arXiv subjects

Hans-Joachim Bungartz

Publications and source records attributed to Hans-Joachim Bungartz.

At least 19 recordsLinked to original sources

arXiv2026

Adaptive Parallel-in-Time Integration with Dynamic Resource Management

As computational resources continue to grow, the strong-scaling limitations of spatial parallelism motivate the pursuit of additional concurrency in the temporal dimension, particularly for applications with hard time constraints, such as weather and climate simulations. The Parallel Full Approximation Scheme in Space and Time (PFASST) is a parallel-in-time method based on Spectral Deferred Corrections (SDC). It computes multiple timesteps concurrently by coupling fine- and coarse-grid SDC sweeps using multigrid Full Approximation Scheme (FAS) corrections. However, PFASST's convergence is often problem-dependent, demanding a variable number of parallel timesteps and, hence, computing resources at different times throughout the simulation. Dynamic Resource Management (DRM) provides a remedy for this challenge by enabling the adaptive adjustment of computational resources and algorithmic parameters at runtime. In this work, we present our novel approach to extending PFASST with DRM, which enables (a) dynamic adaptation of computing resources, (b) adaptive selection of the number of PFASST iterations based on local convergence behavior, and (c) coupling of these two adaptations into a single resizing strategy. With this approach, we demonstrate for the first time that optimal configurations can be identified in real time for each application, rather than relying on static allocation. Furthermore, we show that convergence-informed tuning of PFASST improves resource utilization and convergence efficiency.

cs.CE↗

arXiv2026

The QTF-Backbone: Proposal for a Nationwide Optical Fibre Backbone in Germany for Quantum Technology and Time and Frequency Metrology

The recent breakthroughs in the distribution of quantum information and high-precision time and frequency (T&F) signals over long-haul optical fibre networks have transformative potential for physically secure communications, resilience of timing infrastructure (such as that supporting Global Navigation Satellite Systems (GNSS)) and fundamental physics. To date, these capabilities remain confined to isolated testbeds, with quantum and T&F signals accessible, for example in Germany, to only a few institutions. In this white paper we propose the QTF Backbone: a dedicated national fibre-optic infrastructure in Germany for the networked distribution of Quantum and T&F signals using dark fibres and specialised hardware. The QTF Backbone is planned as a four-phase deployment over ten years to ensure scalable, sustainable access for research institutions and industry. The concept builds on successful demonstrations of time and frequency distribution at high Technology Readiness Levels (TRLs) across Europe, including PTB-MPQ links in Germany, REFIMEVE in France, and the Italian LIFT network. The QTF Backbone will enable transformative Research and Development (R&D), support a nationwide QTF ecosystem, and ensure the transition from innovation to deployment. As a national and European hub, it will position Germany and Europe at the forefront of quantum networking, as well as T&F transfer.

physics.ins-det↗

arXiv2026

Rational neural networks for tracking complex singularities of nonlinear PDEs

We present a neural network-based method for numerical analytic continuation of solutions of nonlinear partial differential equations (PDEs) and detection of their complex singularities. The proposed framework employs "unsafe" Padé activation units (PAUs) as activation functions, together with a novel backpropagation-free method for computing the weights and biases of the hidden layers. The training procedure is designed specifically for learning meromorphic functions with pole-type singularities. Unlike existing methods with fixed hidden-layer parameters, the proposed approach treats the weights and biases as time-dependent functions, allowing the network to adapt to the evolution of the complex singularities. Using this method, we can efficiently locate the complex singularities of the extended solution, track their trajectories over time, and, based on this dynamics, infer the formation of characteristic phenomena in the solutions of nonlinear PDEs. To demonstrate the performance of our method, we analyze three well-known cases: (1) the nonlinear heat equation, which exhibits finite-time blow up; (2) the nonlinear Burgers equation, which develops a shock; and (3) the nonlinear Schrödinger equation, in which rogue waves form.

math.NA↗

arXiv2026

Embedding-based Methods for Linear Solver Performance Prediction

The solution of large, sparse linear systems often dominates the computational effort of scientific applications and is a frequent optimization target. Modern libraries provide numerous solver and preconditioner configurations, but their performance varies significantly across problem instances. Previous works have addressed the selection of an optimal solver, but are typically limited by the problem set addressed (e.g., only symmetric positive definite matrices), the use of expensive matrix features, or the complexity of the approach. This work proposes a modular, low-cost embedding-based framework for solver selection that decouples performance modeling from feature representation and downstream prediction. Solver-problem relationships are learned directly from observed performance data, while inexpensive numerical features are used to project unseen problems into the learned embedding space. The framework focuses on multilabel prediction and evaluation using user-centric metrics, such as MAPE and nDCG, which better reflect relative performance. Experiments on 621 matrices from the SuiteSparse matrix collection across 101 PETSc solver configurations demonstrate a 17% increase in top-prediction accuracy over classical feature-based models when expensive numerical features are included, along with reductions of 37% in mean average percentage error (MAPE) and 46% in top-prediction error (1-error). When restricted to a reduced feature set, the embedding approach remains competitive, while still consistently achieving ca. 24% lower MAPE and 1-error across a broad range of problems.

