# Deep Learning in Deterministic Computational Mechanics

arXiv: https://arxiv.org/abs/2309.15421 · HTML: https://mlsanity.com/paper/2309.15421/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 237 of its 640 references that are in the map.
- First posted on arXiv 27 Sep 2023.

## Builds on (most cited first, 30 of 237)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)

## Built on by (most cited first, 21 of 21)

- [A finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations](https://mlsanity.com/paper/2404.00074/) (2024)
- [BiLO: Bilevel Local Operator Learning for PDE Inverse Problems](https://mlsanity.com/paper/2404.17789/) (2024)
- [An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning](https://mlsanity.com/paper/2408.13222/) (2024)
- [Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materials](https://mlsanity.com/paper/2410.05281/) (2024)
- [Neural Networks for Generating Better Local Optima in Topology Optimization](https://mlsanity.com/paper/2407.17957/) (2024)
- [A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials](https://mlsanity.com/paper/2605.31231/) (2026)
- [Data Publishing in Mechanics and Dynamics: Challenges, Guidelines, and Examples from Engineering Design](https://mlsanity.com/paper/2410.18358/) (2024)
- [Recurrent U-Net-Based Graph Neural Network (RUGNN) for Accurate Deformation Predictions in Sheet Material Forming](https://mlsanity.com/paper/2507.11547/) (2025)
- [Information Security Based on LLM Approaches: A Review](https://mlsanity.com/paper/2507.18215/) (2025)
- [Graph Network-based Structural Simulator: Graph Neural Networks for Structural Dynamics](https://mlsanity.com/paper/2510.25683/) (2025)
- [Robustness investigation of cross-validation based quality measures for model assessment](https://mlsanity.com/paper/2408.04391/) (2024)
- [CNN-powered micro- to macro-scale flow modeling in deformable porous media](https://mlsanity.com/paper/2501.06466/) (2025)
- [Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks](https://mlsanity.com/paper/2506.17726/) (2025)
- [Trustworthy AI-based crack-tip segmentation using domain-guided explanations](https://mlsanity.com/paper/2507.20658/) (2025)
- [Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variables](https://mlsanity.com/paper/2508.00959/) (2025)
- [A Comparison of Surrogate Constitutive Models for Viscoplastic Creep Simulation of HT-9 Steel](https://mlsanity.com/paper/2509.22667/) (2025)
- [Contactless estimation of continuum displacement and mechanical compressibility from image series using a deep learning based framework](https://mlsanity.com/paper/2602.07065/) (2026)
- [Non-Invasive Reconstruction of Cardiac Activation Dynamics Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.03832/) (2026)
- [An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interaction](https://mlsanity.com/paper/2605.00937/) (2026)
- [Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges](https://mlsanity.com/paper/2606.20015/) (2026)
- [HyperShape: Hyperelasticity Across Diverse Shapes](https://mlsanity.com/paper/2608.09938/) (2026)

## Abstract (arXiv)

The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within this field, we provide an overview of deep learning in deterministic computational mechanics. Five main categories are identified and explored: simulation substitution, simulation enhancement, discretizations as neural networks, generative approaches, and deep reinforcement learning. This review focuses on deep learning methods rather than applications for computational mechanics, thereby enabling researchers to explore this field more effectively. As such, the review is not necessarily aimed at researchers with extensive knowledge of deep learning -- instead, the primary audience is researchers at the verge of entering this field or those who attempt to gain an overview of deep learning in computational mechanics. The discussed concepts are, therefore, explained as simple as possible.