinear dynamical systems},
+	volume = {113},
+	url = {https://www.pnas.org/doi/abs/10.1073/pnas.1517384113},
+	doi = {10.1073/pnas.1517384113},
+	abstract = {Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.},
+	pages = {3932--3937},
+	number = {15},
+	journaltitle = {Proceedings of the National Academy of Sciences},
+	author = {Brunton, Steven L. and Proctor, Joshua L. and Kutz, J. Nathan},
+	urldate = {2025-02-26},
+	date = {2016-04-12},
+	note = {Publisher: Proceedings of the National Academy of Sciences},
+	file = {Full Text PDF:C\:\\Users\\danwi\\Zotero\\storage\\6R643NFZ\\Brunton et al. - 2016 - Discovering governing equations from data by sparse identification of nonlinear dynamical systems.pdf:application/pdf},
+}