cs.CE↗

arXiv2026

Time-dependent global sensitivity analysis of the Doyle-Fuller-Newman model

The Doyle-Fuller-Newman model is arguably the most ubiquitous electrochemical model in lithium-ion battery research. Since it is a highly nonlinear model, its input-output relations are still poorly understood. Researchers therefore often employ sensitivity analyses to elucidate relative parametric importance for certain use cases. However, some methods are ill-suited for the complexity of the model and appropriate methods often face the downside of only being applicable to scalar quantities of interest. We implement a novel framework for global sensitivity analysis of time-dependent model outputs and apply it to a drive cycle simulation. We conduct a full and a subgroup sensitivity analysis to resolve lowly sensitive parameters and explore the model error when unimportant parameters are set to arbitrary values. Our findings suggest that the method identifies insensitive parameters whose variations cause only small deviations in the voltage response of the model. By providing the methodology, we hope research questions related to parametric sensitivity for time-dependent quantities of interest, such as voltage responses, can be addressed more easily and adequately in simulative battery research and beyond.

cond-mat.mtrl-sci↗

arXiv2025

Tuning of Vectorization Parameters for Molecular Dynamics Simulations in AutoPas

Molecular Dynamics simulations can help scientists to gather valuable insights for physical processes on an atomic scale. This work explores various techniques for SIMD vectorization to improve the pairwise force calculation between molecules in the scope of the particle simulation library AutoPas. The focus lies on the order in which particle values are loaded into vector registers to achieve the most optimal performance regarding execution time or energy consumption. As previous work indicates that the optimal MD algorithm can change during runtime, this paper investigates simulation-specific parameters like particle density and the impact of the neighbor identification algorithms, which distinguishes this work from related projects. Furthermore, AutoPas' dynamic tuning mechanism is extended to choose the optimal vectorization order during runtime. The benchmarks show that considering different particle interaction orders during runtime can lead to a considerable performance improvement for the force calculation compared to AutoPas' previous approach.

cs.DC↗

arXiv2025

Linked Cell Traversal Algorithms for Three-Body Interactions in Molecular Dynamics

In this work, algorithms for the parallel computation of three-body interactions in molecular dynamics are developed. While traversals for the computation of pair interactions are readily available in the literature, here, such traversals are extended to allow for the computation between molecules stored across three cells. A general framework for the computation of three-body interactions in linked cells is described, and then used to implement the corresponding traversals. In addition, our analysis is combined with the commonly used cutoff conditions, because they influence the total workload of the computation of interactions. The combinations between traversals and truncation conditions are validated using the well-known Lennard-Jones fluid. Validation case studies are taken from the literature and configured into homogeneous and inhomogeneous scenarios. Finally, strong scalability and performance in terms of molecule updates are measured at node-level.

cs.CE↗

arXiv2025

The Multiple Time-Stepping Method for 3-Body Interactions in High Performance Molecular Dynamics Simulations

Understanding the complex behavior of molecular systems is fundamental to fields such as physics, materials science, and biology. Molecular dynamics (MD) simulations are crucial tools for studying atomic-level dynamics. This work focuses on improving the efficiency of MD simulations involving two-body and three-body interactions. Traditional two-body potentials often can not fully capture the complexity of molecular systems, making the inclusion of three-body interactions important. However, these interactions are in a cubic complexity class, compared to a quadratic one for two-body interactions, and therefore are computationally expensive, even when a cutoff distance is applied. One way to improve efficiency is to use the r-RESPA multiple time-stepping algorithm to reduce the number of three-body interaction calculations. In this work, we investigate this method in the context of High Performance Computing (HPC) methods that parallelize the calculations. In particular, we investigate a communication-reducing distributed-memory parallel method from literature and present a novel shared-memory parallel cutoff method, implemented in the particle simulation library AutoPas. The results and methods are discussed, providing insights into potential advancements in MD simulation efficiency.

cs.CE↗

arXiv2025

Algorithm Selection in Short-Range Molecular Dynamics Simulations

Numerous algorithms and parallelisations have been developed for short-range particle simulations; however, none are optimally performant for all scenarios. Such a concept led to the prior development of the particle simulation library AutoPas, which implemented many of these algorithms and parallelisations and could select and tune these over the course of the simulation as the scenario changed. Prior works have, however, used only naive approaches to the algorithm selection problem, which can lead to significant overhead from trialling poorly performing algorithmic configurations. In this work, we investigate this problem in the case of Molecular Dynamics simulations. We present three algorithm selection strategies: an approach which makes performance predictions from past data, an expert-knowledge fuzzy logic-based approach, and a data-driven random forest-based approach. We demonstrate that these approaches can achieve speedups of up to 4.05 compared to prior approaches and 1.25 compared to a perfect configuration selection without dynamic algorithm selection. In addition, we discuss the practicality of the strategies in comparison to their performance, to highlight the tractability of such solutions.

