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Electronic structure simulations allow researchers to compute fundamental properties of materials without the need for experimentation. As such, they routinely aid in propelling scientific advancements across materials science and chemical applications. Over the past decades, density functional theory (DFT) has emerged as the most popular technique for electronic structure simulations, due to its excellent balance between accuracy and computational cost. Yet, pressing societal and technological questions demand solutions for problems of ever-increasing complexity. Even the most efficient DFT implementations are no longer capable of providing answers in an adequate amount of time and with available computational resources. Thus, there is a growing interest in machine learning (ML) based approaches within the electronic structure community, aimed at providing models that replicate the predictive power of DFT at negligible cost. Within this work it will be shown that such ML-DFT approaches, up until now, do not succeed in fully encapsulating the level of electronic structure predictions DFT provides. Based on this assessment, a novel approach to ML-DFT models is presented within this thesis. An exhaustive framework for training ML-DFT models based on a local representation of the electronic structure is developed, including minute treatment of technical issues such as data generation techniques and hyperparameter optimization strategies. Models found via this framework recover the wide array of predictive capabilities of DFT simulations at drastically reduced cost, while retaining DFT levels of accuracy. It is further demonstrated how such models can be used across differently sized atomic systems, phase boundaries and temperature ranges, underlining the general usefulness of this approach.

We present the Materials Learning Algorithms (MALA) package, a scalable machine learning framework designed to accelerate density functional theory (DFT) calculations suitable for large-scale atomistic simulations. Using local descriptors of the atomic environment, MALA models efficiently predict key electronic observables, including local density of states, electronic density, density of states, and total energy. The package integrates data sampling, model training and scalable inference into a unified library, while ensuring compatibility with standard DFT and molecular dynamics codes. We demonstrate MALA's capabilities with examples including boron clusters, aluminum across its solid-liquid phase boundary, and predicting the electronic structure of a stacking fault in a large beryllium slab. Scaling analyses reveal MALA's computational efficiency and identify bottlenecks for future optimization. With its ability to model electronic structures at scales far beyond standard DFT, MALA is well suited for modeling complex material systems, making it a versatile tool for advanced materials research.

DeGeCI is a command line tool that generates fully automated de novo gene predictions from mitochondrial nucleotide sequences by using a reference database of annotated mitogenomes which is represented as a de Bruijn graph. The input genome is mapped to this graph, creating a subgraph, which is then post-processed by a clustering routine. Version 1.1 of DeGeCI offers a web front-end for GUI-based input. It also introduces a new taxonomic filter pipeline that allows the species in the reference database to be restricted to a user-specified taxonomic classification and allows for gene boundary optimization when providing the translation table of the input genome.

This repository contains data to test, develop and debug MALA and MALA based runscripts. If you plan to do machine-learning tests ("Does this network implementation work? Is this new data loading strategy working?"), this is the right data to test with. It is NOT production level data!

Retrained Models and Scripts for Aluminum at 298K and 933K Authors - Fiedler, Lenz (HZDR/CASUS) - Cangi, Attila (HZDR/CASUS) Affiliations: HZDR - Helmholtz-Zentrum Dresden-Rossendorf CASUS - Center for Advanced Systems Understanding Data set description This data sets contains models, scripts and inference results for aluminum at room temperature and the melting point. Training data, hyperparameters and general methodology follow Ref. [1]. The models here are retrained versions of the ones discussed in this publication, and therefore retrained versions of the models contained in Ref. [2]. As such, data from Ref. [2] has been used. Only a subset of models contained in Ref. [1] have been retrained, namely the room temperature model, one liquid and one solid melting point model with four training snapshot each, and the final melting point hybrid model (six training snapshots per phase). Furthermore, for both the hybrid melting temperature model and the room temperature model, multiple models with different initializations were trained. All models were trained with the MALA code [3] version 1.2.1. They show better accuracy than their original counterparts, as they were trained using the inter-snapshot shuffling algorithm first discussed for the MALA code in Ref. [4]. [1] - "Accelerating finite-temperature Kohn-Sham density functional theory with deep neural networks", Physical Review B, doi.org/10.1103/PhysRevB.104.035120 [2] - "RODARE", doi.org/10.14278/rodare.2485 (v1.0.0) [3] - "MALA", Zenodo, doi.org/10.5281/zenodo.5557254 [4] - "Machine learning the electronic structure of matter across temperatures", Physical Review B, doi.org/10.1103/PhysRevB.108.125146 Contents - The models themselves, labeled as either Al298K or Al933K, given as one .zip file per model - For 933K, additionally "liquid", "solid" and "hybrid" denotes the

