# Theory-Guided Machine Learning for Process Simulation of Advanced Composites

arXiv: https://arxiv.org/abs/2103.16010 · HTML: https://mlsanity.com/paper/2103.16010/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 59 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils](https://mlsanity.com/paper/1608.03990/) (2016)
- [An Iterative Scientific Machine Learning Approach for Discovery of Theories Underlying Physical Phenomena](https://mlsanity.com/paper/1909.13718/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Machine Learning Framework for Real-time Inverse Modeling and Multi-objective Process Optimization of Composites for Active Manufacturing Control](https://mlsanity.com/paper/2104.11342/) (2021)
- [Residual fourier neural operator for thermochemical curing of composites](https://mlsanity.com/paper/2111.10262/) (2021)
- [Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics](https://mlsanity.com/paper/2606.02145/) (2026)

## Abstract (arXiv)

Science-based simulation tools such as Finite Element (FE) models are routinely used in scientific and engineering applications. While their success is strongly dependent on our understanding of underlying governing physical laws, they suffer inherent limitations including trade-off between fidelity/accuracy and speed. The recent rise of Machine Learning (ML) proposes a theory-agnostic paradigm. In complex multi-physics problems, however, creating large enough datasets for successful training of ML models has proven to be challenging. One promising strategy to bridge the divide between these approaches and take advantage of their respective strengths is Theory-Guided Machine Learning (TGML) which aims to integrate physical laws into ML algorithms. In this paper, three case studies on thermal management during processing of advanced composites are presented and studied using FE, ML and TGML. A structured approach to incrementally adding increasingly complex physics to training of TGML model is presented. The benefits of TGML over ML models are seen in more accurate predictions, particularly outside the training region, and ability to train with small datasets. One benefit of TGML over FE is significant speed improvement to potentially develop real-time feedback systems. A recent successful implementation of a TGML model to assess producibility of aerospace composite parts is presented.