cs.CE↗

arXiv2024

Multi-fidelity Gaussian process surrogate modeling for regression problems in physics

One of the main challenges in surrogate modeling is the limited availability of data due to resource constraints associated with computationally expensive simulations. Multi-fidelity methods provide a solution by chaining models in a hierarchy with increasing fidelity, associated with lower error, but increasing cost. In this paper, we compare different multi-fidelity methods employed in constructing Gaussian process surrogates for regression. Non-linear autoregressive methods in the existing literature are primarily confined to two-fidelity models, and we extend these methods to handle more than two levels of fidelity. Additionally, we propose enhancements for an existing method incorporating delay terms by introducing a structured kernel. We demonstrate the performance of these methods across various academic and real-world scenarios. Our findings reveal that multi-fidelity methods generally have a smaller prediction error for the same computational cost as compared to the single-fidelity method, although their effectiveness varies across different scenarios.

stat.ML↗

arXiv2023

Multi-fidelity Constrained Optimization for Stochastic Black Box Simulators

Constrained optimization of the parameters of a simulator plays a crucial role in a design process. These problems become challenging when the simulator is stochastic, computationally expensive, and the parameter space is high-dimensional. One can efficiently perform optimization only by utilizing the gradient with respect to the parameters, but these gradients are unavailable in many legacy, black-box codes. We introduce the algorithm Scout-Nd (Stochastic Constrained Optimization for N dimensions) to tackle the issues mentioned earlier by efficiently estimating the gradient, reducing the noise of the gradient estimator, and applying multi-fidelity schemes to further reduce computational effort. We validate our approach on standard benchmarks, demonstrating its effectiveness in optimizing parameters highlighting better performance compared to existing methods.

math.OC↗

arXiv2023

Efficient and Scalable Kernel Matrix Approximations using Hierarchical Decomposition

With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense depending on the kernel. A global method, i.e. a method that requires all data points simultaneously, scales with the data dimension N and not with the intrinsic dimension d; the complexity for an exact dense eigendecomposition leads to $\mathcal{O}(N^{3})$. We have combined the two frameworks, $\mathsf{datafold}$ and $\mathsf{GOFMM}$. The first framework computes diffusion maps, where the computational bottleneck is the eigendecomposition while with the second framework we compute the eigendecomposition approximately within the iterative Lanczos method. A hierarchical approximation approach scales roughly with a runtime complexity of $\mathcal{O}(Nlog(N))$ vs. $\mathcal{O}(N^{3})$ for a classic approach. We evaluate the approach on two benchmark datasets -- scurve and MNIST -- with strong and weak scaling using OpenMP and MPI on dense matrices with maximum size of $100k\times100k$.

math.NA↗

arXiv2023

Multi-fidelity No-U-Turn Sampling

Markov Chain Monte Carlo (MCMC) methods often take many iterations to converge for highly correlated or high-dimensional target density functions. Methods such as Hamiltonian Monte Carlo (HMC) or No-U-Turn Sampling (NUTS) use the first-order derivative of the density function to tackle the aforementioned issues. However, the calculation of the derivative represents a bottleneck for computationally expensive models. We propose to first build a multi-fidelity Gaussian Process (GP) surrogate. The building block of the multi-fidelity surrogate is a hierarchy of models of decreasing approximation error and increasing computational cost. Then the generated multi-fidelity surrogate is used to approximate the derivative. The majority of the computation is assigned to the cheap models thereby reducing the overall computational cost. The derivative of the multi-fidelity method is used to explore the target density function and generate proposals. We select or reject the proposals using the Metropolis Hasting criterion using the highest fidelity model which ensures that the proposed method is ergodic with respect to the highest fidelity density function. We apply the proposed method to three test cases including some well-known benchmarks to compare it with existing methods and show that multi-fidelity No-U-turn sampling outperforms other methods.

math.NA↗

arXiv2023

Multilevel Monte Carlo estimators for derivative-free optimization under uncertainty

