projects | CRC 1639 NuMeriQS

A01

Sat, 20 Jan 2024 17:07:25 +0100

Investigating energy-device systems with computational methods requires large timescales and an accurate treatment of all the atomic interactions present, thus this project aims to develop methods that can efficiently yield accurate results for this purpose. In order to overcome the limitations of conventional Ab Initio Molecular Dynamics (AIMD), the project will employ Hamiltonian Monte Carlo (HMC) approaches as well as Machine Learning based Force Fields trained using ab initio data from AIMD simulations. Overall this project aims to unlock new possibilities in investigating highly complex systems and to provide valuable insights into materials used in energy devices.

A02

Sat, 20 Jan 2024 17:07:25 +0100

This project aims to achieve large-scale implementations of many-body electronic structure theories using automatic code generation. The developments aims at addressing a number of pressing issues in the Development of quantum chemical ab initio methods including legacy code, code of uncertain correctness, code of overwhelming complexity, and hardware adaptability. The main goal is to arrive at highly optimised codes for large scale computing platforms While reducing development times by many orders of magnitude or enabling the possibility of implementation of theories that are too complex for humans. The proposed code generation chain consists of three steps: an equation generator, a factorizer for optimal generation of intermediates, and the actual code generator producing host- and hardware-specific high-level code.

A03

Sat, 20 Jan 2024 17:07:25 +0100

This project aims to develop fast methods to quantify the uncertainty in properties of liquids predicted by computational chemistry methods like Molecular Dynamics (MD) simulations, Ab Initio MD (AIMD) simulations, and Quantum Cluster Equilibrium (QCE) calculations. The focus is on liquids, such as water, alcohols, and ionic liquids. The goal is to improve computational efficiency by using proven and newly developed multi-fidelity approaches to handle random errors in input quantities. By quantifying the resulting uncertainties, the project seeks to gain a better understanding and develop new computational methods in computational chemistry. These methods can have broader applications and be beneficial to other projects of the CRC.

A04

Sat, 20 Jan 2024 17:07:25 +0100

Quantum many-body systems as well as multiple other areas of physics heavily rely on discrete time evolution using so-called Trotterization techniques. This project aims to derive maximally precise Trotterizations at minimal computational cost. The first goal is to construct optimised higher order Trotter schemes for two operators based on their theoretical efficiencies. Next, the results are going to be generalised for a higher number of operators. The third goal is to understand and integrate in-practice deviations from the theoretical efficiencies into the framework. Lastly, efficient Trotterization is pivotal for digital quantum computing, and the fourth goal is hence to transfer the results to quantum computing applications.

A05

Sat, 20 Jan 2024 17:07:25 +0100

The project aims to improve Ab initio molecular dynamics (AIMD) simulations and the analysis of their results for liquid systems in theoretical chemistry. The approach involves running multiple AIMD simulations simultaneously and using novel graph algorithms to exchange and analyze trajectory data. This will enable the study of more complex molecular systems and emergent structural properties. The goal is to make more efficient use of computer resources, improve application performance, and investigate complex chemical problems. The use of Modular Supercomputing Architecture (MSA) will match diverse workflow requirements and provide valuable insights for next-generation MSA-systems.

A06

Sat, 20 Jan 2024 17:07:25 +0100

Periodically driven quantum many-body systems are relevant for describing recent experiments in ultracold atom experiments and can be characterized by the structure of the eigenstates of the unitary generator of their dynamics. Accessing these states is a great computational challenge due to the exponential growth of the state space with system size and the dense structure of the generator. In this project, we will develop a high-performance technique for calculating exact eigenstates of such generators based on a complex polynomial transformation and the exploitation of symmetries of the system.

B01

Sat, 20 Jan 2024 17:07:25 +0100

The project aims to describe emergent phenomena in low-dimensional systems, such as graphene, nanoribbons, and nanotubes, which require strong-interaction techniques due to their highly non-linear electronic behavior. These systems exhibit exotic phenomena tied to their underlying topology, resulting in topological insulators and superconductors, with potential applications in topological quantum computing. An Effective Field Theory (EFT) will be formulated to identify relevant degrees of freedom and investigate multi-particle dynamics. The project will use numerical simulations to determine Low-Energy Constants (LECs) for the EFT, considering length scales and non-locality of topological effects in different low-dimensional geometries.

B02

Sat, 20 Jan 2024 17:07:25 +0100

This project aims to develop an open-source software framework for efficient and scalable numerical simulations in Lattice Field Theory (LFT). It will address increasing complexity in LFT problems and adapt to evolving heterogeneous hardware platforms. New algorithmic techniques, including Machine Learning (ML) methods, will be integrated with scalable algorithms to explore inaccessible regions of the parameter landscape. The expanded scope of addressable physical problems and the insights gained in the efficient use of heterogeneous and modular supercomputing platforms have the potential to be translated to multiple projects of this CRC.

B03

Sat, 20 Jan 2024 17:07:25 +0100

The project aims to investigate high-dimensional integration and quadrature methods for lattice field theories. Predicting the average value of an observable in a high-dimensional space is a challenging problem, typically addressed using Monte Carlo (MC) and Markov Chain Monte Carlo (MCMC) methods. Deterministic quadrature methods like Quasi Monte Carlo (QuasiMC) and sparse grid quadrature can however achieve higher convergence rates. The project aims to explore these advanced techniques for lattice gauge theories.

B04

Sat, 20 Jan 2024 17:07:25 +0100

The project aims to improve theoretical predictions for hadron collider experiments like the LHC. Current computational complexities and lack of analytic solutions for the appearing integrals are among the main obstacles to achieving the precision required by the experiments. The project will investigate novel numerical approaches for evaluating multi-dimensional Feynman integrals. Divergences will be dealt with by constructing local counterterms at the integrand level. We will then explore the application of hp-quadrature methods for the numerical evaluation of the finite remainders, as an alternative to to the Monte Carlo approach. The goal is to provide a proof of concept for novel numerical algorithms to evaluate two-loop integrals that are currently challenging to compute using conventional techniques.

B05

Sat, 20 Jan 2024 17:07:25 +0100

The goal of this project is to determine the spectrum of baryon resonances which encodes the key to understand the strong force at medium energies. The extraction of the spectrum from data is challenging and sophisticated, but numerically very costly, dynamical coupled-channel models are the method of choice. A systematic quantification of uncertainties, however, is so far not possible. This project proposes to transition to Bayesian parameter estimation using the Hamiltonian Monte Carlo (HMC) algorithm, allowing for a determination of resonance parameter uncertainties in a statistically well-defined way. This innovation will raise baryon spectroscopy to the next level of precision.

B06

Sat, 20 Jan 2024 17:07:25 +0100

The main challenge in Lattice Quantum Chromodynamics (LQCD) computations is efficiently solving large sparse linear systems of the form Dz = b, where D depends on a gauge field U and a mass constant m. Current simulation methods spend more than 90% of the computational time on this task, making it crucial to develop more efficient scalable linear solvers for LQCD. This project aims to develop a robust and efficient linear solver using novel algebraic multigrid / algebraic multiscale techniques and integrating Machine Learning (ML) techniques into the solver setup.

C01

Sat, 20 Jan 2024 17:07:25 +0100

This project aims at combining complementary path integral Lagrangian and Hamiltonian methods in order to investigate lattice gauge theories from first principles. For this, efficient digitisations of non-Abelian gauge theories will be investigated and tested, a non-perturbative matching protocol between the Lagrangian and Hamiltonian lattice formulations will be developed and, as a first application, the running coupling constant in an Abelian gauge theory in 2+1 dimensions will be determined. In the long term these developments will offer the possibility to study gauge theories, and in particular quantum chromodynamics, in regions of parameter space not accessible today by using quantum computing and tensor network methods.

C02

Sat, 20 Jan 2024 17:07:25 +0100

The main goal of this project is to combine different methodologies effectively, leveraging their strengths against weaknesses. By integrating hybrid stochastic techniques with machine learning, multidimensional Tensor Networks, and the Iterative Configuration Expansion from quantum chemistry, our long term goal is to create a powerful approach to challenging quantum many-body systems. The objective is to unlock investigations of currently inaccessible quantum many-body systems at finite chemical potential, particularly focusing on QCD at finite baryon density and models for high-Tc superconductors.

C03

Sat, 20 Jan 2024 17:07:25 +0100

This project focuses on using tensor networks, quantum computing, and machine learning to study topological effects in lattice gauge theories (LGTs) of increasing complexity. The initial goal will be the simulation of (2+1)-dimensional LGTs with tensor networks and quantum computing, focusing on compact quantum electrodynamics (QED) with a topological Chern-Simons term. In particular, we aim to map out the phase diagram and study implications for condensed-matter physics, such as topological mass generation and the quantum Hall effect. Moreover, in collaboration with project C02, we will use machine learning enhanced Monte Carlo methods to study the Chern Simons-term in QED. Long-term plans include extending these methods to (3+1)-dimensional LGTs, including Lattice Quantum Chromodynamics with the θ-term.

Z01

Sat, 20 Jan 2024 17:07:25 +0100

NuMeriQS administrative project.

Z02

Sat, 20 Jan 2024 17:07:25 +0100

This project addresses the need for high performance computing expertise in many of the scientific projects in the NuMeriQS CRC. It offers central support, focusing on performance optimisation and addressing challenges related to the heterogeneous supercomputing resources. The project closely collaborates with Juelich Supercomputing Center (JSC). This allows the project to access diverse hardware architectures for benchmarking and co-design purposes through JSC industry partners. In its first funding phase, it supports Research Software Engineering (RSE) activities, reproducible benchmarking, application performance engineering and scaling analysis. In subsequent funding phases this foundation shall be extended to support the application of the numerical methods developed within the CRC to larger and more complex chemical and physical systems which will also require projects to employ correspondingly larger and more complex supercomputing hardware.