A Fast Learning-Based Surrogate of Electrical Machines using a Reduced Basis

A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs, which are PDEs that depend on a set of parameters but are also temporal and spatial processes. Our contribution is a method hybridizing the Proper Orthogonal Decomposition and several Support Vector Regression machines. This method is conceived to work in real-time, thus aimed for being used in the context of digital twins, where a user can perform an interactive analysis of results based on the proposed surrogate. We present promising results on two use cases concerning electrical machines. These use cases are not toy examples but are produced an industrial computational code, they use meshes representing non-trivial geometries and contain non-linearities.

High Throughput Training of Deep Surrogates from Large Ensemble Runs

Recent years have seen a surge in deep learning approaches to accelerate numerical solvers, which provide faithful but computationally intensive simulations of the physical world. These deep surrogates are generally trained in a supervised manner from limited amounts of data slowly generated by the same solver they intend to accelerate. We propose an open-source framework that enables the online training of these models from a large ensemble run of simulations. It leverages multiple levels of parallelism to generate rich datasets. The framework avoids I/O bottlenecks and storage issues by directly streaming the generated data. A training reservoir mitigates the inherent bias of streaming while maximizing GPU throughput. Experiment on training a fully connected network as a surrogate for the heat equation shows the proposed approach enables training on 8TB of data in 2 hours with an accuracy improved by 47% and a batch throughput multiplied by 13 compared to a traditional offline procedure.

Training Deep Surrogate Models with Large Scale Online Learning

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of computationally demanding solvers. Recently, deep learning algorithms have emerged as a viable alternative for obtaining fast solutions for PDEs. Models are usually trained on synthetic data generated by solvers, stored on disk and read back for training. This paper advocates that relying on a traditional static dataset to train these models does not allow the full benefit of the solver to be used as a data generator. It proposes an open source online training framework for deep surrogate models. The framework implements several levels of parallelism focused on simultaneously generating numerical simulations and training deep neural networks. This approach suppresses the I/O and storage bottleneck associated with disk-loaded datasets, and opens the way to training on significantly larger datasets. Experiments compare the offline and online training of four surrogate models, including state-of-the-art architectures. Results indicate that exposing deep surrogate models to more dataset diversity, up to hundreds of GB, can increase model generalization capabilities. Fully connected neural networks, Fourier Neural Operator (FNO), and Message Passing PDE Solver prediction accuracy is improved by 68%, 16% and 7%, respectively.

Simulation-Based Parallel Training

Numerical simulations are ubiquitous in science and engineering. Machine learning for science investigates how artificial neural architectures can learn from these simulations to speed up scientific discovery and engineering processes. Most of these architectures are trained in a supervised manner. They require tremendous amounts of data from simulations that are slow to generate and memory greedy. In this article, we present our ongoing work to design a training framework that alleviates those bottlenecks. It generates data in parallel with the training process. Such simultaneity induces a bias in the data available during the training. We present a strategy to mitigate this bias with a memory buffer. We test our framework on the multi-parametric Lorenz's attractor. We show the benefit of our framework compared to offline training and the success of our data bias mitigation strategy to capture the complex chaotic dynamics of the system.