Optimization is a key tool for scientific and engineering applications, however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest. Optimization under uncertainty (OUU) deals with this endeavor and requires uncertainty quantification analyses at several design locations. The cost of OUU is proportional to the cost of performing a forward uncertainty analysis at each design location visited, which makes the computational burden too high for high-fidelity simulations with significant computational cost. From a high-level standpoint, an OUU workflow typically has two main components: an inner loop strategy for the computation of statistics of the quantity of interest, and an outer loop optimization strategy tasked with finding the optimal design, given a merit function based on the inner loop statistics. In this work, we propose to alleviate the cost of the inner loop uncertainty analysis by leveraging the so-called Multilevel Monte Carlo (MLMC) method. MLMC has the potential of drastically reducing the computational cost by allocating resources over multiple models with varying accuracy and cost. The resource allocation problem in MLMC is formulated by minimizing the computational cost given a target variance for the estimator. We consider MLMC estimators for statistics usually employed in OUU workflows and solve the corresponding allocation problem. For the outer loop, we consider a derivative-free optimization strategy implemented in the SNOWPAC library; our novel strategy is implemented and released in the Dakota software toolkit. We discuss several numerical test cases to showcase the features and performance of our novel approach with respect to the single fidelity counterpart, based on standard Monte Carlo evaluation of statistics.

stat.CO↗

arXiv2022

Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. It generalizes the previously developed context-aware bi-fidelity Monte Carlo method to hierarchies of multiple models and to more general types of low-fidelity models. When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets. This is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs and typically ignore the context in which the learned models will be used in upstream tasks. The proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies of a wide range of types of low-fidelity models such as sparse-grid and deep-network models. Numerical experiments with the gyrokinetic simulation code \textsc{Gene} show speedups of up to two orders of magnitude compared to standard estimators when quantifying uncertainties in small-scale fluctuations in confined plasma in fusion reactors. This corresponds to a runtime reduction from 72 days to about four hours on one node of the Lonestar6 supercomputer at the Texas Advanced Computing Center.

math.NA↗

arXiv2022

Neural Nets with a Newton Conjugate Gradient Method on Multiple GPUs

Training deep neural networks consumes increasing computational resource shares in many compute centers. Often, a brute force approach to obtain hyperparameter values is employed. Our goal is (1) to enhance this by enabling second-order optimization methods with fewer hyperparameters for large-scale neural networks and (2) to perform a survey of the performance optimizers for specific tasks to suggest users the best one for their problem. We introduce a novel second-order optimization method that requires the effect of the Hessian on a vector only and avoids the huge cost of explicitly setting up the Hessian for large-scale networks. We compare the proposed second-order method with two state-of-the-art optimizers on five representative neural network problems, including regression and very deep networks from computer vision or variational autoencoders. For the largest setup, we efficiently parallelized the optimizers with Horovod and applied it to a 8 GPU NVIDIA P100 (DGX-1) machine.

cs.LG↗

arXiv2022

FAIR data enabling new horizons for materials research

The prosperity and lifestyle of our society are very much governed by achievements in condensed matter physics, chemistry and materials science, because new products for sectors such as energy, the environment, health, mobility and information technology (IT) rely largely on improved or even new materials. Examples include solid-state lighting, touchscreens, batteries, implants, drug delivery and many more. The enormous amount of research data produced every day in these fields represents a gold mine of the twenty-first century. This gold mine is, however, of little value if these data are not comprehensively characterized and made available. How can we refine this feedstock; that is, turn data into knowledge and value? For this, a FAIR (findable, accessible, interoperable and reusable) data infrastructure is a must. Only then can data be readily shared and explored using data analytics and artificial intelligence (AI) methods. Making data 'findable and AI ready' (a forward-looking interpretation of the acronym) will change the way in which science is carried out today. In this Perspective, we discuss how we can prepare to make this happen for the field of materials science.

cond-mat.mtrl-sci↗

arXiv2021

Data-driven low-fidelity models for multi-fidelity Monte Carlo sampling in plasma micro-turbulence analysis

The linear micro-instabilities driving turbulent transport in magnetized fusion plasmas (as well as the respective nonlinear saturation mechanisms) are known to be sensitive with respect to various physical parameters characterizing the background plasma and the magnetic equilibrium. Therefore, uncertainty quantification is essential for achieving predictive numerical simulations of plasma turbulence. However, the high computational costs of the required gyrokinetic simulations and the large number of parameters render standard Monte Carlo techniques intractable. To address this problem, we propose a multi-fidelity Monte Carlo approach in which we employ data-driven low-fidelity models that exploit the structure of the underlying problem such as low intrinsic dimension and anisotropic coupling of the stochastic inputs. The low-fidelity models are efficiently constructed via sensitivity-driven dimension-adaptive sparse grid interpolation using both the full set of uncertain inputs and subsets comprising only selected, important parameters. We illustrate the power of this method by applying it to two plasma turbulence problems with up to $14$ stochastic parameters, demonstrating that it is up to four orders of magnitude more efficient than standard Monte Carlo methods measured in single-core performance, which translates into a runtime reduction from around eight days to one hour on 240 cores on parallel machines.

physics.comp-ph↗