Deep Learning in Computational Mechanics
an honest reference

Note

This work is incomplete and under active development.

About

neuralmech is a collection of ml-enhanced physics solvers & optimizers answering

When and where is deep learning useful in numerical simulation?

Features

• simplistic & extendable implementations
• reproducible results
• associated to the succesor of deep learning in computational mechanics: a completely new book growing out of the earlier edititions:

As this project is ongoing, feedback is highly welcome. Finished chapters are available on request under a personal-use, non-redistribution license — feel free to reach out via email. By requesting a copy, you agree to the license terms included in the document.

Chapters available on request

• Computational Mechanics Meets Artificial Intelligence (chapter 1)
• Fundamental Machine Learning (chapter 2)
• Artificial Neural Networks (chapter 3)

• Neural Network Architectures (chapter 4)
• Probabilistic Machine Learning (chapter 5)
• Governing Equations (chapter 8)
• Numerical Methods (chapter 9)

Chapters in progress

• Machine Learning Algorithms (chapter 6)
• Practical Machine Learning (chapter 7)
• Machine Learning in Computational Mechanics (chapter 10)
• Neural Surrogates (chapter 11)
• Neural Solvers (chapter 12)
• Physics-Informed Neural Networks (chapter 13)
• Constitutive Modeling with Neural Networks (chapter 14)
• Generative Artificial Intelligence (chapter 15)
• Neural Optimization (chapter 16)

• Large Language Models (chapter 17)
• Simulation Acceleration via GPUs (chapter 18)

• Deep Reinforcement Learning (chapter 19)
• Computational Mechanics After Artificial Intelligence (chapter 20)

Requirements

• install via requirements

pip install -r requirements.txt

Note

The requirements are currently broader than necessary and will be trimmed down later.

mlhp

mlhp is included as a git submodule. To clone recursively use

git clone --recurse-submodules https://github.com/cmpmech/neuralmech

• for now, use pip install mlhp (for more advanced physics C++ compilation will be needed)

cuwave

• the GPU finite difference wave solver behind the wave and transient topology optimization drivers
• covered by the requirements, or install it on its own with

pip install cuwave

• needs a cupy matching the installed CUDA toolkit

cufluid

• the GPU lattice Boltzmann fluid solver behind the fluid drivers
• currently private and ongoing work, included as a git submodule in solvers/cufluid; it will be released as a pip package soon
• with access, install it from the submodule with

pip install -e solvers/cufluid

Structure

data/	generated data (small, but gitignored if large)
external_data/	data generation tools with data in data (large, excluded from main repo)
models/	trained networks
results/	results for postprocessing
projects/	main drivers; see projects
DL.py	deep learning utilities
NN.py	network architectures
ML.py	classical machine learning models
postprocessing.py	postprocessing helpers
solvers/	classical physics solvers

Contact

neuralmech@pm.me

License

MIT; see LICENSE.