Reduced-order modeling of unsteady fluid flow using neural network ensembles

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at handling data that are spatially distributed, including solutions to partial differential equations. When applied to unsteady physics problems, ROMs also require a model for time-series prediction of the low-dimensional latent variables. Long short-term memory (LSTM) networks, a type of recurrent neural network useful for modeling sequential data, are frequently employed in data-driven ROMs for autoregressive time-series prediction. When making predictions at unseen design points over long time horizons, error propagation is a frequently encountered issue, where errors made early on can compound over time and lead to large inaccuracies. In this work, we propose using bagging, a commonly used ensemble learning technique, to develop a fully data-driven ROM framework referred to as the CAE-eLSTM ROM that uses CAEs for spatial reconstruction of the full-order model and LSTM ensembles for time-series prediction. When applied to two unsteady fluid dynamics problems, our results show that the presented framework effectively reduces error propagation and leads to more accurate time-series prediction of latent variables at unseen points.

XLB: Distributed Multi-GPU Lattice Boltzmann Simulation Framework for Differentiable Scientific Machine Learning

The lattice Boltzmann method (LBM) has emerged as a prominent technique for solving fluid dynamics problems due to its algorithmic potential for computational scalability. We introduce XLB framework, a Python-based differentiable LBM library which harnesses the capabilities of the JAX framework. The architecture of XLB is predicated upon ensuring accessibility, extensibility, and computational performance, enabling scaling effectively across CPU, multi-GPU, and distributed multi-GPU systems. The framework can be readily augmented with novel boundary conditions, collision models, or simulation capabilities. XLB offers the unique advantage of integration with JAX's extensive machine learning echosystem, and the ability to utilize automatic differentiation for tackling physics-based machine learning, optimization, and inverse problems. XLB has been successfully scaled to handle simulations with billions of cells, achieving giga-scale lattice updates per second. XLB is released under the permissive Apache-2.0 license and is available on GitHub at https://github.com/Autodesk/XLB.