Modern High-performance Computing Systems Research Articles

The Advanced Computing Hub at BSC: Improving fusion codes following modern software engineering standards

Abstract Several dedicated High-Performance Computing (HPC) centers provide essential expertise and support in developing a suitable portfolio of EUROfusion standard codes. Barcelona Supercomputing Center (BSC) is one of these HPC hubs involved in this complex task. Several fusion codes were selected, installed and analyzed to meet the developers’ requirements, ranging from portability to GPU, improving the performance, getting better data management, extending the capacity of coupling with other codes, etc. In this paper, we will describe the work developed by BSC and some of the tasks carried out in this project. We will explain briefly how the project is faced and the work required to create good quality codes, i.e. robust and trustable software capable of running efficiently in modern HPC systems.

Predicting Software Defects in Hybrid MPI and OpenMP Parallel Programs Using Machine Learning

High-performance computing (HPC) and its supercomputers are essential for solving the most difficult issues in many scientific computing domains. The proliferation of computational resources utilized by HPC systems has resulted in an increase in the associated error rates. As such, modern HPC systems promote a hybrid programming style that integrates the message-passing interface (MPI) and open multi-processing (OpenMP). However, this integration often leads to complex defects, such as deadlocks and race conditions, that are challenging to detect and resolve. This paper presents a novel approach: using machine learning algorithms to predict defects in C++-based systems by employing hybrid MPI and OpenMP models. We focus on employing a balanced dataset to enhance prediction accuracy and reliability. Our study highlights the effectiveness of the support vector machine (SVM) classifier, enhanced with term frequency (TF) and recursive feature elimination (RFE) techniques, which demonstrates superior accuracy and performance in defect prediction when compared to other classifiers. This research contributes significantly to the field by providing a robust method for early defect detection in hybrid programming environments, thereby reducing development time, costs and improving the overall reliability of HPC systems.

OBTAINING BULK PRODUCTS FROM CU-SIC METAL-MATRIX COMPOSITE FOR ENERGY-EFFICIENT HEAT-CONDUCTING SYSTEMS

Link for citation: Nikitin D.S., Shanenkov I.I., Nassyrbayev A., Vympina Yu. N., Orlova E.G., Ivashutenko A.S., Sivkov A.A. Obtaining bulk products from Cu-SiC metal-matrix composite for energy-efficient heat-conducting systems. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 7, рр. 93-101. In Rus. The relevance of the research is associated with the rapid development of modern high-performance computing systems, superneurocomputers and artificial intelligence devices. Today such development is held back largely due to the lack of an effective cooling system for high-power elements of their structures. Composite materials Cu-SiC with improved physical, mechanical and thermophysical characteristics can be used to solve problems of heat removal intensification. The main aim of the research is to obtain bulk products from metal-matrix composite Cu-10% SiC with improved physical, mechanical and thermal characteristics by spark plasma sintering. Objects of the research are bulk products from metal-matrix composite Cu-10%SiC. The samples were obtained by spark plasma sintering at temperatures of 700, 750, 800, 850 °C and a pressure of 60 MPa. Methods: spark plasma sintering, X-ray diffractometry (X-ray phase analysis), scanning electron microscopy, indentation, laser flash method. Results. Experimental studies have been carried out to obtain bulk metal-matrix composites with a copper matrix and the addition of reinforcing superhard particles of silicon carbide Cu-10%SiC. The compaction of dispersed composite materials was carried out by spark plasma sintering at various temperatures of 700, 750, 800, and 850 °C. The microstructure and composition of initial dispersed materials and final bulk products have been studied. It is shown that the spark plasma sintering method has advantages for obtaining relatively dense materials with high physical, mechanical and thermal properties. Analysis of the obtained samples showed the formation of a dense (up to ~88 %) homogeneous fine-grained composite structure. The greatest densification of the material is achieved at the highest sintering temperature of 850 °C, which causes this sample to demonstrate the maximum hardness (H=3,63 GPa) and Young's modulus (E=159,63 GPa), as well as the thermal conductivity at room temperature (λ=223 W/m K). The obtained composite materials can be used as structural and functional materials for energy-efficient heat-conducting systems.

Mixed precision support in HPC applications: What about reliability?

