Multiscale Modeling of Matter under Extreme Conditions

11 Sept 2022, 16:00 → 16 Sept 2022, 12:15 Europe/Berlin

Görlitz

Attila Cangi (Center for Advanced Systems Understanding, HZDR), Aurora Pribram-Jones (University of California, Merced)

This workshop brings together experts from the spectrum of available modeling techniques relevant to matter under extreme conditions. The goal is to summarize the state of the art, identify the current caveats of each methodology, and devise strategies on achieving multiscale workflows. 

Flyer_Multiscale_Modeling_MEC.jpg

Sunday 11 September

Informal social get-together (optional)

Monday 12 September

1 Welcome by Program Committee

Morning Session (Monday)

Session Chair: Attila Cangi

2 Probing dynamic materials under extreme conditions using combined in situ X-ray diagnostics

Dynamic shock compression of materials can induce exotic phase transitions and chemical reactions resulting in new material structures that may be interesting for applications if successful recovery to ambient conditions is possible. Specific examples include nanodiamonds formed by dynamic compression of plastics and hexagonal diamond, which is predicted to exceed the hardness of its cubic polymorph, and can form via fast uniaxial compression of highly oriented graphite. New methods of in situ diagnostics at XFEL and synchrotron light sources allow for capturing the multiscale nature of these processes in unprecedented detail. This talk will discuss the state-of-the-art and future developments for measurements of dynamically compressed carbon and plastics applying in situ X-ray diffraction, small angle X-ray scattering and inelastic X-ray scattering as well as optical diagnostics in a single experiment. These methods will further benefit from the increase in repetition rate enabled by the HIBEF drive laser installation at European XFEL.

Speaker: Dominik Kraus (University of Rostock, Germany)

3 New Perspectives for Warm Dense Matter Theory: from Quantum Monte Carlo to Temperature Diagnostics

Warm dense matter (WDM)---an extreme state that is characterized by extreme densities and temperatures---has emerged as one of the most active frontiers in plasma physics and material science. In nature, WDM occurs in astrophysical objects such as giant planet interiors and brown dwarfs. In addition, WDM is highly important for cutting-edge technological applications such as inertial confinement fusion and the discovery of novel materials. In the laboratory, WDM is studied experimentally in large facilities around the globe, and new techniques have facilitated unprecedented insights into exciting phenomena like the formation of nano diamonds at planetary interior conditions [1]. Yet, the interpretation of these experiments requires a reliable diagnostics based on accurate theoretical modeling, which is a notoriously difficult task [2]. In this talk, I give an overview of recent ground-breaking developments in this field [3,4], which will allow for the first time to rigorously treat the intricate interplay of Coulomb coupling with thermal excitations and quantum degeneracy effects. Moreover, I show how cutting-edge quantum Monte Carlo simulation techniques will help to decisively improve density functional theory (DFT) simulations of WDM, thereby opening up unprecedented perspectives and new paradigms such as the experimental and theoretical study of nonlinear effects [5,6]. Finally, I will present a new idea to extract the exact temperature from an X-ray Thomson scattering experiment without any models or simulations [7].

[1] D. Kraus et al., Nature Astronomy 1, 606-611 (2017)
[2] M. Bonitz et al., Physics of Plasmas 27, 042710 (2020)
[3] T. Dornheim et al., Physics Reports 744, 1-86 (2018)
[4] T. Dornheim et al., Physical Review Letters 121, 255001 (2018)
[5] T. Dornheim et al., Physical Review Letters 125, 085001 (2020)
[6] Zh. Moldabekov et al., Journal of Chemical Theory and Computation 18, 2900-2912 (2022)
[7] T. Dornheim et al., arXiv:2206.12805

Speaker: Tobias Dornheim (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

4 Introduction to CASUS

Speaker: Attila Cangi (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

10:45 Coffee Break

5 Can we treat the dynamics of electronic correlations, both accurately and efficiently?

Electronic correlations – Coulomb interaction effects beyond the simple mean field – are crucial for the correct description of warm dense matter. Moreover, correlations are responsible for scattering effects, including Auger-type processes, multiple excitations and so on. When the system is driven out of equilibrium, correlations are strongly modified and undergo their own dynamics [1]. While such processes are difficult to capture with DFT approaches, a systematic treatment of the dynamics of electronic correlations is possible with nonequilibrium Green functions (NEGF) that we have been developing over the past decades. I will give an overview on recent progress in achieving higher accuracy and dramatically speeding up the expensive simulations [2, 3]. I will conclude by presenting first results for the dynamics of electrons in warm dense matter and outline how to bridge the gap from very short to macroscopic times.