Künstliche Intelligenz ist längst nicht mehr nur ein Zukunftsthema, sondern prägt unseren Alltag in vielfältiger Weise. Sie erstellt ganze Kochmagazine, formt den Musikgeschmack und hilft beim Schreiben von Kurznachrichten: Die Künstliche Intelligenz (KI/AI) ist in unserem Alltag angekommen. In unserem Vortrag entführen wir Sie in die Welt der Künstlichen Intelligenz: Von den Ursprüngen und Schlüsselmomenten ihrer Entwicklung, über alltägliche Anwendungen bis hin zu spezialisierten Einsatzgebieten wie in der Medizin. Wir beleuchten, wie KI unseren Alltag bereichert und gleichzeitig Herausforderungen aufwirft, und enden mit einem Ausblick auf die zukünftige Rolle der KI in Gesellschaft und Technologie. Ein kompakter, aber tiefgehender Einblick in das faszinierende Feld der KI erwartet Sie.

Interactions between electrons and nuclei, the principal building blocks of matter, determine all materials properties. Understanding and modeling these interactions therefore is of paramount importance to pressing scientific questions, e.g., in the context of renewable energy solutions or sustainable materials. However, electronic structure simulations often face a trade-off between accuracy and system size . One may simulate materials at quantum-accuracy, but can only do so for a few thousand atoms, even with the most advanced electronic structure tools, such as density functional theory (DFT). Conversely, large-scale simulations suffer from drastically reduced predictive power due to necessary approximations. The Materials Learning Algorithms (MALA) package tackles this challenge by combining neural networks, physically constrained optimization algorithms, and efficient post-processing routines to construct machine-learning models of DFT (ML-DFT). Unlike existing ML approaches, MALA creates ML-DFT models that completely replace DFT, providing access to both scalar quantities like energies and volumetric information about the electronic structure, such as the electronic density. We have demonstrated that MALA can be used with any number of atoms (successfully tested with 100’000 atoms), covering a wide range of temperatures and pressures. MALA enables a promising approach for materials modeling at unattained scale and accuracy.

Density functional theory (DFT) is well-known as the workhorse of electronic structure calculations in materials science and quantum chemistry. However, its applications stretch beyond these traditionally-studied fields, such as to the warm-dense matter (WDM) regime. Under WDM conditions, there are different challenges to consider (compared to ambient conditions) when using DFT. Namely, the electronic structure problem must be solved (i) for large particle numbers, (ii) for a range of temperatures, and (iii) for a range of pressures. Promising solutions were demonstrated for problems (i) and (ii) [1,2] using a recently-developed workflow to machine-learn the local density of states (LDOS) [3]. In this talk, we discuss our progress in developing a solution for problem (iii). This problem presents additional challenges because the LDOS varies quite significantly with changes in the pressure, making it a difficult problem for neural network models. [1] L Fiedler et al., npj Comput Mater 9, 115 (2023) [2] L Fiedler et al., Phys. Rev. B 108, 125146 (2023) [3] J. A. Ellis et al., Phys. Rev. B 104, 035120 (2021)

We introduce machine learning (ML) models that predict the electronic structure of materials across a wide temperature range. Our models employ neural networks and are trained on density functional theory (DFT) data. Unlike other ML models that use DFT data, our models directly predict the local density of states (LDOS) of the electronic structure. This provides several advantages, including access to multiple observables such as the electronic density and electronic total free energy. Moreover, our models account for both the electronic and ionic temperatures independently, making them ideal for applications like laser-heating of matter. We validate the efficacy of our LDOS-based models on a metallic test system. They accurately capture energetic effects induced by variations in ionic and electronic temperatures over a broad temperature range, even when trained on a subset of these temperatures. These findings open up exciting opportunities for investigating the electronic structure of materials under both ambient and extreme conditions.

