Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanics

Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant challenge when dealing with real-world complex examples. In this work, we demonstrate three types of neural network architectures for efficient learning of highly non-linear deformations of solid bodies. The first two architectures are based on the recently proposed CNN U-NET and MAgNET (graph U-NET) frameworks which have shown promising performance for learning on mesh-based data. The third architecture is Perceiver IO, a very recent architecture that belongs to the family of attention-based neural networks--a class that has revolutionised diverse engineering fields and is still unexplored in computational mechanics. We study and compare the performance of all three networks on two benchmark examples, and show their capabilities to accurately predict the non-linear mechanical responses of soft bodies.

MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations

Mesh-based approaches are fundamental to solving physics-based simulations, however, they require significant computational efforts, especially for highly non-linear problems. Deep learning techniques accelerate physics-based simulations, however, they fail to perform efficiently as the size and complexity of the problem increases. Hence in this work, we propose MAgNET: Multi-channel Aggregation Network, a novel geometric deep learning framework for performing supervised learning on mesh-based graph data. MAgNET is based on the proposed MAg (Multichannel Aggregation) operation which generalises the concept of multi-channel local operations in convolutional neural networks to arbitrary non-grid inputs. MAg can efficiently perform non-linear regression mapping for graph-structured data. MAg layers are interleaved with the proposed novel graph pooling operations to constitute a graph U-Net architecture that is robust, handles arbitrary complex meshes and scales efficiently with the size of the problem. Although not limited to the type of discretisation, we showcase the predictive capabilities of MAgNET for several non-linear finite element simulations.

FEM-based Real-Time Simulations of Large Deformations with Probabilistic Deep Learning

For many engineering applications, such as real-time simulations or control, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive. In this work, we propose a highly efficient deep-learning surrogate framework that is able to predict the response of hyper-elastic bodies under load. The surrogate model takes the form of special convolutional neural network architecture, so-called U-Net, which is trained with force-displacement data obtained with the finite element method. We propose deterministic- and probabilistic versions of the framework and study it for three benchmark problems. In particular, we check the capabilities of the Maximum Likelihood and the Variational Bayes Inference formulations to assess the confidence intervals of solutions.

Machine learning in the social and health sciences

The uptake of machine learning (ML) approaches in the social and health sciences has been rather slow, and research using ML for social and health research questions remains fragmented. This may be due to the separate development of research in the computational/data versus social and health sciences as well as a lack of accessible overviews and adequate training in ML techniques for non data science researchers. This paper provides a meta-mapping of research questions in the social and health sciences to appropriate ML approaches, by incorporating the necessary requirements to statistical analysis in these disciplines. We map the established classification into description, prediction, and causal inference to common research goals, such as estimating prevalence of adverse health or social outcomes, predicting the risk of an event, and identifying risk factors or causes of adverse outcomes. This meta-mapping aims at overcoming disciplinary barriers and starting a fluid dialogue between researchers from the social and health sciences and methodologically trained researchers. Such mapping may also help to fully exploit the benefits of ML while considering domain-specific aspects relevant to the social and health sciences, and hopefully contribute to the acceleration of the uptake of ML applications to advance both basic and applied social and health sciences research.

Bayesian Convolutional Neural Networks as probabilistic surrogates for the fast prediction of stress fields in structures with microscale features

Finite Element Analysis (FEA) for stress prediction in structures with microstructural features is computationally expensive since those features are much smaller than the other geometric features of the structure. The accurate prediction of the additional stress generated by such microstructural features therefore requires a very fine FE mesh. Omitting or averaging the effect of the microstructural features from FEA models is standard practice, resulting in faster calculations of global stress fields, which, assuming some degree of scale separability, may then be complemented by local defect analyses. The purpose of this work is to train an Encoder-Decoder Convolutional Neural Networks (CNN) to automatically add local fine-scale stress corrections to coarse stress predictions around defects. We wish to understand to what extent such a framework may provide reliable stress predictions inside and outside the training set, i.e. for unseen coarse scale geometries and stress distributions and/or unseen defect geometries. Ultimately, we aim to develop efficient offline data generation and online data acquisition methods to maximise the domain of validity of the CNN predictions. To achieve these ambitious goals, we will deploy a Bayesian approach providing not point estimates, but credible intervals of the fine-scale stress field, as a means to evaluate the uncertainty of the predictions. The uncertainty quantified by the network will automatically encompass the lack of knowledge due to unseen macro and micro features, and the lack of knowledge due to the potential lack of scale separability. This uncertainty will be used in a Selective Learning framework to reduce the data requirements of the network. In this work we will investigate stress prediction in 2D composite structures with randomly distributed circular pores.