In their quest for exascale and beyond, High-Performance Computing (HPC) systems continue becoming ever larger and more complex. Application developers, on the other hand, leverage novel methods to improve the efficiency of their own codes: a recent trend is the use of floating-point mixed precision, or the careful interlocking of single- and double-precision arithmetic, as a tool to improve performance as well as reduce network and memory boundedness. However, while it is known that modern HPC systems suffer hardware faults at daily rates, the impact of reduced precision on application reliability is yet to be explored. In this work we aim to fill this gap: first, we propose a qualitative survey to identify the branches of HPC where mixed precision is most popular. Second, we show the results of instruction-level fault injection experiments on a variety of representative HPC workloads, comparing vulnerability to Silent Data Errors (SDEs) under different numerical configurations. Our experiments indicate that use of single and mixed precision leads to comparatively more frequent and more severe SDEs, with concerning implications regarding their use on extreme-scale, fault-prone HPC platforms.

Data Extraction and Intelligent Analysis of Aesthetic Laws Accepted by VR Digital Media Art on Film Art Based on NVIDIA GPU Hardware

On the premise of analyzing traditional computer VR technology, this paper explores the application value of VR technology based on NVIDIA GPU hardware in the design of digital media systems, and proposes corresponding application measures to further improve the practical application capability of VR technology. These technologies integrate the achievements of modern high-performance computer systems, artificial intelligence, computer graphics, human-machine interfaces, stereoscopic images, stereophonic sound, measurement control, simulation simulation and other technologies. Analytical models and multi-grained formal conceptual analysis.

Benchmarking energy consumption and latency for neuromorphic computing in condensed matter and particle physics

The massive use of artificial neural networks (ANNs), increasingly popular in many areas of scientific computing, rapidly increases the energy consumption of modern high-performance computing systems. An appealing and possibly more sustainable alternative is provided by novel neuromorphic paradigms, which directly implement ANNs in hardware. However, little is known about the actual benefits of running ANNs on neuromorphic hardware for use cases in scientific computing. Here, we present a methodology for measuring the energy cost and compute time for inference tasks with ANNs on conventional hardware. In addition, we have designed an architecture for these tasks and estimate the same metrics based on a state-of-the-art analog in-memory computing (AIMC) platform, one of the key paradigms in neuromorphic computing. Both methodologies are compared for a use case in quantum many-body physics in two-dimensional condensed matter systems and for anomaly detection at 40 MHz rates at the Large Hadron Collider in particle physics. We find that AIMC can achieve up to one order of magnitude shorter computation times than conventional hardware at an energy cost that is up to three orders of magnitude smaller. This suggests great potential for faster and more sustainable scientific computing with neuromorphic hardware.

RUAD: Unsupervised anomaly detection in HPC systems

The increasing complexity of modern high-performance computing (HPC) systems necessitates the introduction of automated and data-driven methodologies to support system administrators’ effort towards increasing the system’s availability. Anomaly detection is an integral part of improving the availability as it eases the system administrator’s burden and reduces the time between an anomaly and its resolution. However, current state-of-the-art (SOTA) approaches to anomaly detection are supervised and semi-supervised, so they require a human-labelled dataset with anomalies — this is often impractical to collect in production HPC systems. Unsupervised anomaly detection approaches based on clustering, aimed at alleviating the need for accurate anomaly data, have so far shown poor performance.In this work, we overcome these limitations by proposing RUAD, a novel Recurrent Unsupervised Anomaly Detection model. RUAD achieves better results than the current semi-supervised and unsupervised SOTA approaches. This is achieved by considering temporal dependencies in the data and including long-short term memory cells in the model architecture. The proposed approach is assessed on a complete ten-month history of a Tier-0 system (Marconi100 from CINECA with 980 nodes). RUAD achieves an area under the curve (AUC) of 0.763 in semi-supervised training and an AUC of 0.767 in unsupervised training, which improves upon the SOTA approach that achieves an AUC of 0.747 in semi-supervised training and an AUC of 0.734 in unsupervised training. It also vastly outperforms the current SOTA unsupervised anomaly detection approach based on clustering, achieving the AUC of 0.548.

Kinetic consistent MHD algorithm for incompressible conductive fluids

The first ideas concerning the principle of operation of non-mechanical magneto-hydrodynamic pumping systems were originally created at the end of the 1960s during studies of efficient heat exchange systems in nuclear energy sources using liquid metals as coolant. Currently, these ideas are of increasing interest in the creation of many critical technologies that require precise flow control in distributed energy transfer systems, in particular for a new generation of environmentally friendly efficient nuclear power sources.In this regard, computational fluid dynamic methods are an effective instrument for studying complex energy transfer processes, the possibilities of which have been significantly expanded with the creation of modern high-performance computing systems and modern computing technologies.The purpose of this article is to describe an advanced method of the mathematical modeling of magneto-hydrodynamic processes based on kinetic and kinetically consistent models. The novelty of this approach lies in more advanced physical models derived from the Boltzmann kinetic equation with a complex-valued statistical distribution function that includes electromagnetic interactions. The possibility of applying this description to incompressible viscous media (liquid metals) in complex magneto-hydrodynamic systems is shown.The system of equations of the proposed method, a numerical algorithm and the results of the mathematical modeling of a test system for energy transfer using a magneto-hydrodynamic pump and an exchange cavity are presented.

