arXiv subjects

Erik Thiede

Publications and source records attributed to Erik Thiede.

5 recordsLinked to original sources

arXiv2026

Mapping recrystallization trajectories in GaAs using latent space diffraction analysis

Recrystallization in disordered solids proceeds through a sequence of local structural rearrangements that are difficult to resolve using conventional diffraction analysis. In amorphous and partially ordered materials, subtle variations in diffuse scattering, short-range order, and defect-mediated symmetry emergence encode the pathways through which ordering initiates and propagates. Here, we introduce a latent space framework for mapping these pathways directly from \textit{in situ} 4D-STEM diffraction data. A convolutional autoencoder provides a compact representation of structural motifs, and unsupervised clustering identifies recurring microstructural states, including amorphous, paracrystalline, crystalline, twinned, and hybrid intermediates. By tracking these states across temperature, we construct phase trajectory models that reveal the topology of the recrystallization landscape, including metastable basins, branching pathways, hybrid states, and temperature-dependent reorganizations of accessible states. Applied to ion irradiated GaAs, this approach uncovers two distinct recrystallization regimes separated by a transition near 250\textdegree{}C. At low temperature, recrystallization is growth-dominated and dominated by the persistence of amorphous and crystalline states. At high temperature, the transformation landscape reorganizes: hybrid and faulted states become metastable precursors to twinning, polycrystalline regions stabilize, and twinned structures emerge as dominant end states. The latent space representation also identifies amorphous patterns with weak symmetry signatures that precede recrystallization. This reveals structural precursors to ordering that are not captured by conventional descriptors give new insights into how recrystallization is initiated.

cond-mat.mtrl-sci↗

arXiv2024

Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalism

Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard approach to such problems, with one of the most successful methods employing tensor products between various tensors that transform under the spatial group. However, as the number of different tensors and the complexity of relationships between them increase, maintaining parsimony and equivariance becomes increasingly challenging. In this paper, we propose using fusion diagrams, a technique widely employed in simulating SU($2$)-symmetric quantum many-body problems, to design new equivariant components for equivariant neural networks. This results in a diagrammatic approach to constructing novel neural network architectures. When applied to particles within a given local neighborhood, the resulting components, which we term "fusion blocks," serve as universal approximators of any continuous equivariant function defined in the neighborhood. We incorporate a fusion block into pre-existing equivariant architectures (Cormorant and MACE), leading to improved performance with fewer parameters on a range of challenging chemical problems. Furthermore, we apply group-equivariant neural networks to study non-adiabatic molecular dynamics of stilbene cis-trans isomerization. Our approach, which combines tensor networks with equivariant neural networks, suggests a potentially fruitful direction for designing more expressive equivariant neural networks.

cs.LG↗

arXiv2020

Stratification as a general variance reduction method for Markov chain Monte Carlo

The Eigenvector Method for Umbrella Sampling (EMUS) belongs to a popular class of methods in statistical mechanics which adapt the principle of stratified survey sampling to the computation of free energies. We develop a detailed theoretical analysis of EMUS. Based on this analysis, we show that EMUS is an efficient general method for computing averages over arbitrary target distributions. In particular, we show that EMUS can be dramatically more efficient than direct MCMC when the target distribution is multimodal or when the goal is to compute tail probabilities. To illustrate these theoretical results, we present a tutorial application of the method to a problem from Bayesian statistics.

stat.ME↗

arXiv2016

Eigenvector method for umbrella sampling enables error analysis

Umbrella sampling efficiently yields equilibrium averages that depend on exploring rare states of a model by biasing simulations to windows of coordinate values and then combining the resulting data with physical weighting. Here, we introduce a mathematical framework that casts the step of combining the data as an eigenproblem. The advantage to this approach is that it facilitates error analysis. We discuss how the error scales with the number of windows. Then, we derive a central limit theorem for averages that are obtained from umbrella sampling. The central limit theorem suggests an estimator of the error contributions from individual windows, and we develop a simple and computationally inexpensive procedure for implementing it. We demonstrate this estimator for simulations of the alanine dipeptide and show that it emphasizes low free energy pathways between stable states in comparison to existing approaches for assessing error contributions. We discuss the possibility of using the estimator and, more generally, the eigenvector method for umbrella sampling to guide adaptation of the simulation parameters to accelerate convergence.

cond-mat.stat-mech↗

arXiv2015

Sharp entrywise perturbation bounds for Markov chains

For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.

math.NA↗