Theory-guided hard constraint projection (HCP): a knowledge-based data-driven scientific machine learning method

Abstract

Machine learning models have been successfully used in many scientific and engineering fields. However, it remains difficult for a model to simultaneously utilize domain knowledge and experimental observation data. The application of knowledge-based symbolic AI represented by an expert system is limited by the expressive ability of the model, and data-driven connectionism AI represented by neural networks is prone to produce predictions that violate physical mechanisms. In order to fully integrate domain knowledge with observations, and make full use of the prior information and the strong fitting ability of neural networks, this study proposes theory-guided hard constraint projection (HCP). This model converts physical constraints, such as governing equations, into a form that is easy to handle through discretization, and then implements hard constraint optimization through projection. Based on rigorous mathematical proofs, theory-guided HCP can ensure that model predictions strictly conform to physical mechanisms in the constraint patch. The performance of the theory-guided HCP is verified by experiments based on the heterogeneous subsurface flow problem. Due to the application of hard constraints, compared with fully connected neural networks and soft constraint models, such as theory-guided neural networks and physics-informed neural networks, theory-guided HCP requires fewer data, and achieves higher prediction accuracy and stronger robustness to noisy observations.

arXiv comment31 pages, 20 figures, 1 table

References in corpus (19)

• Semi-Supervised Classification with Graph Convolutional Networks
• An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications
• Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
• Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
• Enforcing Analytic Constraints in Neural-Networks Emulating Physical Systems
• Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
• Deep Learning of Subsurface Flow via Theory-guided Neural Network
• Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling
• PDE-Net: Learning PDEs from Data
• The Neural Particle Method -- An Updated Lagrangian Physics Informed Neural Network for Computational Fluid Dynamics
• Towards Interpretable Deep Neural Networks by Leveraging Adversarial Examples
• Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence
• Towards Interpretable Deep Neural Networks by Leveraging Adversarial Examples
• Physics Constrained Learning for Data-driven Inverse Modeling from Sparse Observations
• Deep Learning of Dynamic Subsurface Flow via Theory-guided Generative Adversarial Network
• Physics-constrained indirect supervised learning

Cited by in corpus (7)

• Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios
• Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)
• Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator
• HANNA: Hard-constraint Neural Network for Consistent Activity Coefficient Prediction
• RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Network
• Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning framework
• Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations