# Physics guided machine learning using simplified theories

arXiv: https://arxiv.org/abs/2012.13343 · HTML: https://mlsanity.com/paper/2012.13343/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2020.

## Built on by (most cited first, 23 of 23)

- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Physics guided neural networks for modelling of non-linear dynamics](https://mlsanity.com/paper/2205.06858/) (2022)
- [Deep neural network enabled corrective source term approach to hybrid analysis and modeling](https://mlsanity.com/paper/2105.11521/) (2021)
- [Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution](https://mlsanity.com/paper/2103.14629/) (2021)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directions](https://mlsanity.com/paper/2304.11405/) (2023)
- [Combining physics-based and data-driven techniques for reliable hybrid analysis and modeling using the corrective source term approach](https://mlsanity.com/paper/2206.03451/) (2022)
- [Deep Random Vortex Method for Simulation and Inference of Navier-Stokes Equations](https://mlsanity.com/paper/2206.09571/) (2022)
- [A Review on Organ Deformation Modeling Approaches for Reliable Surgical Navigation using Augmented Reality](https://mlsanity.com/paper/2408.02713/) (2024)
- [Physics Guided Machine Learning for Variational Multiscale Reduced Order Modeling](https://mlsanity.com/paper/2205.12419/) (2022)
- [A novel corrective-source term approach to modeling unknown physics in aluminum extraction process](https://mlsanity.com/paper/2209.10861/) (2022)
- [Differentiable modeling to unify machine learning and physical models and advance Geosciences](https://mlsanity.com/paper/2301.04027/) (2023)
- [Predicting Ship Responses in Different Seaways using a Generalizable Force Correcting Machine Learning Method](https://mlsanity.com/paper/2405.08033/) (2024)
- [Image features of a splashing drop on a solid surface extracted using a feedforward neural network](https://mlsanity.com/paper/2201.09541/) (2022)
- [A Manifold-based Airfoil Geometric-feature Extraction and Discrepant Data Fusion Learning Method](https://mlsanity.com/paper/2206.12254/) (2022)
- [Sparse deep neural networks for modeling aluminum electrolysis dynamics](https://mlsanity.com/paper/2209.05832/) (2022)
- [Decentralized digital twins of complex dynamical systems](https://mlsanity.com/paper/2207.12245/) (2022)
- [Accelerated Digital Twin Learning for Edge AI: A Comparison of FPGA and Mobile GPU](https://mlsanity.com/paper/2512.17941/) (2025)
- [Supplementation of deep neural networks with simplified physics-based features to increase model prediction accuracy](https://mlsanity.com/paper/2204.06764/) (2022)
- [DamFormer: Generalizing Morphologies in Dam Break Simulations Using Transformer Model](https://mlsanity.com/paper/2410.18998/) (2024)
- [Scientific machine learning in Hydrology: a unified perspective](https://mlsanity.com/paper/2506.06308/) (2025)
- [PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles](https://mlsanity.com/paper/2511.15522/) (2025)
- [Neural Operator based Multi-Field Reconstruction of Inner Solar Boundary State](https://mlsanity.com/paper/2608.22782/) (2026)

## Abstract (arXiv)

Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this letter, we introduce a modular physics guided machine learning framework to improve the accuracy of such data-driven predictive engines. The chief idea in our approach is to augment the knowledge of the simplified theories with the underlying learning process. To emphasise on their physical importance, our architecture consists of adding certain features at intermediate layers rather than in the input layer. To demonstrate our approach, we select a canonical airfoil aerodynamic problem with the enhancement of the potential flow theory. We include features obtained by a panel method that can be computed efficiently for an unseen configuration in our training procedure. By addressing the generalizability concerns, our results suggest that the proposed feature enhancement approach can be effectively used in many scientific machine learning applications, especially for the systems where we can use a theoretical, empirical, or simplified model to guide the learning module.