Spectroscopy-Guided Discovery of Three-Dimensional Structures of Disordered Materials with Diffusion Models

The ability to rapidly develop materials with desired properties has a transformative impact on a broad range of emerging technologies. In this work, we introduce a new framework based on the diffusion model, a recent generative machine learning method to predict 3D structures of disordered materials from a target property. For demonstration, we apply the model to identify the atomic structures of amorphous carbons ($a$-C) as a representative material system from the target X-ray absorption near edge structure (XANES) spectra--a common experimental technique to probe atomic structures of materials. We show that conditional generation guided by XANES spectra reproduces key features of the target structures. Furthermore, we show that our model can steer the generative process to tailor atomic arrangements for a specific XANES spectrum. Finally, our generative model exhibits a remarkable scale-agnostic property, thereby enabling generation of realistic, large-scale structures through learning from a small-scale dataset (i.e., with small unit cells). Our work represents a significant stride in bridging the gap between materials characterization and atomic structure determination; in addition, it can be leveraged for materials discovery in exploring various material properties as targeted.

Stratified-NMF for Heterogeneous Data

Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different locations, which may exhibit heterogeneity. We resolve this problem by solving a modified NMF objective, Stratified-NMF, that simultaneously learns strata-dependent statistics and a shared topics matrix. We develop multiplicative update rules for this novel objective and prove convergence of the objective. Then, we experiment on synthetic data to demonstrate the efficiency and accuracy of the method. Lastly, we apply our method to three real world datasets and empirically investigate their learned features.

Efficient Algorithms for the CCA Family: Unconstrained Objectives with Unbiased Gradients

The Canonical Correlation Analysis (CCA) family of methods is foundational in multi-view learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and unified with a Generalized Eigenvalue Problem (GEP) framework. However, classical algorithms for these linear methods are computationally infeasible for large-scale data. Extensions to Deep CCA show great promise, but current training procedures are slow and complicated. First we propose a novel unconstrained objective that characterizes the top subspace of GEPs. Our core contribution is a family of fast algorithms for stochastic PLS, stochastic CCA, and Deep CCA, simply obtained by applying stochastic gradient descent (SGD) to the corresponding CCA objectives. These methods show far faster convergence and recover higher correlations than the previous state-of-the-art on all standard CCA and Deep CCA benchmarks. This speed allows us to perform a first-of-its-kind PLS analysis of an extremely large biomedical dataset from the UK Biobank, with over 33,000 individuals and 500,000 variants. Finally, we not only match the performance of `CCA-family' Self-Supervised Learning (SSL) methods on CIFAR-10 and CIFAR-100 with minimal hyper-parameter tuning, but also establish the first solid theoretical links to classical CCA, laying the groundwork for future insights.

Novel Batch Active Learning Approach and Its Application to Synthetic Aperture Radar Datasets

Active learning improves the performance of machine learning methods by judiciously selecting a limited number of unlabeled data points to query for labels, with the aim of maximally improving the underlying classifier's performance. Recent gains have been made using sequential active learning for synthetic aperture radar (SAR) data arXiv:2204.00005. In each iteration, sequential active learning selects a query set of size one while batch active learning selects a query set of multiple datapoints. While batch active learning methods exhibit greater efficiency, the challenge lies in maintaining model accuracy relative to sequential active learning methods. We developed a novel, two-part approach for batch active learning: Dijkstra's Annulus Core-Set (DAC) for core-set generation and LocalMax for batch sampling. The batch active learning process that combines DAC and LocalMax achieves nearly identical accuracy as sequential active learning but is more efficient, proportional to the batch size. As an application, a pipeline is built based on transfer learning feature embedding, graph learning, DAC, and LocalMax to classify the FUSAR-Ship and OpenSARShip datasets. Our pipeline outperforms the state-of-the-art CNN-based methods.

Multi-modal Variational Autoencoders for normative modelling across multiple imaging modalities

One of the challenges of studying common neurological disorders is disease heterogeneity including differences in causes, neuroimaging characteristics, comorbidities, or genetic variation. Normative modelling has become a popular method for studying such cohorts where the 'normal' behaviour of a physiological system is modelled and can be used at subject level to detect deviations relating to disease pathology. For many heterogeneous diseases, we expect to observe abnormalities across a range of neuroimaging and biological variables. However, thus far, normative models have largely been developed for studying a single imaging modality. We aim to develop a multi-modal normative modelling framework where abnormality is aggregated across variables of multiple modalities and is better able to detect deviations than uni-modal baselines. We propose two multi-modal VAE normative models to detect subject level deviations across T1 and DTI data. Our proposed models were better able to detect diseased individuals, capture disease severity, and correlate with patient cognition than baseline approaches. We also propose a multivariate latent deviation metric, measuring deviations from the joint latent space, which outperformed feature-based metrics.

