Deep learning of thermodynamics-aware reduced-order models from data
This work addresses the challenge of creating efficient, physics-aware reduced-order models for computational mechanics, offering a data-driven approach that ensures thermodynamic laws are preserved, which is incremental in combining existing techniques like autoencoders with structure-preserving networks.
The authors tackled the problem of learning reduced-order models for large-scale physical systems from data, developing a method that uses sparse autoencoders and structure-preserving neural networks to predict time evolution while conserving energy and entropy. They tested it on fluid and solid mechanics examples, achieving guaranteed thermodynamic consistency.
We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders, which reduce the dimensionality of the full order model to a set of sparse latent variables with no prior knowledge of the coded space dimensionality. Then, a second neural network is trained to learn the metriplectic structure of those reduced physical variables and predict its time evolution with a so-called structure-preserving neural network. This data-based integrator is guaranteed to conserve the total energy of the system and the entropy inequality, and can be applied to both conservative and dissipative systems. The integrated paths can then be decoded to the original full-dimensional manifold and be compared to the ground truth solution. This method is tested with two examples applied to fluid and solid mechanics.