[1] A. Niggas et al., Phys. Rev. Lett. 129, 086802 (2022)
[2] N. Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)
[3] J.-P. Joost et al., Phys. Rev. B 105 (16), 165155 (2022)

Speaker: Michael Bonitz (Kiel University, Germany)

12:15 Lunch Break

Afternoon Session (Monday)

Session Chair: John Kozlowski

6 Computing the Entanglement of Large, Many-Electron Systems Using Auxiliary Field Quantum Monte Carlo

The entanglement of a system serves a key measure of its quantum properties that can be used to quantify its utility in quantum information processors. Nonetheless, entanglement is a notoriously challenging and expensive quantity to compute for many-body systems. In this work, we demonstrate how a new recursive formalism can be used to compute the finite temperature properties of quantum systems, including their entanglement and Renyi-2 entropies, in the canonical ensemble within an Auxiliary Field Quantum Monte Carlo (AFQMC) framework. Our approach is capable of obtaining the properties of interacting systems of arbitrary dimensions by integrating over corresponding non-interacting solutions computed via the Auxiliary Partition Function formalism using the Hubbard-Stratonovich Transformation. We show that our approach is not only more stable, but also less expensive than comparable techniques. We then employ this formalism to study the accessible entanglement of electrons in the Hubbard model in the canonical ensemble and how this entanglement differs from that in the grand canonical ensemble. We lastly show how such measures of entanglement can be used to detect the Mott insulator transition in the Hubbard model. Our approach serves as a powerful, yet relatively inexpensive approach for quantifying entanglement and detecting phase transitions in interacting quantum systems.

Speaker: Brenda Rubinstein (Brown University, United States)

7 Ab Initio Static Exchange–Correlation Kernel From DFT

The KS-DFT is the standard method to model the electronic structure due to its accuracy and computational efficiency. The reduction in computation cost compared to other ab initio methods is due to a formally exact mapping onto an effective single-electron problem. DFT calculations of a various material properties require as input the so-called exchange—correlation (XC) kernel. Yet, little is known about the actual kernel of real materials, and hitherto no reliable universal way to compute it has been known. In this work, we present a new methodology to compute the static XC-kernel of any material; which needs no external input apart from the usual XC-functional. The application of the method is demostrated for the uniform electron gas and hydrogen. Moreover, we consider both ambient conditions and the warm-dense matter (WDM) parameters. In addition, our analysis of the static XC-kernel gives us valuable new insights into the construction of the XC-functionals for the application at WDM regime.

Speaker: Zhandos Moldabekov (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

15:45 Coffee Break

8 Correlation and temperature dependence in density functional theory

Adiabatic connection approaches have long been used in ground-state density functional theory for analyzing exact and approximate density functional theory, and it has more recently been applied to both thermal and ensemble versions of the theory. In this talk, I'll introduce the adiabatic connection and what changes for this tool when at the high temperatures and densities common to warm dense matter. I will then discuss how we use the adiabatic connection to explore limiting behavior of the exchange-correlation free energy and to develop new ways to approximate temperature dependence.

Speaker: Aurora Pribram-Jones (University of California, Merced, United States)

Tuesday 13 September

Morning Session (Tuesday)

