# A Combined Data-driven and Physics-driven Method for Steady Heat Conduction Prediction using Deep Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2005.08119 · HTML: https://mlsanity.com/paper/2005.08119/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2020.

## Built on by (most cited first, 5 of 5)

- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)
- [A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domain](https://mlsanity.com/paper/2203.08150/) (2022)
- [Image-based Artificial Intelligence empowered surrogate model and shape morpher for real-time blank shape optimisation in the hot stamping process](https://mlsanity.com/paper/2212.05885/) (2022)
- [Heat Conduction Plate Layout Optimization using Physics-driven Convolutional Neural Networks](https://mlsanity.com/paper/2201.10002/) (2022)

## Abstract (arXiv)

With several advantages and as an alternative to predict physics field, machine learning methods can be classified into two distinct types: data-driven relying on training data and physics-driven using physics law. Choosing heat conduction problem as an example, we compared the data- and physics-driven learning process with deep Convolutional Neural Networks (CNN). It shows that the convergences of the error to ground truth solution and the residual of heat conduction equation exhibit remarkable differences. Based on this observation, we propose a combined-driven method for learning acceleration and more accurate solutions. With a weighted loss function, reference data and physical equation are able to simultaneously drive the learning. Several numerical experiments are conducted to investigate the effectiveness of the combined method. For the data-driven based method, the introduction of physical equation not only is able to speed up the convergence, but also produces physically more consistent solutions. For the physics-driven based method, it is observed that the combined method is able to speed up the convergence up to 49.0% by using a not very restrictive coarse reference.