Due to its balance between accuracy and computational cost, Density Functional Theory (DFT) is one of the most important computational methods within materials science and chemistry. However, current research efforts such as the modeling of matter under extreme conditions demand the application of DFT to larger length scales as well as higher temperatures. Such investigations are currently prohibited due to the computational scaling of DFT. We have recently introduced a machine-learning workflow that replaces modern DFT calculations [1,2,3]. This workflow uses neural networks to predict the electronic structure locally. We show that by employing such an approach, models can be trained to predict the electronic structure of matter across temperature ranges. This paves the way for large-scale simulations of thermodynamically sampled observables relevant to modeling technologically important phenomena such as radiation damage in fusion reactor walls.

info:eu-repo/semantics/published

The properties of electrons in matter are of fundamental importance. They give rise to virtually all molecular and material properties and determine the physics at play in objects ranging from semiconductor devices to the interior of giant gas planets. Modeling and simulation of such diverse applications rely primarily on density functional theory (DFT), which has become the principal method for predicting the electronic structure of matter. While DFT calculations have proven to be very useful to the point of being recognized with a Nobel prize in 1998, their computational scaling limits them to small systems. We have developed a machine learning framework for predicting the electronic structure on any length scale. It shows up to three orders of magnitude speedup on systems where DFT is tractable and, more importantly, enables predictions on scales where DFT calculations are infeasible. Our work demonstrates how machine learning circumvents a long-standing computational bottleneck and advances science to frontiers intractable with any current solutions. This unprecedented modeling capability opens up an inexhaustible range of applications in astrophysics, novel materials discovery, and energy solutions for a sustainable future.

Quantum mechanical calculations of the electronic structure of matter enable accessing interesting thermodynamical properties without the need for prior experimental measurements. Therefore, electronic structure calculations are of great interest in fields such as materials discovery or drug design. At the forefront of such simulations lies density functional theory (DFT), due to its excellent balance between computational accuracy and efficiency. Yet, as pressing environmental and social issues shift the research focus to increasingly complicated systems and conditions, even the most efficient of DFT implementations are approaching their limitations in terms of computational feasibility. A possible route to enable more complex calculations lies with machine learning (ML), i.e., algorithms that are capable of capturing complicated relationships based on large amounts of data.

Hands-on training on machine learning and the MALA library.

Machine learning has emerged as a powerful technique for processing large and complex datasets. Recently it has been utilized for both improving the accuracy and accelerating the computational speed of electronic structure theory. In this chapter, we provide the theoretical background of both density functional theory, the most widely used electronic structure method, and machine learning on a generally accessible level. We provide a brief overview of the most impactful results in recent times. We, further, showcase how machine learning is used to advance static and dynamic electronic structure calculations with concrete examples. This chapter highlights that fusing concepts of machine learning and density functional theory holds the promise to greatly advance electronic structure calculations enabling unprecedented applications for in-silico materials discovery and the search for novel chemical reaction pathways.

Interactions between electrons and nuclei, the principal building blocks of matter, determine all materials properties. Understanding and modeling these interactions therefore is of paramount importance to pressing scientific questions, e.g., in the context of renewable energy solutions or sustainable materials. However, electronic structure simulations often face a trade-off between accuracy and system size . One may simulate materials at quantum-accuracy, but can only do so for a few thousand atoms, even with the most advanced electronic structure tools, such as density functional theory (DFT). Conversely, large-scale simulations suffer from drastically reduced predictive power due to necessary approximations. The Materials Learning Algorithms (MALA) package tackles this challenge by combining neural networks, physically constrained optimization algorithms, and efficient post-processing routines to construct machine-learning models of DFT (ML-DFT). Unlike existing ML approaches, MALA creates ML-DFT models that completely replace DFT, providing access to both scalar quantities like energies and volumetric information about the electronic structure, such as the electronic density. We have demonstrated that MALA can be used with any number of atoms (successfully tested with 100’000 atoms), covering a wide range of temperatures and pressures. MALA enables a promising approach for materials modeling at unattained scale and accuracy.