Session Chair: Kieron Burke

9 TBD

TBD

Speaker: Tom Cowan (Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

10 Electronic transport properties of matter under extreme conditions from density functional theory

The determination of thermoelectric transport coefficients of dense, partially ionized matter is a great challenge for both experiment and theory. In the past two decades, density functional theory (DFT) has evolved to an efficient tool for making theoretical predictions of properties of matter under extreme conditions. Many of these are of high relevance for modelling the interior states, evolution, and magnetic field dynamics of stellar and planetary objects. Here I will give an overview on the generalized Kubo-Greenwood (KG) formalism [1] that is frequently used in calculations of electronic transport properties using the Kohn-Sham states from DFT. Several examples of successful application of this technique to various solid and fluid metals will be presented. Furthermore, a comparison of optical reflectivities of molecular fluids observed in dynamic compression experiments [2] will be made, including a discussion of the influence of the exchange-correlation functional on the DFT results. Finally, the limitations of the KG formalism with respect to its capability of describing electron-electron collisions will be discussed by examining the thermopower and Lorenz number of weakly degenerate hydrogen plasmas. It is shown [3] that the DFT results approach the limiting values for a Lorentz plasma, which is a model system that only considers electron-ion collisions, instead of agreeing with the Spitzer results [4], which were derived taking both electron-ion and electron-electron scattering into account. These recent findings [3] are of substantial importance for future methodical developments to calculate transport properties of matter under extreme conditions and, especially, for correctly assessing the results obtained via the Kubo-Greenwood formalism in relation to experiments and other theoretical approaches. This work is supported by the DFG within the FOR 2440 "Matter under Planetary Interior Conditions - High Pressure, Planetary, and Plasma Physics."

REFERENCES
[1] B. Holst, M. French, and R. Redmer, "Electronic transport coefficients from ab initio simulations and application to dense liquid hydrogen", Phys. Rev. B 83, 235120 (2011).
[2] A. Ravasio, M. Bethkenhagen, J.-A. Hernandez, A. Benuzzi-Mounaix, F. Datchi, M. French, M. Guarguaglini, F. Lefevre, S. Ninet, R. Redmer, and T. Vinci, "Metallization of Shock-Compressed Liquid Ammonia", Phys. Rev. Lett. 126, 025003 (2021).
[3] M. French, G. Röpke, M. Schörner, M. Bethkenhagen, M. P. Desjarlais, and R. Redmer, "Electronic transport coefficients from density functional theory across the plasma plane", Phys. Rev. E 105, 065204 (2022).
[4] L. Spitzer, Jr. and R. Härm, "Transport Phenomena in a Completely Ionized Gas", Phys. Rev. 89, 977 (1953).

Speaker: Martin French (University of Rostock, Germany)

10:30 Coffee Break

11 Electrical conductivity of iron in earth's core from microscopic Ohm's Law

Understanding the electronic transport properties of iron under high temperatures and pressures is essential for constraining geophysical processes. The difficulty of reliably measuring these properties calls for sophisticated theoretical methods that can support diagnostics. We present results of the electrical conductivity within the pressure and temperature ranges found in Earth's core by simulating microscopic Ohm's law using time-dependent density functional theory.

Speaker: Kushal Ramakrishna (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

12 Energy, momentum, and angular-momentum transfer between electrons and nuclei

Describing the coupled dynamics of electrons and nuclei beyond the adiabatic approximation is notoriously difficult. Starting from the full Hamiltonian of interacting electrons and nuclei, we first deduce an exact factorization [1] of the electron-nuclear wave function into a purely nuclear wave packet and a many-electron wave function which parametrically depends on the nuclear coordinates and which has the meaning of a conditional probability amplitude. The equation of motion for the nuclear factor is a standard Schrödinger equation featuring a vector potential and a scalar potential (both being N-body interactions). The time-evolution of the electronic conditional wave function is governed by a non-Hermitian “Hamiltonian” whose propagation nonetheless conserves the norm of the electronic wave function. This non-Hermiticity is essential for the correct description of decoherence [2,3]. For practical calculations, the equations of motion are “density-functionalized”, leading to a coupled set of Kohn-Sham equation for the electrons and nuclei [4]. Furthermore, starting from the nuclear equation of motion of the exact factorization, we deduce subsystem Ehrenfest identities [5] characterizing the energy, momentum, and angular momentum transfer between electrons and nuclei. An electromagnetic-like force operator arising from the scalar and vector potentials in the nuclear equation of motion appears in all three Ehrenfest identities. The magnetic component leads to Lorentz-like forces which couple the motion of different nuclei to each other. Manifestations of these forces will be discussed.

