Understanding, Mapping, and Generating Microstructures with Higher-Order Statistic Euclidean Neural Networks
Abstract
Materials are intrinsically hierarchical, and their properties originate from geometric features at length scales that span 7 orders of magnitude, ranging from Angstroms (10-10 m) to millimeters (10-3 m). Traditional computational approaches require different frameworks for handling logarithmically different length scales. Such algorithms acquire the ability to emulate their assigned regime from specified governing equations or by the behaviors expressed in training data. Yet, nature does not draw boundaries between length scales, so why should we. To master materials, we first need a unified computational framework that spans all length scales. In this proposal, we present a plan to lay the path toward such a unified framework. This is possible by building on a special type of symmetry-preserving artificial neural network that the PI co-invented and whose developer community the PI leads- Euclidean Neural Networks (ENNs). Unlike the contemporary algorithms described above, the underlying mathematical machinery of ENNs is based on geometric tensors and the symmetries of 3D space, which are intrinsically true regardless of length scale. Computational algorithms built from ENNs are on an unprecedentedly equal footing with how nature itself computes reality. Using ENNs, we will develop algorithms that can automate the generation of hierarchical representations of geometry, capable of zooming-in and dynamically generating detail as needed. To do this, we will first develop the core theoretical foundations necessary to create ENN generative algorithms- efficient representations of statistical distributions over Euclidean and permutation symmetries, robust methods for sampling from these representations, and generative models that can represent variable sized structures in a symmetry-preserving manner. Once developed, we will investigate the latent representations they learn. These learned unified representations of atomistic systems will aid future efforts in (1) accelerating our understanding of multiscale materials phenomena, (2) aid in optimizing experiments, and (3) enable new strategies for materials design.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 05, 2025
- Source ID
- FA95502410067
Entities
People
- Tess Smidt
Organizations
- Air Force Office of Scientific Research
- Massachusetts Institute of Technology
- United States Air Force