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

Abstract

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.

23 pages 12 figures 1 table

References in corpus (15)

• Adam: A Method for Stochastic Optimization
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• An overview of gradient descent optimization algorithms
• Turbulence Modeling in the Age of Data
• Surrogate Modeling for Fluid Flows Based on Physics-Constrained Deep Learning Without Simulation Data
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Data-driven computational mechanics
• Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows
• Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks
• Accelerating Eulerian Fluid Simulation With Convolutional Networks
• Deep Learning the Physics of Transport Phenomena
• Deep Generative Markov State Models
• DNN and CNN with Weighted and Multi-task Loss Functions for Audio Event Detection
• Weakly-Supervised Deep Learning of Heat Transport via Physics Informed Loss

Cited by in corpus (4)

• Physics-driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks
• Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
• Generative Adversarial Networks with Physical Evaluators for Spray Simulation of Pintle Injector
• A study on using image based machine learning methods to develop the surrogate models of stamp forming simulations