[1] A. Abedi, N.T. Maitra, E.K.U. Gross, PRL 105, 123002 (2010).
[2] F. Agostini, S.K. Min, I. Tavernelli, E.K.U. Gross, J Phys Chem Lett 8, 3048 (2017).
[3] S.K. Min, F. Agostini, E.K.U. Gross, PRL 115, 073001 (2015).
[4] R. Requist, E.K.U. Gross, PRL 117, 193001 (2016).
[5] Chen Li, R. Requist, E.K.U. Gross, PRL 128, 113001 (2022).

Speaker: Hardy Gross (Hebrew University of Jersusalem, Israel)

12:15 Lunch Break

Afternoon Session (Tuesday)

Session Chair: Hardy Gross

13 Towards multiscale modeling of non-LTE conditions: validation of microscopic models

Multiscale modeling of matter away from local thermodynamic equilibrium (i.e., non-LTE conditions) requires the tabulation of material properties over not just temperature, pressure, and density - but the state of the ambient radiation field, as well. This compounds the typical computational demands of using multi-atom first principles models to create such tables by introducing yet another (high-dimensional) independent state variable and imposing conditions that test the limits of the attendant theories. To confront the problem of multiscale non-LTE simulation, it is thus essential to validate average-atom models with moderate fidelity and high computational efficiency against high-fidelity multi-atom models with vastly less computational efficiency. I will describe work that we have been doing to validate and improve average atom models against multi-atom models based on real-time time-dependent density functional theory, in this context. I will primarily focus on comparisons made between the two in the context of stopping power and dynamic structure factor calculations, but I will give secondary focus to ongoing work aimed at understanding more fundamental quantities (namely collision rates) that might be a better point of comparison. This work was supported by SNL's LDRD program, project number 222396. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

Speaker: Andrew Baczewski (Sandia National Laboratories, United States)

14 Beyond the Coulomb Interaction: Why the Relativistic Description of Photons and Matter Matters

Most functionals used in density functional theory are based on the Coulomb interaction. This approximation to the more fundamental interaction found in quantum electrodynamics (QED) may be inadequate for matter under extreme conditions. I'll discuss what is missing and how to account for some relativistic effects using expansions in powers of 1/c. By analogy with electron-phonon coupled superconductivity, I'll also show how a fully relativistic mean-field version of QED can be derived.

Speaker: Kay Dewhurst (Max Planck Institute of Microstructure Physics, Germany)

16:00 Coffee Break

15 Femtosecond-laser induced ultrafast melting in Si and the possibility to control it

Femtosecond-laser pulses can induce structural phenomena like solid-to-solid phase transitions and ultrafast melting in crystalline structures. The main reason for the appearance of such effects is the ultrafast modification of the bonding properties in the induced nonthermal state consisting of extremely hot electrons and nearly unaffected cold ions. Although melting is a stochastic process in thermodynamical equilibrium, we show that in the laser excited nonthermal case some coherences are preserved or created. Moreover, by performing ab initio molecular dynamics simulations of the excitation of silicon by a series of laser pulses, we demonstrate that it is possible to control nonthermal melting by light. Analyzing the energy flow in quasimomentum space, we found that the ultrafast disordering atomic motion can be stopped and redirected depending on the delay between the pulses. Essential for the controlling mechanism is the appearance of an intermediate state in the excitation process that shows a laser-induced coherent motion of the atoms. The appearing oscillation follows directly the bond softening of the
material and can be connected to laser-changed thermal phonon frequencies.

Speaker: Tobias Zier (University of California, Merced, United States)

Wednesday 14 September

Morning Session (Wednesday)