A Scalable Partitioned Approach to Model Massive Nonstationary Non-Gaussian Spatial Datasets

Nonstationary non-Gaussian spatial data are common in many disciplines, including climate science, ecology, epidemiology, and social sciences. Examples include count data on disease incidence and binary satellite data on cloud mask (cloud/no-cloud). Modeling such datasets as stationary spatial processes can be unrealistic since they are collected over large heterogeneous domains (i.e., spatial behavior differs across subregions). Although several approaches have been developed for nonstationary spatial models, these have focused primarily on Gaussian responses. In addition, fitting nonstationary models for large non-Gaussian datasets is computationally prohibitive. To address these challenges, we propose a scalable algorithm for modeling such data by leveraging parallel computing in modern high-performance computing systems. We partition the spatial domain into disjoint subregions and fit locally nonstationary models using a carefully curated set of spatial basis functions. Then, we combine the local processes using a novel neighbor-based weighting scheme. Our approach scales well to massive datasets (e.g., 2.7 million samples) and can be implemented in nimble, a popular software environment for Bayesian hierarchical modeling. We demonstrate our method to simulated examples and two massive real-world datasets acquired through remote sensing.

Feasibility study for the creation and implementation of an instrumental complex for determining and predicting the technical characteristics of locomotives

A modern tool for research and rapid prototyping of new developments are various methods of digital system modeling. When creating or upgrading any electric transport systems and electric rolling stock, the correct choice of all elements of the traction power supply system and electric rolling stock is of great importance. To solve this problem, it is necessary to take into account the movement of a set of moving loads in the form of electric transport in power supply systems of various levels and, at the same time, to study not only the mechanical processes of electric transport movement, but also the electromagnetic processes of interaction of electric transport with the traction power supply system and the electric power system, as well as their mutual interaction. electromagnetic influence on each other. The construction of a software and hardware complex for real-time simulation of the joint operation of electric power systems, traction power supply systems and electric trains corresponds to the modern moment. The implementation of such a system is possible using modern high-performance computing systems or stationary supercomputers with integrated hardware that increase the speed of calculating stiff systems of differential equations that describe large electro-magnetic-mechanical systems. Such computing software and hardware systems are quite expensive. The article describes the composition of such a complex and the feasibility study for its development and implementation.

ALPACA - a level-set based sharp-interface multiresolution solver for conservation laws

ALPACA is a simulation environment for simulating hyperbolic and (incompletely) parabolic conservation laws with multiple distinct and immiscible phases. As prominent example, consider the compressible Navier-Stokes equations (NSE). Solutions to these equations give insight and understanding of many important engineering applications. Numerical simulations of nonlinear parabolic systems of equations are very challenging for their complex nonlinear dynamics including the propagations of discontinuities such as shocks and phase interfaces. Accurate predictions require high temporal and spatial resolutions for such multi-scale problems. We utilize low dissipation high-resolution methods to capture the dynamics inside the separate phases. Their interaction is modeled by a sharp-interface level-set method with conservative interface-interaction. This allows to accurately locate the interface position and to easily prescribe arbitrary coupling conditions. We tackle the resulting immense computational loads by using a block-based multiresolution (MR) algorithm and adaptive local time stepping. The level-set treatment is integrated into the MR algorithm with little overhead by employing a smart tagging system and adaptive storage of the fluid data in the MR nodes. We embed these methods in a C++20 object-oriented modular framework using state-of-the-art programming paradigms. Furthermore, our implementation is capable to exploit the multiple levels of parallelism in modern high-performance computing (HPC) systems efficiently. We demonstrate the capabilities of our framework by simulating a variety of compressible multi-phase flow problems. Problem-sizes are of O(1010) effective degree of freedom (DOFs). By the use of MR, we typically achieve memory and compute compressions of >90%. We demonstrate near-optimal parallel performance for scaling runs using O(104) cores, regardless of the employed numerical models. Program summaryProgram Title: ALPACA - Adaptive Level-set Parallel Code AlpacaCPC Library link to program files:https://doi.org/10.17632/5zr3sg83ct.1Developer's repository link:https://gitlab.lrz.de/nanoshock/ALPACALicensing provisions: GPLv3Programming language: C++20Supplementary material: Code: Copy of the git repository, Videos: Air-helium shock bubble interaction (front and back view), Air-R22 shock bubble interaction, Three bubble shock interface interaction.Nature of problem: Numerical simulation of conservation laws such as the compressible Navier-Stokes equation with several interacting gaseous and liquid phases remains challenging even today. These flows often involve singularities such as shocks and interfaces as well as instabilities driven by their interaction. The inherent highly nonlinear dynamics of those systems leads to a broad range of temporal and spatial scales that have to be resolved. There exists a variety of mutually exclusive numerical models that are able to tackle these challenges. Those, however, are computationally expensive and require computational power that is offered only by large-scale state-of-the-art distributed-memory machines.Solution method: We have developed a modular simulation environment for conservation laws allowing exchange of numerical methods without loss of parallel performance. Computational efficiency is enhanced by employing multi-resolution schemes with adaptive local-time stepping. Our block-based implementation of these schemes is parallelized using the Message Passing Interface and exploits vectorization capabilities of the compute hardware. To simulate distinct and immiscible phases inside the computational domain, we utilize a sharp-interface level-set method. The level-set method allows to accurately locate the interface position and to easily prescribe arbitrary coupling conditions. The narrow-band approach reduces the computational load of the level-set method. We extend this method by a smart tagging system that exploits the block-based nature of the algorithm and further reduces the computational load. The simulation framework is written in modern C++20 and provides a Python interface for integration in Machine Learning and Uncertainty Quantification toolchains. We use parallel HDF5 in combination with XDMF to output field quantities. CMake is used as build system. We have completely annotated the source code using doxygen-style comments, allowing automated documentation generation in different formats. The source code is equipped with CI/CD-automated unit tests and an exhaustive integration test suite.Additional comments including restrictions and unusual features: ALPACA relies on open-source third-party libraries for input and testing. These are packaged as git submodules and automatically integrated. ALPACA is tested on Linux and macOS.

