Deep Generative Models that Solve PDEs: Distributed Computing for Training Large Data-Free Models

TL;DR

This paper introduces a distributed deep learning framework that enables training large-scale neural PDE solvers efficiently, overcoming previous computational limitations and demonstrating practical applicability in scientific computing.

Contribution

The paper presents a scalable software framework for distributed training of large neural PDE models, including novel features like loss integrity and distributed optimization methods.

Findings

Framework scales well on cloud and HPC clusters.

Distributed higher-order optimization is 2-3x faster than SGD.

Neural PDE solvers trained at unprecedented sizes.

Abstract

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been recently reported that successfully solve PDEs, with examples including deep feed forward networks, generative networks, and deep encoder-decoder networks. However, practical adoption of these approaches is limited by the difficulty in training these models, especially to make predictions at large output resolutions ($\geq 1024 \times 1024$). Here we report on a software framework for data parallel distributed deep learning that resolves the twin challenges of training these large SciML models - training in reasonable time as well as distributing the storage requirements. Our framework provides several out of the box functionality including (a) loss integrity independent of number of processes, (b) synchronized batch normalization, and (c) distributed higher-order optimization methods. We show excellent scalability of this framework on both cloud as well as HPC clusters, and report on the interplay between bandwidth, network topology and bare metal vs cloud. We deploy this approach to train generative models of sizes hitherto not possible, showing that neural PDE solvers can be viably trained for practical applications. We also demonstrate that distributed higher-order optimization methods are $2-3\times$ faster than stochastic gradient-based methods and provide minimal convergence drift with higher batch-size.