In this talk, I will present our recent advancements in utilizing machine learning to significantly enhance the efficiency of electronic structure calculations [1]. In particular, I will focus on our efforts to accelerate Kohn-Sham density functional theory calculations at finite temperatures by incorporating deep neural networks within the Materials Learning Algorithms framework [2,3]. Our results demonstrate substantial gains in calculation speed for metals across their melting point. Furthermore, our implementation of automated machine learning has resulted in significant savings in computational resources when identifying optimal neural network architectures, thereby laying the foundation for large-scale investigations [4]. I will also showcase our most recent breakthrough, which enables neural-network-driven electronic structure calculations for systems containing over 100,000 atoms [5]. [1] L. Fiedler, K. Shah, M. Bussmann, A. Cangi, Phys. Rev. Materials 6, 040301, (2022). [2] A. Cangi, J. A. Ellis, L. Fiedler, D. Kotik, N. A. Modine, V. Oles, G. A. Popoola, S. Rajamanickam, S. Schmerler, J. A. Stephens, A. P. Thompson, MALA, https://doi.org/10.5281/zenodo.5557254 (2021). [3] J. A. Ellis, L. Fiedler, G. A. Popoola, N. A. Modine, J. A. Stephens, A. P. Thompson, A. Cangi, Phys. Rev. B 104, 035120 (2021). [4] L. Fiedler, N. Hoffmann, P. Mohammed, G. A. Popoola, T. Yovell, V. Oles, J. A. Ellis, S. Rajamanickam, A. Cangi, Mach. Learn.: Sci. Technol. 3, 045008 (2022). [5] L. Fiedler, N. A. Modine, S. Schmerler, D. J. Vogel, G. A. Popoola, A. P. Thompson, S. Rajamanickam, A. Cangi, arXiv:2210.11343 (2022).

# Authors: - Fiedler, Lenz (HZDR / CASUS) - Cangi, Attila (HZDR / CASUS) # Affiliations: HZDR - Helmholtz-Zentrum Dresden-Rossendorf CASUS - Center for Advanced Systems Understanding # Dataset description - System: Be256 - Temperature(s): 3750K, 7500K, 10000K - Mass density(ies): 1.915 gcc - Crystal Structure: bcc (material mp-20 in the materials project) - Number of atomic snapshots: 50    - 30 (3750K)    - 10 (7500K)    - 10 (10000) - Contents:    - ideal crystal structure: no    - MD trajectory: no    - Atomic positions: no    - DFT inputs: no    - DFT outputs (energies): yes    - SNAP vectors: no    - LDOS vectors: yes (partially, see below)         - dimensions: 160x80x80x250       - note: LDOS parameters are the same for all sizes of the unit cell    - trained networks: no # Data generation Ideal crystal structures were obtained using the Materials Project. (https://materialsproject.org/materials/mp-87/) DFT-MD calculations were performed using the Vienna Ab initio Simulation Package (https://www.vasp.at/, VASP). DFT calculations were performed using QuantumESPRESSO. For the VASP calculations, the standard VASP pseudopotentials were used. For Quantum Espresso, pslibrary was used (https://dalcorso.github.io/pslibrary/). The LDOS was preprocessed using MALA. # Dataset structure Each temperature folder contains the following folders: - ldos: holds the LDOS vectors (LDOS was not calculated for all snapshots!) - dft_outputs: holds the outputs from the DFT calculations, i.e. energies in the form of a QE output file Please note that the numbering of the snapshots is contiguous per temperature/mass density/number of atoms, and o

# Data and Scripts for "Machine learning the electronic structure of matter across temperatures" This dataset contains data and calculation scripts for the publication "Machine learning the electronic structure of matter across temperatures". Its goal is to enable interested parties to reproduce the experiments we have carried out. ## Prerequesites The following software versions are needed for the python scripts: - `python`: 3.8.x - `mala`: 1.2.0 - `numpy`: 1.23.0 (lower version may work) Further, make sure you have downloaded additional data such as local pseudopotentials and training data. ## Contents - `data_analysis/`: Contains scripts contain useful functions to reproduce the analysis carried out on the provided data. - `model_training/`: Contains scripts that allow the training and testing of the models discussed in the accompanying publication. - `trained_models`: Contains the models discussed in the accompanying publication. Per data set, five models with different random initializations were trained. re> 