Score-based denoising for atomic structure identification

We propose an accurate method for removing thermal vibrations that complicate the task of analyzing complex dynamics in atomistic simulation of condensed matter. Our method iteratively subtracts thermal noises or perturbations in atomic positions using a denoising score function trained on synthetically noised but otherwise perfect crystal lattices. The resulting denoised structures clearly reveal underlying crystal order while retaining disorder associated with crystal defects. Purely geometric, agnostic to interatomic potentials, and trained without inputs from explicit simulations, our denoiser can be applied to simulation data generated from vastly different interatomic interactions. Followed by a simple phase classification tool such as the Common Neighbor Analysis, the denoiser outperforms other existing methods and reaches perfect classification accuracy on a recently proposed benchmark dataset consisting of perturbed crystal structures (DC3). Demonstrated here in a wide variety of atomistic simulation contexts, the denoiser is general, robust, and readily extendable to delineate order from disorder in structurally and chemically complex materials.

An iterative unbiased geometric approach to identifying crystalline order and disorder via denoising score function model

In atomistic simulations of solids, ability to classify crystal phases and lattice defects in the presence of thermal fluctuations is essential for gaining deeper insights into the simulated dynamics. The need for accurate and efficient characterization methods is especially acute in presently emerging large-scale simulations of multi-phase systems far from equilibrium. Taking the perspective that delineating order and disorder features from ubiquitous thermal vibrations is akin to extracting signal from noise, we consider classification of ordered phases and identification of disordered crystal defects to be fundamentally the same problem and address them both with a unified approach: a denoising score function that removes thermal noise and recovers any underlying crystalline order-disorder. Built on a rotationally equivariant graph neural network (NequIP), the denoiser was trained entirely with synthetically noised structures and requires no simulation data during training. To demonstrate its denoising capabilities, the denoiser is shown to effectively remove thermal vibrations of BCC, FCC, and HCP crystal structures without impacting the underlying disordered defects, including point defects, dislocations, grain boundaries, and liquid disorder. In particular the denoiser was applied to two relatively complex MD simulations that present practical challenges: a Cu solidification trajectory involving a polymorphic nucleus, and a trajectory of BCC Ta undergoing plastic deformation resulting in dislocation networks and point defect clusters. In both cases the denoiser facilitates or trivializes the subsequent characterization of the order-disorder features. Lastly, we outline future work to extend our denoising model to more complex crystal structures and to multi-element systems.

A Generalized EigenGame with Extensions to Multiview Representation Learning

Generalized Eigenvalue Problems (GEPs) encompass a range of interesting dimensionality reduction methods. Development of efficient stochastic approaches to these problems would allow them to scale to larger datasets. Canonical Correlation Analysis (CCA) is one example of a GEP for dimensionality reduction which has found extensive use in problems with two or more views of the data. Deep learning extensions of CCA require large mini-batch sizes, and therefore large memory consumption, in the stochastic setting to achieve good performance and this has limited its application in practice. Inspired by the Generalized Hebbian Algorithm, we develop an approach to solving stochastic GEPs in which all constraints are softly enforced by Lagrange multipliers. Then by considering the integral of this Lagrangian function, its pseudo-utility, and inspired by recent formulations of Principal Components Analysis and GEPs as games with differentiable utilities, we develop a game-theory inspired approach to solving GEPs. We show that our approaches share much of the theoretical grounding of the previous Hebbian and game theoretic approaches for the linear case but our method permits extension to general function approximators like neural networks for certain GEPs for dimensionality reduction including CCA which means our method can be used for deep multiview representation learning. We demonstrate the effectiveness of our method for solving GEPs in the stochastic setting using canonical multiview datasets and demonstrate state-of-the-art performance for optimizing Deep CCA.

Efficient, Interpretable Atomistic Graph Neural Network Representation for Angle-dependent Properties and its Application to Optical Spectroscopy Prediction

Graph neural networks (GNNs) are attractive for learning properties of atomic structures thanks to their intuitive, physically informed graph encoding of atoms and bonds. However, conventional GNN encodings do not account for angular information, which is critical for describing complex atomic arrangements in disordered materials, interfaces, and molecular distortions. In this work, we extend the recently proposed ALIGNN encoding, which incorporates bond angles, to also include dihedral angles (ALIGNN-d), and we apply the model to capture the structures of aqua copper complexes for spectroscopy prediction. This simple extension is shown to lead to a memory-efficient graph representation capable of capturing the full geometric information of atomic structures. Specifically, the ALIGNN-d encoding is a sparse yet equally expressive representation compared to the dense, maximally-connected graph, in which all bonds are encoded. We also explore model interpretability based on ALIGNN-d by elucidating the relative contributions of individual structural components to the optical response of the copper complexes. Lastly, we briefly discuss future developments to validate the computational efficiency and to extend the interpretability of ALIGNN-d.