Deep Learning and Computational Physics (Lecture Notes)

• URL: http://arxiv.org/abs/2301.00942v1
• Date: Tue, 3 Jan 2023 03:56:19 GMT
• Title: Deep Learning and Computational Physics (Lecture Notes)
• Authors: Deep Ray, Orazio Pinti, Assad A. Oberai
• Abstract summary: Notes should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics. Use concepts from computational physics to develop an understanding of deep learning algorithms. Several novel deep learning algorithms can be used to solve challenging problems in computational physics.
• Score: 0.5156484100374059
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics. The main objective of these notes is to introduce a student who is familiar with concepts in linear algebra and partial differential equations to select topics in deep learning. These lecture notes exploit the strong connections between deep learning algorithms and the more conventional techniques of computational physics to achieve two goals. First, they use concepts from computational physics to develop an understanding of deep learning algorithms. Not surprisingly, many concepts in deep learning can be connected to similar concepts in computational physics, and one can utilize this connection to better understand these algorithms. Second, several novel deep learning algorithms can be used to solve challenging problems in computational physics. Thus, they offer someone who is interested in modeling a physical phenomena with a complementary set of tools.

Related papers

• Mathematical theory of deep learning [0.46040036610482665]
  It covers fundamental results in approximation theory, optimization theory, and statistical learning theory. The book aims to equip readers with foundational knowledge on the topic.
  arXiv  Detail & Related papers  (2024-07-25T20:37:12Z)
• Mathematics of Neural Networks (Lecture Notes Graduate Course) [0.0]
  The course is intended as an introduction to neural networks for mathematics students at the graduate level. The lecture notes were made to be as self-contained as possible so as to be accessible for any student with a moderate mathematics background. The course also included coding tutorials and assignments in the form of a set of Jupyter notebooks.
  arXiv  Detail & Related papers  (2024-03-06T08:45:29Z)
• Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory [4.066869900592636]
  This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail.
  arXiv  Detail & Related papers  (2023-10-31T11:01:23Z)
• Towards a Holistic Understanding of Mathematical Questions with Contrastive Pre-training [65.10741459705739]
  We propose a novel contrastive pre-training approach for mathematical question representations, namely QuesCo. We first design two-level question augmentations, including content-level and structure-level, which generate literally diverse question pairs with similar purposes. Then, to fully exploit hierarchical information of knowledge concepts, we propose a knowledge hierarchy-aware rank strategy.
  arXiv  Detail & Related papers  (2023-01-18T14:23:29Z)
• A Survey of Deep Learning for Mathematical Reasoning [71.88150173381153]
  We review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. Recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning.
  arXiv  Detail & Related papers  (2022-12-20T18:46:16Z)
• From Quantum Graph Computing to Quantum Graph Learning: A Survey [86.8206129053725]
  We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions. For its practicability and wide-applicability, we give a brief review of typical graph learning techniques. We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research.
  arXiv  Detail & Related papers  (2022-02-19T02:56:47Z)
• The Physics of Machine Learning: An Intuitive Introduction for the Physical Scientist [0.0]
  This article is intended for physical scientists who wish to gain deeper insights into machine learning algorithms. We begin with a review of two energy-based machine learning algorithms, Hopfield networks and Boltzmann machines, and their connection to the Ising model. We then delve into additional, more "practical," machine learning architectures including feedforward neural networks, convolutional neural networks, and autoencoders.
  arXiv  Detail & Related papers  (2021-11-27T15:12:42Z)
• Physics-based Deep Learning [22.248409468073145]
  Digital book contains a practical and comprehensive introduction to everything related to deep learning in the context of physical simulations. Includes hands-on code examples in the form of Jupyter notebooks to quickly get started. Beyond standard supervised learning from data, we'll look at physical loss constraints, more tightly coupled learning algorithms with differentiable simulations, as well as reinforcement learning and uncertainty modeling.
  arXiv  Detail & Related papers  (2021-09-11T09:38:02Z)
• Ten Quick Tips for Deep Learning in Biology [116.78436313026478]
  Machine learning is concerned with the development and applications of algorithms that can recognize patterns in data and use them for predictive modeling. Deep learning has become its own subfield of machine learning. In the context of biological research, deep learning has been increasingly used to derive novel insights from high-dimensional biological data.
  arXiv  Detail & Related papers  (2021-05-29T21:02:44Z)
• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges [50.22269760171131]
  The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. This text is concerned with exposing pre-defined regularities through unified geometric principles. It provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers.
  arXiv  Detail & Related papers  (2021-04-27T21:09:51Z)
• Spiking Neural Networks Hardware Implementations and Challenges: a Survey [53.429871539789445]
  Spiking Neural Networks are cognitive algorithms mimicking neuron and synapse operational principles. We present the state of the art of hardware implementations of spiking neural networks. We discuss the strategies employed to leverage the characteristics of these event-driven algorithms at the hardware level.
  arXiv  Detail & Related papers  (2020-05-04T13:24:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.