Chris Cantwell

Mario Lino, Stathi Fotiadis, Anil A. Bharath et al.

Numerical simulators are essential tools in the study of natural fluid-systems, but their performance often limits application in practice. Recent machine-learning approaches have demonstrated their ability to accelerate spatio-temporal predictions, although, with only moderate accuracy in comparison. Here we introduce MultiScaleGNN, a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics in problems encompassing a range of length scales and complex boundary geometries. We demonstrate this method on advection problems and incompressible fluid dynamics, both fundamental phenomena in oceanic and atmospheric processes. Our results show good extrapolation to new domain geometries and parameters for long-term temporal simulations. Simulations obtained with MultiScaleGNN are between two and four orders of magnitude faster than those on which it was trained.

Mario Lino, Stati Fotiadis, Anil A. Bharath et al.

Numerical simulation is an essential tool in many areas of science and engineering, but its performance often limits application in practice or when used to explore large parameter spaces. On the other hand, surrogate deep learning models, while accelerating simulations, often exhibit poor accuracy and ability to generalise. In order to improve these two factors, we introduce REMuS-GNN, a rotation-equivariant multi-scale model for simulating continuum dynamical systems encompassing a range of length scales. REMuS-GNN is designed to predict an output vector field from an input vector field on a physical domain discretised into an unstructured set of nodes. Equivariance to rotations of the domain is a desirable inductive bias that allows the network to learn the underlying physics more efficiently, leading to improved accuracy and generalisation compared with similar architectures that lack such symmetry. We demonstrate and evaluate this method on the incompressible flow around elliptical cylinders.

Mario Lino, Chris Cantwell, Anil A. Bharath et al.

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine learning approaches have demonstrated their ability to accelerate spatio-temporal predictions, although, with only moderate accuracy in comparison. Here we introduce MultiScaleGNN, a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics. MultiScaleGNN represents the physical domain as an unstructured set of nodes, and it constructs one or more graphs, each of them encoding different scales of spatial resolution. Successive learnt message passing between these graphs improves the ability of GNNs to capture and forecast the system state in problems encompassing a range of length scales. Using graph representations, MultiScaleGNN can impose periodic boundary conditions as an inductive bias on the edges in the graphs, and achieve independence to the nodes' positions. We demonstrate this method on advection problems and incompressible fluid dynamics. Our results show that the proposed model can generalise from uniform advection fields to high-gradient fields on complex domains at test time and infer long-term Navier-Stokes solutions within a range of Reynolds numbers. Simulations obtained with MultiScaleGNN are between two and four orders of magnitude faster than the ones on which it was trained.

Mario Lino, Chris Cantwell, Stathi Fotiadis et al.

We investigate the performance of fully convolutional networks to simulate the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net architecture and analyse how well it generalises to geometric configurations not seen during training. We demonstrate that a modified U-Net architecture is capable of accurately predicting the height distribution of waves on a liquid surface within curved and multi-faceted open and closed geometries, when only simple box and right-angled corner geometries were seen during training. We also consider a separate and independent 3D CNN for performing time-interpolation on the predictions produced by our U-Net. This allows generating simulations with a smaller time-step size than the one the U-Net has been trained for.

Stathi Fotiadis, Eduardo Pignatelli, Mario Lino Valencia et al.

Dynamical systems can be modelled by partial differential equations and numerical computations are used everywhere in science and engineering. In this work, we investigate the performance of recurrent and convolutional deep neural network architectures to predict the surface waves. The system is governed by the Saint-Venant equations. We improve on the long-term prediction over previous methods while keeping the inference time at a fraction of numerical simulations. We also show that convolutional networks perform at least as well as recurrent networks in this task. Finally, we assess the generalisation capability of each network by extrapolating in longer time-frames and in different physical settings.

Jeremy Cohen, Chris Cantwell, Neil Chue Hong et al.

Developing software to undertake complex, compute-intensive scientific processes requires a challenging combination of both specialist domain knowledge and software development skills to convert this knowledge into efficient code. As computational platforms become increasingly heterogeneous and newer types of platform such as Infrastructure-as-a-Service (IaaS) cloud computing become more widely accepted for HPC computations, scientists require more support from computer scientists and resource providers to develop efficient code and make optimal use of the resources available to them. As part of the libhpc stage 1 and 2 projects we are developing a framework to provide a richer means of job specification and efficient execution of complex scientific software on heterogeneous infrastructure. The use of such frameworks has implications for the sustainability of scientific software. In this paper we set out our developing understanding of these challenges based on work carried out in the libhpc project.