# A Review of Physics-based Machine Learning in Civil Engineering

arXiv: https://arxiv.org/abs/2110.04600 · HTML: https://mlsanity.com/paper/2110.04600/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 159 references that are in the map.
- First posted on arXiv 9 Oct 2021.

## Builds on (most cited first, 28 of 28)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Optimal approximation of continuous functions by very deep ReLU networks](https://mlsanity.com/paper/1802.03620/) (2018)
- [Deep Network Approximation for Smooth Functions](https://mlsanity.com/paper/2001.03040/) (2020)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [A unified deep artificial neural network approach to partial differential equations in complex geometries](https://mlsanity.com/paper/1711.06464/) (2017)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification](https://mlsanity.com/paper/1802.00850/) (2018)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks](https://mlsanity.com/paper/2008.13547/) (2020)
- [Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modeling](https://mlsanity.com/paper/1909.08118/) (2019)
- [HybridNet: Integrating Model-based and Data-driven Learning to Predict Evolution of Dynamical Systems](https://mlsanity.com/paper/1806.07439/) (2018)
- [JUNIPR: a Framework for Unsupervised Machine Learning in Particle Physics](https://mlsanity.com/paper/1804.09720/) (2018)
- [Physics Guided Machine Learning Methods for Hydrology](https://mlsanity.com/paper/2012.02854/) (2020)
- [Physics-Informed Neural Network Method for Solving One-Dimensional Advection Equation Using PyTorch](https://mlsanity.com/paper/2103.09662/) (2021)
- [Enhancing predictive skills in physically-consistent way: Physics Informed Machine Learning for Hydrological Processes](https://mlsanity.com/paper/2104.11009/) (2021)
- [Natural Language Processing Accurately Categorizes Indications, Findings and Pathology Reports from Multicenter Colonoscopy](https://mlsanity.com/paper/2108.11034/) (2021)

## Built on by (most cited first, 9 of 9)

- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity](https://mlsanity.com/paper/2303.13634/) (2023)
- [A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problems](https://mlsanity.com/paper/2406.02615/) (2024)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [Machine Learning-based Prediction of Porosity for Concrete Containing Supplementary Cementitious Materials](https://mlsanity.com/paper/2112.07353/) (2021)
- [Wastewater Pipe Condition Rating Model Using K- Nearest Neighbors](https://mlsanity.com/paper/2202.11049/) (2022)
- [Wastewater Pipe Rating Model Using Natural Language Processing](https://mlsanity.com/paper/2202.13871/) (2022)
- [Use of BNNM for interference wave solutions of the gBS-like equation and comparison with PINNs](https://mlsanity.com/paper/2210.12154/) (2022)
- [Estimating irregular water demands with physics-informed machine learning to inform leakage detection](https://mlsanity.com/paper/2309.02935/) (2023)

## Abstract (arXiv)

The recent development of machine learning (ML) and Deep Learning (DL) increases the opportunities in all the sectors. ML is a significant tool that can be applied across many disciplines, but its direct application to civil engineering problems can be challenging. ML for civil engineering applications that are simulated in the lab often fail in real-world tests. This is usually attributed to a data mismatch between the data used to train and test the ML model and the data it encounters in the real world, a phenomenon known as data shift. However, a physics-based ML model integrates data, partial differential equations (PDEs), and mathematical models to solve data shift problems. Physics-based ML models are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear equations. Physics-based ML, which takes center stage across many science disciplines, plays an important role in fluid dynamics, quantum mechanics, computational resources, and data storage. This paper reviews the history of physics-based ML and its application in civil engineering.