From 34d98f99973fc395ffb506a4f88823559f6bbe66 Mon Sep 17 00:00:00 2001 From: Daniel Date: Sat, 1 Mar 2025 13:14:37 +0100 Subject: [PATCH] Related Work: finished equation learning section; started GPGPU section --- thesis/chapters/relwork.tex | 13 ++++-- thesis/main.pdf | Bin 304363 -> 333777 bytes thesis/references.bib | 83 ++++++++++++++++++++++++++++++++++++ 3 files changed, 92 insertions(+), 4 deletions(-) diff --git a/thesis/chapters/relwork.tex b/thesis/chapters/relwork.tex index 9bb6155..185bf6c 100644 --- a/thesis/chapters/relwork.tex +++ b/thesis/chapters/relwork.tex @@ -6,18 +6,23 @@ The goal of this chapter is to provide an overview of equation learning to estab % 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. A lot of research is done in this field. \textcite{keijzer_scaled_2004} and \textcite{korns_accuracy_2011} presented ways of improving the quality of symbolic regression algorithms, making symbolic regression more feasible for problem-solving. Additionally, \textcite{jin_bayesian_2020} proposed an alternative to genetic programming (GP) for the use in symbolic regression. Their approach increased the quality of the results noticeably compared to GP alternatives. The first two approaches are more concerned with the quality of the output, while the third is also concerned with interpretability and reducing memory consumption. Heuristics like GP or neural networks as used by \textcite{werner_informed_2021} in their equation learner can help with finding good solutions faster, accelerating scientific progress. One key part of equation learning in general is the computational evaluation of the generated equations. As this is an expensive operation, improving the performance reduces computation times and in turn, helps all approaches to find solutions more quickly. -% probably a quick detour to show how a generated equation might look and why evaluating them is expensive +Symbolic regression is a subset of equation learning, that specialises more towards discovering mathematical equations. A lot of research is done in this field. \textcite{keijzer_scaled_2004} and \textcite{korns_accuracy_2011} presented ways of improving the quality of symbolic regression algorithms, making symbolic regression more feasible for problem-solving. Additionally, \textcite{jin_bayesian_2020} proposed an alternative to genetic programming (GP) for the use in symbolic regression. Their approach increased the quality of the results noticeably compared to GP alternatives. The first two approaches are more concerned with the quality of the output, while the third is also concerned with interpretability and reducing memory consumption. \textcite{bartlett_exhaustive_2024} also describe an approach to generate simpler and higher quality equations while being faster than GP algorithms. Heuristics like GP or neural networks as used by \textcite{werner_informed_2021} in their equation learner can help with finding good solutions faster, accelerating scientific progress. As seen by these publications, increasing the quality of generated equations but also increasing the speed of finding these equations is a central part in symbolic regression and equation learning in general. This means research in improving the computational performance of these algorithms is desired. -% talk about cases where porting algorithms to gpus helped increase performance. This will be the transition the the below sections +The expressions generated by an equation learning algorithm can look like this $x_1 + 5 - \text{abs}(p_1) * \text{sqrt}(x_2) / 10 + 2 \char`^ 3$. They consist of several unary and binary operators but also of constants, variables and parameters and expressions mostly differ in length and the kind of terms in the expressions. Per iteration many of these expressions are generated and in addition, matrices of values for the variables and parameters are also created. One row of the variable matrix corresponds to one instantiation of all expressions and this matrix contains multiple rows. This leads to a drastic increase of instantiated expressions that need to be evaluated. Parameters are a bit simpler, as they can be treated as constants for one iteration but can have a different value on another iteration. This means that parameters do not increase the number of expressions that need to be evaluated. However, the increase in evaluations introduced by the variables is still drastic and therefore increases the algorithm runtime significantly. \section[GPGPU]{General Purpose Computation on Graphics Processing Units} -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 +Graphics cards (GPUs) are commonly used to increase the performance of many different applications. Originally they were designed to improve performance and visual quality in games. \textcite{dokken_gpu_2005} first described the usage of GPUs for general purpose programming. They have shown how the graphics pipeline can be used for GPGPU programming. Because this approach also requires the programmer to understand the graphics terminology, this was not a great solution. Therefore, Nvidia released CUDA\footnote{\url{https://developer.nvidia.com/cuda-toolkit}} in 2007 with the goal of allowing developers to program GPUs independent of the graphics pipeline and terminology. A study of the programmability of GPUs with CUDA and the resulting performance has been conducted by \textcite{huang_gpu_2008}. They found that GPGPU programming has potential, even for non-embarassingly parallel problems. Research is also done in making the low level CUDA development simpler. \textcite{han_hicuda_2011} have described a directive-based language to make development simpler and less error-prone, while retaining the performance of handwritten code. To drastically simplify CUDA development \textcite{besard_effective_2019} showed that it is possible to develop with CUDA in the high level programming language Julia\footnote{\url{https://julialang.org/}} while performing similar to CUDA written in C. In a subsequent study \textcite{lin_comparing_2021} found that high performance computing (HPC) on the CPU and GPU in Julia performs similar to HPC development in C. This means that Julia can be a viable alternative to Fortran, C and C++ in the HPC field and has the additional benefit of developer comfort since it is a high level language with modern features such as garbage-collectors. \textcite{besard_rapid_2019} have also shown how the combination of Julia and CUDA help in rapidly developing HPC software. While this section and thesis in general talk about CUDA, as it is a widely used framework for GPGPU programming, there also exist alternatives by AMD called ROCm\footnote{\url{https://www.amd.com/de/products/software/rocm.html}} and a vendor independent alternative called OpenCL\footnote{\url{https://www.khronos.org/opencl/}}. + +talk about the fields GPGPU really helped make performance improvements (weather simulations etc). Then describe how it differs from classical programming. talk about architecture (SIMD/SIMT; a lot of "slow" cores). \subsection[PTX]{Parallel Thread Execution} Describe what PTX is to get a common ground for the implementation chapter. 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