Graph-based multi-core higher-order time integration of linear autonomous partial differential equations

Modern high-performance computing (HPC) systems rely on increasingly complex nodes with a steadily growing number of cores and matching deep memory hierarchies. In order to fully exploit them, algorithms must be explicitly designed to exploit these features. In this work we address this challenge for a widely used class of application kernels: polynomial-based time integration of linear autonomous partial differential equations.We build on prior work [1] of a cache-aware, yet sequential solution and provide an innovative way to parallelize it, while addressing cache-awareness across a large number of cores. For this, we introduce a dependency graph driven view of the algorithm and then use both static graph partitioning and dynamic scheduling to efficiently map the execution to the underlying platform. We implement our approach on top of the widely available Intel Threading Building Blocks (TBB) library, although the concepts are programming model agnostic and can apply to any task-driven parallel programming approach.We demonstrate the performance of our approach for a 2nd, 4th and 6th order time integration of the linear advection equation on three different architectures with widely varying memory systems and achieve an up to 60% reduction of wall clock time compared to a conventional, state-of-the-art non-cache-aware approach.

ST-CAC: a low-cost crosstalk avoidance coding mechanism based on three-valued numerical system

Appearances of specific transition patterns during data transfer in bus lines of modern high-performance computing systems, such as communicating structures of accelerators for deep convolutional neural networks, commercial Network on Chips, and memories, can lead to crosstalk faults. With the shrinkage of technology size, crosstalk faults occurrence boosts and leads to degradation of reliability and performance, as well as the increasing power consumption of lines. One effective way to alleviate crosstalk faults is to avoid the appearance of these specific transition patterns by using numerical-based crosstalk avoidance codes (CACs). However, a serious problem with numerical-based CACs is their overheads in terms of required additional bus lines for representing code words. To solve this problem, in this paper we present a novel CAC that is based on the use of three symbols (three-value) to represent the code words in the bus lines, rather than classical binary CACs based on binary, i.e., 0 and 1 symbols. Our proposed CAC, named summation-based tri-value crosstalk avoidance code (ST-CAC), reduces the worst-case delay in bus lines with respect to binary CACs, and it can efficiently be applied to any arbitrary channel width of lines. The use of three symbols to represent code words in ST-CAC enables to increase the number of code words of a numerical system without increasing the number of required bus lines significantly. The experimental results show that CACs based on the use of three symbols can reduce the number of additional lines compared to binary CACs by 33%. Moreover, we show in the paper, that the delay of wires in the presence our ST-CAC can reduce by 33% with respect to state-of-the-art binary value CACs.

