We’ve recently posted first versions of our works that target deep learning for numerical simulations in the context of **metrics and reduced spaces**.

The first one, the **Learned Simulation Metric** (**LSiM**), employs a Siamese network architecture that is motivated by the mathematical properties of a metric. We leverage a controllable data generation setup with partial differential equation (PDE) solvers to create increasingly different outputs from a reference simulation in a controlled environment. A central component of our learned metric is a specialized loss function that introduces knowledge about the correlation between single data samples into the training process. We demonstrate it’s usefulness with a wide range of data sets, from fluid flow with Navier-Stokes, to weather data from real-world measurements.

The second paper targets **controlled latent space** mappings, i.e., a “subdivision” of the latent space vector for different physical fields. Here, we focus on single-phase smoke simulations in 2D and 3D based on the incompressible Navier-Stokes (NS) equations. To achieve stable predictions for long-term flow sequences, a convolutional neural network (CNN) is trained for spatial compression in combination with a temporal prediction network that consists of stacked Long Short-Term Memory (LSTM) layers. The central idea is a novel latent space subdivision (LSS) to separate the respective input quantities into individual parts of the encoded latent space domain. This allows to distinctively alter the encoded quantities without interfering with the remaining latent space values and hence maximizes external control.

For details you can check out our webpages for Learning Similarity Metrics for Numerical Simulations and Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow.