machine learning

Deep Conservation: A latent dynamics model for exact satisfaction of physical conservation laws

This work proposes an approach for latent dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, we compute a low-dimensional embedding of the high-dimensional dynamical-system state using deep …

Time-series machine-learning error models for approximate solutions to parameterized dynamical systems

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in [Freno, Carlberg, …

Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning

Data I/O poses a significant bottleneck in large-scale CFD simulations; thus, practitioners would like to significantly reduce the number of times the solution is saved to disk, yet retain the ability to recover any field quantity (at any time …

Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations

This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an …

Error modeling for surrogates of dynamical systems using machine learning

A machine-learning-based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (e.g., random forests, LASSO) to map a …

The ROMES method for statistical modeling of reduced-order-model error

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive 'error indicators' to a …