A wide range of scientific fields, such as forensics, anthropology, medicine, and molecular evolution, benefits from the analysis of mitogenomic data. With the development of new sequencing technologies, the amount of mitochondrial sequence data to be analyzed has increased exponentially over the last few years. The accurate annotation of mitochondrial DNA is a prerequisite for any mitogenomic comparative analysis. To sustain with the growth of the available mitochondrial sequence data, highly efficient automatic computational methods are, hence, needed. Automatic annotation methods are typically based on databases that contain information about already annotated (and often pre-curated) mitogenomes of different species. However, the existing approaches have several shortcomings: 1) they do not scale well with the size of the database; 2) they do not allow for a fast (and easy) update of the database; and 3) they can only be applied to a relatively small taxonomic subset of all species. Here, we present a novel approach that does not have any of these aforementioned shortcomings, (1), (2), and (3). The reference database of mitogenomes is represented as a richly annotated de Bruijn graph. To generate gene predictions for a new user-supplied mitogenome, the method utilizes a clustering routine that uses the mapping information of the provided sequence to this graph. The method is implemented in a software package called DeGeCI (De Bruijn graph Gene Cluster Identification). For a large set of mitogenomes, for which expert-curated annotations are available, DeGeCI generates gene predictions of high conformity. In a comparative evaluation with MITOS2, a state-of-the-art annotation tool for mitochondrial genomes, DeGeCI shows better database scalability while still matching MITOS2 in terms of result quality and providing a fully automated means to update the underlying database. Moreover, unlike MITOS2, DeGeCI can be run in parallel on several processors to make use of mo

Background Identifying the locations of gene breakpoints between species of different taxonomic groups can provide useful insights into the underlying evolutionary processes. Given the exact locations of their genes, the breakpoints can be computed without much effort. However, often, existing gene annotations are erroneous, or only nucleotide sequences are available. Especially in mitochondrial genomes, high variations in gene orders are usually accompanied by a high degree of sequence inconsistencies. This makes accurately locating breakpoints in mitogenomic nucleotide sequences a challenging task. Results This contribution presents a novel method for detecting gene breakpoints in the nucleotide sequences of complete mitochondrial genomes, taking into account possible high substitution rates. The method is implemented in the software package DeBBI. DeBBI allows to analyze transposition- and inversion-based breakpoints independently and uses a parallel program design, allowing to make use of modern multi-processor systems. Extensive tests on synthetic data sets, covering a broad range of sequence dissimilarities and different numbers of introduced breakpoints, demonstrate DeBBI ’s ability to produce accurate results. Case studies using species of various taxonomic groups further show DeBBI ’s applicability to real-life data. While (some) multiple sequence alignment tools can also be used for the task at hand, we demonstrate that especially gene breaks between short, poorly conserved tRNA genes can be detected more frequently with the proposed approach. Conclusion The proposed method constructs a position-annotated de-Bruijn graph of the input sequences. Using a heuristic algorithm, this graph is searched for particular structures, called bulges, which may be associated with the breakpoint locations. Despite the large size of these structures, the algorithm only requires a small number of graph traversal steps.

We introduce a practical hybrid approach that combines orbital-free density functional theory (DFT) with Kohn-Sham DFT for speeding up first-principles molecular dynamics simulations. Equilibrated ionic configurations are generated using orbital-free DFT for subsequent Kohn-Sham DFT molecular dynamics. This leads to a massive reduction of the simulation time without any sacrifice in accuracy. We assess this finding across systems of different sizes and temperature, up to the warm dense matter regime. To that end, we use the cosine distance between the time series of radial distribution functions representing the ionic configurations. Likewise, we show that the equilibrated ionic configurations from this hybrid approach significantly enhance the accuracy of machine-learning models that replace Kohn-Sham DFT. Our hybrid scheme enables systematic first-principles simulations of warm dense matter that are otherwise hampered by the large numbers of atoms and the prevalent high temperatures. Moreover, our finding provides an additional motivation for developing kinetic and noninteracting free energy functionals for orbital-free DFT.

The properties of electrons in matter are of fundamental importance. They give rise to virtually all molecular and material properties and determine the physics at play in objects ranging from semiconductor devices to the interior of giant gas planets. Modeling and simulation of such diverse applications rely primarily on density functional theory (DFT), which has become the principal method for predicting the electronic structure of matter. While DFT calculations have proven to be very useful to the point of being recognized with a Nobel prize in 1998, their computational scaling limits them to small systems. We have developed a machine learning framework for predicting the electronic structure on any length scale. It shows up to three orders of magnitude speedup on systems where DFT is tractable and, more importantly, enables predictions on scales where DFT calculations are infeasible. Our work demonstrates how machine learning circumvents a long-standing computational bottleneck and advances science to frontiers intractable with any current solutions. This unprecedented modeling capability opens up an inexhaustible range of applications in astrophysics, novel materials discovery, and energy solutions for a sustainable future.

