Physical invariance in neural networks for subgrid-scale scalar flux modeling
Hugo Frezat, Guillaume Balarac, Julien Le Sommer, Ronan Fablet, Redouane Lguensat
Abstract
A physics informed approach is applied to neural networks for subgrid-scale scalar flux modeling. We show that several invariances of the scalar transport equation are not enforced by existing parametric models, which reduce their interpretability and question their application. A new architecture embedding these invariances as hard and soft constraints is proposed. Through different flow configurations, we show that the proposed constraints increase both the performances and the generalization capabilities of the model.
Topics & Concepts
Scalar (mathematics)InterpretabilityArtificial neural networkGeneralizationEmbeddingParametric statisticsMathematicsPhysical systemApplied mathematicsComputer scienceFlow (mathematics)Flux (metallurgy)Statistical physicsControl theory (sociology)PhysicsArtificial intelligenceAttractorMathematical analysisDeep neural networksModel Reduction and Neural NetworksGenerative Adversarial Networks and Image SynthesisNeural Networks and Reservoir Computing