A Taylor Based Sampling Scheme for Machine Learning in Computational Physics

Paul Novello (1, 2, 3) , Gaël Poëtte (1) , David Lugato (1) , Pietro Marco Congedo (2, 3)

1 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
2 X - École polytechnique
3 PLATON - Uncertainty Quantification in Scientific Computing and Engineering

Machine Learning (ML) is increasingly used to construct surrogate models for physical simulations. We take advantage of the ability to generate data using numerical simulations programs to train ML models better and achieve accuracy gain with no performance cost. We elaborate a new data sampling scheme based on Taylor approximation to reduce the error of a Deep Neural Network (DNN) when learning the solution of an ordinary differential equations (ODE) system.

Domaines: Physique mathématique [math-ph]; Machine Learning [stat.ML]

Paul Novello, Gaël Poëtte, David Lugato, Pietro Marco Congedo. A Taylor Based Sampling Scheme for Machine Learning in Computational Physics. 2019. ⟨hal-03114984v1⟩