A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale electronic structure calculations are still challenging despite modern software approaches and advances in high-performance computing. The silver lining in this regard is the use of machine learning to accelerate electronic structure calculations -- this line of research has recently gained growing attention. The grand challenge therein is finding a suitable machine-learning model during a process called hyperparameter optimization. This, however, causes a massive computational overhead in addition to that of data generation. We accelerate the construction of machine-learning surrogate models by roughly two orders of magnitude by circumventing excessive training during the hyperparameter optimization phase. We demonstrate our workflow for Kohn-Sham density functional theory, the most popular computational method in materials science and chemistry.

We strive to popularize the usage of uncertainty quantification methods in machine learning through publications and application in various projects covering diverse fields from regression and classification to instance segmentation. In addition, we employ domain shift detection techniques to tackle population-level out-of-distribution scenarios. In all cases, the goal is to assess model prediction validity given unseen test data.

While the high efficiency of Density Functional Theory (DFT) calculations have enabled many important materials science application over the past decades, modern scientific problems require accurate electronic structure data beyond the scales attainable with DFT. For instance, the modeling of materials at extreme conditions across multiple length and time scales, which is important for the understanding for physical phenomena such as radiation damages in fusion reactor walls, evades ab-initio treatment. One possible method to obtain such models at near ab-initio accuracy are DFT surrogate models, that, based on machine learning (ML) algorithms, reproduce DFT results at a fraction of the cost. One drawback of the ML workflow is the need for hyperparameter optimization, i.e., the need to tune the employed ML algorithm in order to best perform on the given dataset. Manually performing this optimization becomes prohibitive if a wide range of materials and conditions is eventually to be treated. Here, we present results of an hyperparameter study in an effort to find optimal surrogate models for aluminium at ambient conditions [1], that investigates how modern hyperparameter optimization techniques can be used to automate large parts of the model selection process and eventually move towards automated surrogate model creation. The models are based upon the Materials Learning Algorithms (MALA) package [2] and the therein implemented LDOS based machine learning workflow [3]. [1]: https://www.doi.org/10.14278/rodare.1107 [2]: https://www.doi.org/10.5281/zenodo.5557254 [3]: https://www.doi.org/10.1103/PhysRevB.104.035120

While Density Functional Theory (DFT) is the most common tool for the investigation of materials under extreme conditions, its scaling behavior with respect to both system size and temperature makes large scale simulations challenging. Yet, progress in this regard would enable accurate modeling of planetary interiors or radiation damage in fusion reactor walls. One possible route to alleviate these scaling problems is through the use of surrogate models, i.e., machine-learning models. These are trained on DFT data and are able to reproduce DFT observables at comparable accuracy, but negligible computational cost. In order to actually be useful for such investigations, existing models need to be able to work across length scales and be transferable within desired temperature ranges. Here we show how models based on local mappings of electronic structure information [1], implemented in the Materials Learning Algorithms (MALA) package [2] can be trained on small number of atoms and select temperatures, yet perform accurately when used to make predictions for extended systems within a range of temperatures.

Understanding the properties of matter under extreme conditions is essential for advancing our fundamental understanding of astrophysical objects and guides the search for exoplanets, it propels the discovery of materials exhibiting novel properties that emerge under high temperatures and pressure, it enables novel technologies such as nuclear fusion, and supports diagnostics of experiments at large-scale brilliant photon sources. While modeling in this challenging research domain has so far relied on first-principles methods [1,2], these turn out to be computationally too expensive for simulations at the required time and length scales. Reduced models, such as average-atom models [3], come at a reduced computational and are useful by connecting atomistic details with hydrodynamics simulations, but they provide less accuracy. Artificial intelligence (AI) has great potential for accelerating electronic structure calculations to hitherto unattainable scales [4]. I will present our recent efforts on accomplishing speeding up Kohn-Sham density functional theory calculations with deep neural networks in terms of our Materials Learning Algorithms framework [5,6] by illustrating results for metals across their melting point. Furthermore, our results towards automated machine-learning save orders of magnitude in computational efforts for finding suitable neural networks and set the stage for large-scale AI-driven investigations [7]. [1] T. Dornheim, A. Cangi, K. Ramakrishna, M. Böhme, S. Tanaka, J. Vorberger, Phys. Rev. Lett. 125, 235001 (2020). [2] K. Ramakrishna, A. Cangi, T. Dornheim, J. Vorberger, Phys. Rev. B 103, 125118 (2021). [3] T. J. Callow, E. Kraisler, S. B. Hansen, A. Cangi, Phys. Rev. Research 4, 023055 (2022). [4] L. Fiedler, K. Shah, M. Bussmann, A. Cangi, Phys. Rev. Materials 6, 040301 (2022). [5] A. Cangi et al., MALA, https://doi.org/10.5281/zenodo.5557254 (2021). [6] J. A. Ellis, L. Fiedler, G. A. Popoola, N. A. Modine, J. A. Stephens, A. P. Thompson, A.

