2022/11/21 by Chloe Paliard, Nils Thuerey, Paliard, Chloe +3 · 1 citation
Computer Science · Environmental Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Computer science #Degrees of freedom (physics and chemistry) #FOS: Computer and information sciences #Flow (mathematics) #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine learning #Mathematics #Model Reduction and Neural Networks #Physical space #Physics #Representation (politics) #Space (punctuation) #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.2211.11298
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore training deep neural network models in conjunction with physics simulations via partial differential equations (PDEs), using the simulated degrees of freedom as latent space for a neural network. In contrast to previous work, this paper treats the degrees of freedom of the simulated space purely as tools to be used by the neural network. We demonstrate this concept for learning reduced representations, as it is extremely challenging to faithfully preserve correct solutions over long time-spans with traditional reduced representations, particularly for solutions with large amounts of small scale features. This work focuses on the use of such physical, reduced latent space for the restoration of fine simulations, by training models that can modify the content of the reduced physical states as much as needed to best satisfy the learning objective. This autonomy allows the neural networks to discover alternate dynamics that significantly improve the performance in the given tasks. We demonstrate this concept for various fluid flows ranging from different turbulence scenarios to rising smoke plumes.