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 emphasize 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 the 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.

Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution

“…Therefore, one of the active research thrusts is to leverage methodologies for the combination of physics‐based and neural network models, a rapidly emerging field that came to be known as physics‐guided AI or physics‐guided ML (PGML). To this end, we have recently introduced a PGML framework where information from simplified physics‐based models is incorporated within neural network architectures to improve the generalizability of data‐driven models [258]. The central idea in the PGML framework is to embed the knowledge from simplified theories directly into an intermediate layer of the neural network as shown in Figure 2.…”

“…Usually, for the regression problems, the cost function is the mean squared error between true and predicted output, that is, . In the PGML framework [258], the neural network can be augmented with the output of the simplified physics‐based model. The features extracted from simplified physics‐based models are embedded into hidden layers along with latent variable.…”

“…As demonstrated in predicting aerodynamic loads [258], the PGML framework is successful in significantly reducing the model uncertainty (captured using the prediction from multiple models initialized with different parameters) of the neural network. It has been shown that the PGML framework also enhances the generalizability of the neural network based surrogate model since it predicts the quantity of interests more accurately for unseen conditions.…”

Information geometry for multiparameter models: New perspectives on the origin of simplicity

“…Furthermore, large black-box models also do not lead to explicit, declarative knowledge in the same way as minimal, parsimonious representation [87]. The nascent fields of explainable AI [88] and physics-guided machine learning [89][90][91] may also benefit from simplification in a context-adaptive way.…”

Image features of a splashing drop on a solid surface extracted using a feedforward neural network

“…For example, the ability of a deep convolutional neural network (CNN) to accurately classify images has been widely exploited in search engines, face recognition, and cancer diagnosis, among many other tasks [27,28,29,30]. Already in the field of fluid mechanics [31], ANNs have been utilized for various purposes [32,33,34,35,36,37,38,39], such as bubble pattern recognition [40], turbulence modeling [41,42,43], and classification of vortex wakes [44].…”