Peerasait Prachaseree

Saeed Mohammadzadeh, Peerasait Prachaseree, Emma Lejeune

Recently, there has been a growing interest in applying machine learning methods to problems in engineering mechanics. In particular, there has been significant interest in applying deep learning techniques to predicting the mechanical behavior of heterogeneous materials and structures. Researchers have shown that deep learning methods are able to effectively predict mechanical behavior with low error for systems ranging from engineered composites, to geometrically complex metamaterials, to heterogeneous biological tissue. However, there has been comparatively little attention paid to deep learning model calibration, i.e., the match between predicted probabilities of outcomes and the true probabilities of outcomes. In this work, we perform a comprehensive investigation into ML model calibration across seven open access engineering mechanics datasets that cover three distinct types of mechanical problems. Specifically, we evaluate both model and model calibration error for multiple machine learning methods, and investigate the influence of ensemble averaging and post hoc model calibration via temperature scaling. Overall, we find that ensemble averaging of deep neural networks is both an effective and consistent tool for improving model calibration, while temperature scaling has comparatively limited benefits. Looking forward, we anticipate that this investigation will lay the foundation for future work in developing mechanics specific approaches to deep learning model calibration.

Peerasait Prachaseree, Emma Lejeune

Engineered systems typically separate mechanical function from information processing, whereas biological systems can exploit physical structure as a medium for information processing and computation. Motivated by this contrast, recent work in mechanics has explored embedding information-processing capabilities directly into mechanical structures. However, quantitative frameworks for evaluating such capabilities remain limited. Here we address a foundational question: how does information propagate through a solid body? Using elastic bodies as a model system, we apply information-theoretic tools to treat an elastic domain as an information encoder and quantify how information transmits from applied loads to discrete sensor locations. We further connect these measures to familiar mechanical phenomena, including Saint-Venant's effect and principal stress lines. Moving toward design, we show how geometry and architected materials can tune transmission, enabling elastic domains to either transmit or block information. Overall, this work advances quantifiable metrics and benchmark tasks for mechanical intelligence, supporting comparable designs of mechanically embodied information processing.

Peerasait Prachaseree, Emma Lejeune

From designing architected materials to connecting mechanical behavior across scales, computational modeling is a critical tool in solid mechanics. Recently, there has been a growing interest in using machine learning to reduce the computational cost of physics-based simulations. Notably, while machine learning approaches that rely on Graph Neural Networks (GNNs) have shown success in learning mechanics, the performance of GNNs has yet to be investigated on a myriad of solid mechanics problems. In this work, we examine the ability of GNNs to predict a fundamental aspect of mechanically driven emergent behavior: the connection between a column's geometric structure and the direction that it buckles. To accomplish this, we introduce the Asymmetric Buckling Columns (ABC) dataset, a dataset comprised of three sub-datasets of asymmetric and heterogeneous column geometries where the goal is to classify the direction of symmetry breaking (left or right) under compression after the onset of instability. Because of complex local geometry, the "image-like" data representations required for implementing standard convolutional neural network based metamodels are not ideal, thus motivating the use of GNNs. In addition to investigating GNN model architecture, we study the effect of different input data representation approaches, data augmentation, and combining multiple models as an ensemble. While we were able to obtain good results, we also showed that predicting solid mechanics based emergent behavior is non-trivial. Because both our model implementation and dataset are distributed under open-source licenses, we hope that future researchers can build on our work to create enhanced mechanics-specific machine learning pipelines for capturing the behavior of complex geometric structures.