Machine learning strategies for systems with invariance properties

By Julia Ling, Reese E. Jones, Jeremy A. Templeton. Journal of Computational Physics, 2016

368 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d2b75239967af9a554f00dcde4c71be07bd25b95

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In Aerospace Engineering

In Statistical and Nonlinear Physics

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Citations in the corpus

A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database (2019, background): “The first approach enforces known physical constraints into data-driven models [32,33], which can be considered as a data-fit type surrogate model.”
Explainable Machine Learning for Scientific Insights and Discoveries (2019, methodology): “A related approach for RANS-modeled Reynolds stresses for high-speedflat-plate turbulent boundary layers was presented in [63], which uses a systematic approach with basis tensor invariants proposed by [64].”
Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils (2016, background): “Finally, respecting realizability limits [18,32] and invariance properties [31] will be”
Applications of Deep Learning to Ocean Data Inference and Subgrid Parameterization (2018, methodology): “A machine learning algorithm trained on region-limited data would have to adapt to new regions with different physics; this task is well suited to deepneuralnetworks,whichareknownforastrongabilitytogeneralize(Goodfellowetal.,2016;Krizhevsky et al., 2012; LeCun et al., 2015).”
Mean Field Analysis of Deep Neural Networks (2019, background): “Neural networks also find increasing more applications in engineering, robotics, medicine, and finance (see [21], [22], [43], [15], [32], [1], [36], [37], [38], and [39]).”
Turbulence Modeling in the Age of Data (2018, background): “The work of Ling and Templeton (2015) illustrated a scheme for crafting features based on ﬂow physics and normalizing them using local quantities; later work has expanded this approach by using invariants of a tensorial set (Ling et al. 2016a).”
Machine learning methods for turbulence modeling in subsonic flows around airfoils (2018, background): “[20-23] embedded the invariance property into deep neural networks firstly and demonstrated the advantage over the architecture without this property.”
Mean Field Analysis of Neural Networks: A Law of Large Numbers (2018, methodology): “Neural networks are being used in reduced-form models of the Navier--Stokes equation in turbulent conditions (see [34] and [35]).”
Machine Learning for Fluid Mechanics (2019, background): “This provides an innovative and simple approach to embed known physical symmetries and invariances into the learning architecture (Ling et al. 2016a), which we believe will be essential in future eﬀorts that combine learning for physics.”
Quantification of model uncertainty in RANS simulations: A review (2018, background): “, S, , p, k), referred to as the integrity basis [145].”
Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework (2017, methodology): “The systematic approach of invariant feature construction proposed in [15] is employed to expand the input space for given raw tensorial mean flow variables.”
Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data (2016, positive): “It is worth noting that the recent work of Ling et al. [31] aimed to relieve the modeler from such burdens by using a basis of invariants of tensors relevant in the speciﬁc application (e.g., strain rate S in turbulence modeling).”
Hamiltonian Neural Networks for solving differential equations (2020, neutral): “…and particularly neural networks (NNs), have been used to explore those data and forecast the future behavior of complex dynamical systems [1]–[5], improve turbulence models [6]–[9], discover differential equations (DEs) [10]– [13], and ﬁnd approximate solutions for those equations [14], [15].”
Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks (2018, neutral): “[17] considered deep neural networks to predict the anisotropic tensor using a neural network structure with embedded invariance [18].”