Session Chair: Tim Callow

16 Synergy between multi-scale and multi-platform simulations and HED experiments at high power laser facilities

With the dawn of novel high-power laser facilities, unprecedented energies and intensities have been achieved to access previously unseen extreme states of matter. These states not only span over a wide range of conditions, but also time scales. However, all our theoretical models and connected computer simulations are limited to specific parameter spaces and time scales. This means that no single simulation is capable of accurately describing the full scope of the plasma evolution in such experiments by itself. Our group has thus combined efforts of multiple teams to access novel multi-scale simulations to support our experiments by combining the inputs and outputs of multiple simulation platforms that each tackle a different regime or time-scale of the plasma evolution. We present three examples, where these composite simulations have been performed in order to capture the full experiment. We will discuss projects where particle-in-cell (PIC) simulations [1,2] were used to model the laser-target interaction on short-time scales and their output was then fed into a magneto-hydrodynamics simulation performed by the FLASH code [3] or multifluid simulations to describe the subsequent plasma evolution on a longer time scale to match our experimental measurements from PW lasers interacting with solid foil targets. We will also present a reverse process where a magneto-hydrodynamics simulation [3,4] was used to evolve two plasma jets forming a shockwave on a long spatial (mm) and temporal (ns) scales, but the output of these simulations was then used as input for PIC simulations [1] and continuum-kinetic simulations [5] in order to model the nonlocal kinetic effects within the shock structure that formed in this collision. These simulations are a preparation for an upcoming OMEGA shot day.

[1] M. Bussmann et al., Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis on - SC ’13, 1–12 (2013).
[2] Y. Sentoku and A. Kemp, Journal of Computational Physics 227, 6846 (2008).
[3] B. Fryxell et al., Astrophys. J., Suppl. Ser. 131, 273 (2000).
[4] M. Holec, J. Nikl, and S. Weber, Phys. Plasmas 25, 032704 (2018). [5] A. Hakim and J. Juno, SC20: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, IEEE Press, (2020).

Speaker: Katerina Falk (Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

17 SNAP and Beyond: Machine Learning Interatomic Potentials in LAMMPS

Molecular dynamics (MD) is a powerful materials simulation approach whose accuracy is limited by the interatomic potential (IAP). The quest for improved accuracy has resulted in a decades-long growth in the complexity of IAPs, many of which are now implemented in Sandia's LAMMPS MD code[1]. Traditional physics-based IAPs are now being rapidly supplanted by machine-learning IAPs. In 2015 we published the SNAP (Spectral Neighbor Analysis Potential) machine-learning approach and released it in LAMMPS, providing an automated methodology for generating accurate and robust application-specific IAPs [2]. SNAP is formulated in terms of a set of general four-body descriptors that characterize the local neighborhood of each atom. This approach has been used to develop potentials for diverse materials, including metals (Ta, W), metal alloys (AlNbTi), III-V semiconductors (InP), plasma-facing materials (W/Be/He/H/N), and even magnetic materials such as iron. Each SNAP IAP is trained on quantum electronic structure calculations of energy, force, and stress for many small configurations of atoms. Cross-validation analysis and evaluation on test problems are used to further improve IAP fidelity and robustness. Varying the number of SNAP descriptors allows a continuous tradeoff between computational cost and accuracy. The resultant potentials enable high-fidelity large-scale MD simulations of these materials, yielding insight into their behavior on lengthscales and timescales unreachable by other methods. The relatively large computational cost of SNAP is offset by combining LAMMPS' spatial parallel algorithms with Kokkos-based hierarchical multithreading, enabling the efficient use of Peta- to Exa-scale CPU and GPU platforms, allowing large-scale production simulations on the DOE Summit supercomputer at 30 ns/day with millions to billions of atoms. Finally, I will discuss opportunities to expand the flexibility of the SNAP approach by combining SNAP descriptors with neural network energy models, as well as replacing SNAP descriptors with the more general Atomic Cluster Expansion descriptors.

[1] Thompson et al., Comp. Phys. Comm., 271:108171, 2022. http://dx.doi.org/10.1016/j.cpc.2021.108171
[2] Thompson et al., J. Comp. Phys., 285:316, 2015. http://dx.doi.org/10.1016/j.jcp.2014.12.018

Speaker: Aidan Thompson (Center for Computing Research, Sandia National Laboratories, Unites States)

