Physics guided machine learning using simplified theories

Abstract

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.

References in corpus (17)

• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles
• Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks
• Deep Neural Networks for Data-Driven Turbulence Models
• Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks
• Sub-grid modelling for two-dimensional turbulence using neural networks
• Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
• Probabilistic neural networks for fluid flow surrogate modeling and data recovery
• Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
• Data-driven recovery of hidden physics in reduced order modeling of fluid flows
• Sub-grid scale model classification and blending through deep learning
• A long short-term memory embedding for hybrid uplifted reduced order models
• Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows
• Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence
• Fast divergence-conforming reduced basis methods for steady Navier-Stokes flow
• Interface learning in fluid dynamics: statistical inference of closures within micro-macro coupling models
• Interface learning of multiphysics and multiscale systems

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