With the growth of computational resources, the scope of electronic structure simulations has increased greatly. Artificial intelligence and robust data analysis hold the promise to accelerate large-scale simulations and their analysis to hitherto unattainable scales. Machine learning is a rapidly growing field for the processing of such complex datasets. It has recently gained traction in the domain of electronic structure simulations, where density functional theory takes the prominent role of the most widely used electronic structure method. Thus, DFT calculations represent one of the largest loads on academic high-performance computing systems across the world. Accelerating these with machine learning can reduce the resources required and enables simulations of larger systems. Hence, the combination of density functional theory and machine learning has the potential to rapidly advance electronic structure applications such as in-silico materials discovery and the search for new chemical reaction pathways. We provide the theoretical background of both density functional theory and machine learning on a generally accessible level. This serves as the basis of our comprehensive review including research articles up to December 2020 in chemistry and materials science that employ machine-learning techniques. In our analysis, we categorize the body of research into main threads and extract impactful results. We conclude our review with an outlook on exciting research directions in terms of a citation analysis.

A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale electronic structure calculations are still challenging despite modern software approaches and advances in high-performance computing. The silver lining in this regard is the use of machine learning to accelerate electronic structure calculations -- this line of research has recently gained growing attention. The grand challenge therein is finding a suitable machine-learning model during a process called hyperparameter optimization. This, however, causes a massive computational overhead in addition to that of data generation. We accelerate the construction of neural network models by roughly two orders of magnitude by circumventing excessive training during the hyperparameter optimization phase. We demonstrate our workflow for Kohn-Sham density functional theory, the most popular computational method in materials science and chemistry.

Density Functional Theory (DFT) is the most common tool for investigating materials under extreme conditions, yet its scaling behavior with respect to both system size and temperature prohibits large scale simulations in such regimes. Progress in this regard would enable accurate modeling of planetary interiors or radiation damage in fusion reactor walls. One possible route to alleviate these scaling problems is through the use of surrogate models, i.e., machine-learning models. These are trained on DFT data and are able to reproduce DFT predictions of energies and forces at comparable accuracy, but negligible computational cost. Yet, in order to avoid repeated costly training data generation, models need to be able to transfer across length scales. Here, we present such transferability results. They show how learning local information can allow models to extrapolate to length scales that are not attainable with standard DFT methods. The models are based upon the Materials Learning Algorithms (MALA) package [1] and the therein implemented LDOS based machine learning workflow [2]. [1]: https://github.com/mala-project [2]: J. A. Ellis et al., Phys. Rev. B 104, 035120, 2021

The focus of this project is to accelerate and transform the workflow of multiscale materials modeling by developing an integrated toolchain seamlessly combining DFT, SNAP, LAMMPS, (shown in Figure 1-1) and a machine-learning (ML) model that will more efficiently extract information from a smaller set of first-principles calculations. Our ML model enables us to accelerate first-principles data generation by interpolating existing high fidelity data, and extend the simulation scale by extrapolating high fidelity data ( 10 2 atoms) to the mesoscale ( 10 4 atoms). It encodes the underlying physics of atomic interactions on the microscopic scale by adapting a variety of ML techniques such as deep neural networks (DNNs), and graph neural networks (GNNs). We developed a new surrogate model for density functional theory using deep neural networks. The developed ML surrogate is demonstrated in a workflow to generate accurate band energies, total energies, and density of the 298K and 933K Aluminum systems. Furthermore, the models can be used to predict the quantities of interest for systems with more number of atoms than the training data set. We have demonstrated that the ML model can be used to compute the quantities of interest for systems with 100,000 Al atoms. When compared with 2000 Al system the new surrogate model is as accurate as DFT, but three orders of magnitude faster. We also explored optimal experimental design techniques to choose the training data and novel Graph Neural Networks to train on smaller data sets. These are promising methods that need to be explored in the future.