10:30 Coffee Break

18 Machine learning-based quantum accurate interatomic potentials for warm dense aluminum

Modeling warm dense matter is relevant for various applications including the interior of gas giants and exoplanets, inertial confinement fusion, and ablation of metals. Ongoing and upcoming experimental campaigns in photon sources around the globe rely on numerical simulations which are accurate on the level of electronic structures. In that regard, density functional theory molecular dynamics (DFT-MD) simulations [1] have been widely used to compute the dynamical and thermodynamical properties of warm dense matter. However, two challenges impede further progress: (1) DFT-MD becomes computationally infeasible with increasing temperature (2) finite-size effects render many computational observables inaccurate, because DFT-MD is limited to a few hundred atoms on current HPC platforms. Recently, molecular dynamics simulations using machine learning-based interatomic potentials (ML-IAP) could overcome these computational limitations. Here, we propose a method to construct ML-IAPs from DFT data based on SNAP descriptors [2]. We present our results for aluminum. In particular, we investigate the transferability of ML-IAPs over a large range of temperatures (1000 to 100000 K) and pressures (ambient to 800 GPa), which currently is a topic of active research. To test the transferability of the SNAP potential, we calculate thermal conductivity, viscosity, diffusion coefficient, and sound velocity in and out of the data training range. References:

[1]. G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).
[2]. A. P. Thompson, L. P. Swiler, C. R. Trott, S. M. Foiles, and G. J. Tucker, J. Comput. Phys., 285, 316-330, 2015.

Speaker: Sandeep Kumar (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

19 Coupled magnetic and molecular dynamics: Methodology and application to iron under high-pressure and temperature conditions

Our presentation will first introduce a methodology aiming at simulating magneto-elastic phenomena. The approach is based on coupled classical spin dynamics and molecular dynamics. We will review the approach and its implementation in the LAMMPS code. After describing recent success of this methodology, we will point at some of its limitations.

We will then show how machine-learning interatomic potentials (ML-IAPs) trained on first-principles data, allowed us to circumvent some of those limitations. In particular, ML-IAPs were coupled to magneto-elastic spin Hamiltonians, altogether consistently trained on first-principles data.

Finally, we will display how the generated models can be used to simulate magneto-elastic phase transitions in iron, such as the Curie transition and its impact of thermophysical properties, the alpha to epsilon magneto-structural phase transition, or to perform high-pressure shock compression simulations.

Speaker: Julien Tranchida (CEA Cadarache, France)

12:15 Lunch Break

Afternoon Session (Wednesday)

Session Chair: Aidan Thompson

20 Average-atom-type models for warm dense matter

Material properties of warm dense matter, like equation of state and conductivity, are needed for modeling stars, fusion plasmas, and high-energy-density experiments. Since the beginning of this field, average atom models have been used to provide such data. In this talk, I will give an abridged introduction, historical perspective, and review of modern average atom models and methods. I will highlight their strengths and discuss recent approaches to improvements on both the physical model and numerical stability.

Speaker: Charles Starrett (Los Alamos National Laboratory, United States)

21 Benchmarking pressures and ionization states for an average-atom model under warm dense matter conditions

Average-atom models are an essential tool in modelling the warm dense matter regime, because they can be used to compute key quantities, such as equation-of-state data, for a fraction of the computational cost of higher-fidelity simulations such as DFT-MD. However, a variety of different models exist, and it is important to benchmark these models to understand their limitations and expected accuracy under various conditions. In this presentation, we focus on two key properties in WDM — the mean ionization state and pressure — for a range of materials, densities and temperatures. Through comparison with higher-fidelity simulations and experimental results, we probe the accuracy of an average-atom model, considering various choices of approximation within that model. We demonstrate a well-chosen average-atom model, under the right conditions, can yield close agreement with these benchmarks.

Speaker: Timothy Callow (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

15:45 Coffee Break

16:15 Free afternoon

19:00 Conference Dinner

Thursday 15 September

Morning Session (Thursday)

Session Chair: Andrew Baczewski

22 Transitions in matter induced by intense X-ray radiation and their diagnostics.

X-ray induced structural transitions in solids are in focus of this talk. Depending on the dose absorbed, an irradiation with a femtosecond X-ray pulse can trigger an ultrafast electronic or structural transition in solid materials. In magnetic materials, an X-ray triggered ultrafast demagnetization can occur. In this talk, selected study cases for these transitions are presented. Dedicated theoretical modeling reveals complex multistage evolution of the irradiated systems, confirmed by experimental measurements performed at X-ray free-electron-laser facilities. Challenges remaining for the modeling and quest for further improvements of transition diagnostics are discussed.

