Deep Learning and Computational Physics (Lecture Notes)
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Abstract (arXiv)
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.
Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 20 of its 34 references that are in the map. First posted on arXiv 3 Jan 2023.
Builds on
20 of 34 references.
References · 20
- 2015Deep Residual Learning for Image Recognitioncited by 52,096
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
- 2022Generative Adversarial Networkscited by 5,627
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
- 2017Improved Training of Wasserstein GANscited by 2,235
- 2014Conditional Generative Adversarial Netscited by 2,162
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
- 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 233
8 more
- 2019Universal Approximation with Deep Narrow Networkscited by 200
- 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEscited by 116
- 2019The phase diagram of approximation rates for deep neural networkscited by 88
- 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 87
- 2018Deep Bayesian Inversioncited by 61
- 2021Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priorscited by 29
- 2022Variationally Mimetic Operator Networkscited by 19
- 2022The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problemscited by 15
Built on by
Citing papers per year: 2023: 2; 2024: 0; 2025: 0; 2026: 2.
4 papers.
- 2023Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINNcited by 6
- 2023Size Lowerbounds for Deep Operator Networkscited by 6
- 2026Fine-Tuning Small Reasoning Models for Quantum Field Theorycited by 1
- 2026Advances in Scientific Machine Learning for Coupled Fluid Flow and Transportcited by 0
- 2026Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport17 Jun 2026
- 2026Fine-Tuning Small Reasoning Models for Quantum Field Theory21 Apr 2026
- 2023Size Lowerbounds for Deep Operator Networks11 Aug 2023
- 2023Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINN10 Apr 2023