Beryllium data set for Machine Learning applications re> This dataset contains DFT inputs, outputs, LDOS data and fingerprint vectors for a beryllium cell at ambient conditions and varying sizes. Different levels of k-grid convergence were employed: -  Gamma point (gamma_point) -  total energy convergence (k-grid converged to 1meV/atom to total energy difference, total_energy_convergence) -  LDOS convergence (k-grid converged to LDOS without unphyiscal oscillations, ldos_convergence) The data set contains a .zip file for each system size (see below), as well as one .zip file containing sample scripts for recalculation and preprocessing of data. The cutoff energy was converged with respect to the energy convergence and held fixed 40Ry for all three levels of k-grids. Note that not for all sizes of unit cells data for all types of k-grid were generated. 
Authors: - Fiedler, Lenz (HZDR / CASUS) - Cangi, Attila (HZDR / CASUS) Affiliations: HZDR - Helmholtz-Zentrum Dresden-Rossendorf CASUS - Center for Advanced Systems Understanding Dataset description - Total size: 143G GB - System: Be128, Be256, Be512, Be1024, Be2048 - Temperature(s): 298K - Mass density(ies): 1.896 gcc - Crystal Structure: hpc (material mp-87 in the materials project) - Number of atomic snapshots: 145 - 40 (Be128) - 35 (Be256) - 30 (Be512) - 20 (Be1024) - 10 (Be2048) - Contents: - ideal crystal structure: yes - MD trajectory: yes - Atomic positions: yes - DFT inputs: yes - DFT outputs (energies): yes - SNAP vectors: yes (partially, see below) - dimensions: XxYxZx94 (last dimension: first three entries are x,y,z coordinates, data size is 91), where X, Y, Z are: - 

# Data and Scripts for "Accelerating Equilibration in First-Principles Molecular Dynamics with Orbital-Free Density Functional Theory" This dataset contains data and calculation scripts for the publication "Boosting first-principles molecular dynamics with orbital-free density functional theory". Its goal is to enable interested parties to reproduce the experiments we have carried out. ## Prerequesites The following software versions are needed for the python scripts: - `python`: 3.8.x - `mala`: 1.1.0 (with `dftpy` installed) Further, make sure you have a working `Quantum ESPRESSO` and `VASP` installation and have downloaded additional data such as local pseudopotentials and ML models (for references, see publication). ## Contents - `scripts/`: Example scripts for the three principal python tasks associated with out work: ML inference, trajectory analysis and OF-DFT-MD runs (via DFTPy). The scripts are general blueprints for these experiments and can be adjusted to perform all of the calculations given in the publication. - `data/`: Contains raw calculation data for the three investigated systems (hydrogen, beryllium and aluminium). Since the main goal of this work is to compare OF-DFT-MD initialized and ideal crystal structure initialized trajectories and inferences, each of the three system-folders contains a `MD_ideal_crystal_structure` and `MD_ofdft_init` folder, with ideal crystal structure and OF-DFT-MD initialized data, respectively. Therein, contents may differ; e.g. aluminium contains DFT calculation data, for beryllium data is divided by system size and Nosé mass, while for hydrogen data for different temperatures is given. re> 

Scripts and Models for "Predicting the Electronic Structure of Matter on Ultra-Large Scales" This data set contains scripts and models to reproduce the results of our manuscript "Physics-informed Machine Learning Models for Scalable Density Functional Theory Calculations". The scripts are supposed to be used in conjunction with the ab-initio data sets also published alongside our research article. Requirements python>=3.7.x mala>=1.1.0 ase numpy Contents | Folder name | Description | |------------------|--------------------------------------------------| | data_analysis/ | Run script for RDF calculations | | model_inference/ | Run script to run inference based on MALA models | | model_training/ | Run script to train MALA models | | trained_models/ | Trained models for beryllium and aluminium | re> 

This repository contains scripts to reproduce the results of the publication "Electronic Structure Machine Learning Surrogates without Training". Training data has to be downloaded separately.