Speaker: Beata Ziaja-Motyka (CFEL, DESY, Hambug, Germany & IFJ PAN, Krakow, Poland)

23 Analysis of X-ray Diffraction by Machine Learning

The long term and sustainable success of the X-ray community essentially depends on its ability to meet growing challenges in handling and analysing data of increasing volume and complexity. Machine Learning (ML) provide a smart solution enabling a dramatic increase in the output of X ray scattering facilities regarding acceleration of data analysis, optimization of beam time usage and, consequently, growth of publication rate. Analysis of scattering data is a very time consuming process as it requires solving an ill-posed inverse problem to infer properties of the imaged object.

During the talk we will be discussing two state-of-the-art methods to solve this task:

1) ML-based estimation of the most important paramenters of the object in a single step given the experimentally acquired scattering image;
2) iterative ML assisted phasing based on automatic differentiation that can be very easily used for fast reconstruction of multiple X-ray scattering modalities such as CDI, mono & polychromatic Ptychography as well as Holography.
Some parameters exhibit low contribution to the acquired data which also hampers reliable predictions and discrimitation of these parameters. We show that normalising flows can be used to recover the predictive posterior distribution of these parameters to resolve ambiguous situations and provide information about the reilability of the estimate.

Speaker: Nico Hoffmann (Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

10:30 Coffee Break

24 Physics-Informed Neural Networks for Quantum Dynamics of Electrons

Time-dependent density functional theory (TDDFT) is an important method for simulating dynamical processes in quantum many-body systems. We explore the feasibility of physics-informed neural networks as a surrogate for TDDFT. We examine the computational efficiency and convergence behaviour of these solvers to state-of-the-art numerical techniques on models and small molecular systems. The method developed here has the potential to accelerate the TDDFT workflow, enabling the simulation of large-scale calculations of electron dynamics in matter exposed to strong electromagnetic fields, high temperatures, and pressures.

Speaker: Karan Shah (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

25 Accelerating Kohn-Sham Density Functional Theory with Neural Networks

Artificial intelligence (AI) has great potential for accelerating electronic structure calculations to hitherto unattainable scales [1]. I will present our recent efforts on accomplishing speeding up Kohn-Sham density functional theory calculations at finite temperatures with deep neural networks in terms of our Materials Learning Algorithms framework [2,3] 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 [4]. Finally, I will conclude with a preview of our most recent result that enables neural-network-driven electronic structure calculations for systems containing more than 100,000 atoms.

[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, arXiv:2202.09186 (2022).

Speaker: Attila Cangi (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

12:15 Lunch Break

Afternoon Session (Thursday)

Session Chair: Karan Shah

26 Warm Dense Matter, Quantum Hydrodynamics, and Shocks

The experimental and computational investigation of equilibrium and non-equilibrium many-body plasmas with partially or fully degenerate electrons is an intellectually challenging and stimulating problem. Warm dense matter is of particular interest since it exists at the intersection of condensed matter and ideal plasmas physics where particle correlations and quantum degeneracy are all important. A wide variety of theoretical methods have been developed and are in routine use for studying warm dense matter. This includes density functional theory, time-dependent density functional theory, kinetic equations and Green functions. Recently, there has been a resurgence in s “simpler” approach based on quantum hydrodynamics (QHD). QHD has a long and interesting history, dating back to Madelung and Bohm. In this talk, we discuss the historical and recent developments in QHD. We will discuss the implementation of a QHD capability in the multi-physics code MIRANDA and its application to shock physics. We use QHD MIRANDA with Fermi pressure, Bohm pressure, exchange, and Poisson to better understand shock propagation and shock structure in degenerate matter. We compare the shock physics described by QHD with that of classical fluid equations.

Speaker: Frank Graziani (Lawrence Livermore National Laboratory, United States)

27 Transferability of DFT surrogate models: Temperature and system size

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.

[1]: J. A. Ellis et al., Phys. Rev. B 104, 035120, 2021

Speaker: Lenz Fiedler (CASUS, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

15:45 Coffee Break

28 Computational Challenges in the development of a surrogate model for Density Functional Theory

This talk focuses on addressing the computational challenges in the development of a surrogate model for density functional theory. We detail three problems and solution that all have a common thread in reducing training time while building a scalable and robust model. We look at an approach that uses atom-centered density of states (ADOS) and graph neural networks to predict the ADOS as opposed to the grid-based approach. Second, we use an experimental design approach with the ADOS model to select the training data that we need to include to improve the model accuracy. Finally, I will describe a data flow hardware that could potentially improve the training time by avoiding expensive memory movement costs. Together, this would provide a solution to the original challenge from the perspective of new physics-based approaches, incremental training or careful data selection, and exploiting improvements in computer architectures.

