Topological data analysis of vortices in the magnetically-induced current density in LiH molecule

Olejniczak, Małgorzata; Tierny, Julien

doi:10.1039/d2cp05893f

Cited by 7 publications

(1 citation statement)

References 42 publications

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“…To address this issue, Topological Data Analysis (TDA) [28] has shown over the years its ability to reveal, in a generic, robust and efficient manner, the main structural patterns hidden in complex datasets, in particular for visual data analysis tasks [44]. Successful applications have been documented in multiple fields (turbulent combustion [19], [41], material sciences [43], [81], nuclear energy [57], fluid dynamics [49], [63], bioimaging [3], [14], quantum chemistry [64], [65] or astrophysics [79], [82]). Among the representations studied in TDA, the merge tree [22] (Fig.…”

Section: Introductionmentioning

confidence: 99%

Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

Pont¹,

Vidal²,

Tierny³

2023

IEEE Trans. Visual. Comput. Graphics

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This paper presents a computational framework for the Wasserstein auto-encoding of merge trees (MT-WAE), a novel extension of the classical auto-encoder neural network architecture to the Wasserstein metric space of merge trees. In contrast to traditional auto-encoders which operate on vectorized data, our formulation explicitly manipulates merge trees on their associated metric space at each layer of the network, resulting in superior accuracy and interpretability. Our novel neural network approach can be interpreted as a non-linear generalization of previous linear attempts [72] at merge tree encoding. It also trivially extends to persistence diagrams. Extensive experiments on public ensembles demonstrate the efficiency of our algorithms, with MT-WAE computations in the orders of minutes on average. We show the utility of our contributions in two applications adapted from previous work on merge tree encoding [72]. First, we apply MT-WAE to data reduction and reliably compress merge trees by concisely representing them with their coordinates in the final layer of our auto-encoder. Second, we document an application to dimensionality reduction, by exploiting the latent space of our auto-encoder, for the visual analysis of ensemble data. We illustrate the versatility of our framework by introducing two penalty terms, to help preserve in the latent space both the Wasserstein distances between merge trees, as well as their clusters. In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a C++ implementation that can be used for reproducibility.

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Section: Introductionmentioning

confidence: 99%

Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

Pont¹,

Vidal²,

Tierny³

2023

IEEE Trans. Visual. Comput. Graphics

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Interoperable workflows by exchanging grid-based data between quantum-chemical program packages

Focke,

De Santis,

Wolter

et al. 2024

The Journal of Chemical Physics

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Quantum-chemical subsystem and embedding methods require complex workflows that may involve multiple quantum-chemical program packages. Moreover, such workflows require the exchange of voluminous data that go beyond simple quantities, such as molecular structures and energies. Here, we describe our approach for addressing this interoperability challenge by exchanging electron densities and embedding potentials as grid-based data. We describe the approach that we have implemented to this end in a dedicated code, PyEmbed, currently part of a Python scripting framework. We discuss how it has facilitated the development of quantum-chemical subsystem and embedding methods and highlight several applications that have been enabled by PyEmbed, including wave-function theory (WFT) in density-functional theory (DFT) embedding schemes mixing non-relativistic and relativistic electronic structure methods, real-time time-dependent DFT-in-DFT approaches, the density-based many-body expansion, and workflows including real-space data analysis and visualization. Our approach demonstrates, in particular, the merits of exchanging (complex) grid-based data and, in general, the potential of modular software development in quantum chemistry, which hinges upon libraries that facilitate interoperability.

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