Speaker: Siva Rajamanickam (Sandia National Laboratories, United States)

Friday 16 September

Morning Session (Friday)

Session Chair: Tobias Dornheim

29 High-fidelity particle-in-cell simulations at multiple scales

The particle-in-cell method is central to providing a kinetic description of the relativstic, nonlinear plasma dynamics -- particularly when interacting with ultrashort laser pulses and particle beams. Its broad applicability ranges from advanced plasma accelerators of electrons or ions, warm dense matter to astrophysics. A major challenge to a better understanding is to integrate disparate spatial and temporal scales, as well as physics into consistent, predictive models that can be compared to experimental results. While the large-scale dynamics is often determined by hydrodynamic evolution, the microscale physics includes ionization, radiation processes from infrared to xrays, atomic physics, as well as QED effects. Interfacing and integrating domain-specific numerical codes, such as particle trackers, FEL codes, requires data standards for seamless data exchange. Based on recent examples from plasma accelerator research using the 3D3V particle-in-cell code PIConGPU, I will outline the state-of-the art and challenges of particle-in-cell simulations to and show current strategies of solving them in large-scale simulations on heterogenous high-performance computing environments.

Speaker: Alexander Debus (Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf, Germany)

30 Conditional probability DFT and warm dense matter

Recently, our group suggested an alternative approach to standard DFT calculations. In CP-DFT, we use Kohn-Sham calculations to find conditional probability densities at every point in a system. These are then integrated to yield the exchange-correlation energy, thereby avoiding the need (and many of the failures) to find the energy via an approximate functional. We found that we could reproduce (reasonably accurately) the uniform gas ground-state energy and free energy as a function of temperature, as well as having no self-interaction error for one-electron systems, and being able to correctly dissociate the H2 molecule. I will summarize our progress toward using this to generate the temperature dependence of PBE.

[1] Bypassing the Energy Functional in Density Functional Theory: Direct Calculation of Electronic Energies from Conditional Probability Densities Ryan J. McCarty, Dennis Perchak, Ryan Pederson, Robert Evans, Yiheng Qiu, Steven R. White, and Kieron Burke, Phys. Rev. Lett. 125, 266401 (2020).
[2] Correlation energy of the uniform gas determined by ground state conditional probability density functional theory Dennis Perchak, Ryan J. McCarty, and Kieron Burke, Phys. Rev. B 105, 165143 (2022).
[3] Conditional probability density functional theory Ryan Pederson, Jielun Chen, Steven R. White, and Kieron Burke, to appear in Phys Rev B (2022).

Speaker: Kieron Burke (University of California, Irvine, United States)

10:30 Coffee Break

31 Thermal PBE for Warm Dense Matter Calculations

Finite-Temperature Density Functional Theory (FT-DFT) has played a significant role in the study of warm dense matter over the past few decades. However, modern FT-DFT calculations typically make use of ground-state approximations to the exchange-correlation (XC) free energy, ignoring its temperature dependence. While overall the ground-state approximation is valid in both the low- and high-temperature limits, the quantitative ramifications of this approximation are unknown and may be crucial to our current understanding of warm dense matter. To correct this, we calculate the temperature dependence of PBE through a sequence of Kohn-Sham CP-DFT calculations [1] that yield accurate exchange-correlation holes at finite temperatures. We will present the results of this thermal PBE and compare with existing suggestions in the literature.

[1] R. J. McCarty, et al. “Bypassing the Energy Functional in Density Functional Theory: Direct Calculation of Electronic Energies from Conditional Probability Densities.” Phys. Rev. Lett. 125, 266401 (2020).

We acknowledge funding from the Department of Energy Award No. DE-FG02-08ER46496.

Speaker: John Kozlowski (University of California, Irvine, United States)

32 Closing Remarks