AAP4All: An Adaptive Auto Parallelization of Serial Code for HPC Systems

High Performance Computing (HPC) technologies are emphasizing to increase the system performance across many disciplines. The primary challenge in HPC systems is how to achieve massive performance by minimum power consumption. However, the modern HPC systems are configured by adding the powerful and energy efficient multi-cores/many-cores parallel computing devices such as GPUs, MIC, and FPGA etc. Due to increasing the complexity of one chip many-cores/multi-cores systems, only well-balanced and optimized parallel programming technique is the solution to provide substantial increase in performance under power consumption limitations. Conventionally, the researchers face various barriers while parallelizing their serial code because they don’t have enough experience to use parallel programming techniques in optimized way. However, to address these obstacles and achieve massive performance under power consumption limitations, we propose an Adaptive and Automatic Parallel programming tool (AAP4All) for both homogeneous and heterogeneous computing systems. A key advantage of proposed tool is an auto recognition of computer system architecture, then translate automatically the input serial C++ code into parallel programming code for that particular detected system. We also evaluate the performance and power consumption while computing the proposed AAP4All model on different computer architectures, and compare the results with existing state-of-the-art parallel programming techniques. Results show that the proposed model increases the system performance substantially by reducing power consumption as well as serial to parallel transformation effort.

A Proposed Data Partitioning Approach on Heterogeneous HPC Platforms: Data Locality Perspective

We propose a new data partitioning approach to improve the performance of heterogeneous parallel applications in modern high-performance computing (HPC) systems. Existing approaches do not consider an important aspect that has a critical impact on the performance of parallel applications: the method of assigning partitions to each processor so as to minimize the communication cost and hence minimize data movement, which dominates energy and performance cost. Such an aspect for managing data locality is important for a large range of applications. Therefore, to achieve efficient data partitioning, we propose a method for distribution considering this aspect. Our algorithm seeks to minimize execution time by using two models. The first is a fine-grained computational model of heterogeneous processors, which is sufficiently adequate and accurate to guarantee efficient partitioning results that maximize utilization. The second is a communication model of heterogeneous processors to minimize data motion and hide communication overheads. The correctness of our algorithm was analyzed and validated. The complexity of our algorithm is approximately of order <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</b> ( <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</b> × <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">log</b> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</b> + <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</b> × <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</b> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>2</b></sup> ), where s is problem size/steps (where steps is the step size between data points in the computational model of each processor), and p is the number of heterogeneous processors. The experiments were performed on AZIZ supercomputer using two types of applications: an application with no dependency between its partitions, i.e., matrix multiplication, and another one with high dependency between its partitions, i.e., the Jacobi method. The results show the efficiency of our algorithm in improving performance.

Application of the Dorovsky model for taking into account the fluid saturation of geological media

The discovery of oil deposits with complex internal structures requires an improvement of available seismic survey methods. The development of modern high-performance computing systems provides an opportunity to use more sophisticated mathematical models. This paper aims to investigate seismic wave propagation in porous fluid-saturated media. The Dorovsky three velocity model was formulated in the two-dimensional case and its numerical solution was obtained with the grid-characteristic method. The computational domain consisted of three layers with different rheology: a water layer, a porous fluid-saturated layer, and an elastic layer. Explicit contact conditions were derived between them and successfully applied with the help of Riemann invariants. The curvature of geological layers was taken into consideration by means of structured hexahedral grids. The time evolution of the spatial distribution of stress tensors and material velocity vectors were calculated and analyzed. These signals contain a mixture of volume, surface, transmitted and reflected waves.

Effects of Using a Memory Stalled Core for Handling MPI Communication Overlapping in the SOR Solver on SX-ACE and SX-Aurora TSUBASA

Modern high-performance computing (HPC) systems consist of a large number of nodes featuring multi-core processors. Many computational fluid dynamics (CFD) codes utilize a Message Passing Interface (MPI) to exploit the potential of such systems. In general, the MPI communication costs increase as the number of MPI processes increases. In this paper, we discuss performance of the code in which a core is used as a dedicated communication core when the core cannot contribute to the performance improvement due to memory-bandwidth limitations. By using the dedicated communication core, the communication operations are overlapped with computation operations, thus enabling highly efficient computation by exploiting the limited memory bandwidth and idle cores. The performance evaluation shows that this code can hide the MPI communication times of 90% on the supercomputer SX-ACE system and 80% on the supercomputer SX-Aurora TSUBASA system, and the performance of the successive over-relaxation (SOR) method is improved by 32% on SX-ACE and 20% on SX-Aurora TSUBASA.

Simulation of Seismic Wave Propagation in a Multicomponent Oil Deposit Model

A seismic survey is perhaps the most common geophysical technique used to locate potential oil and natural gas deposits in the geologic structures. Thanks to the rapid development of modern high-performance computing systems, the computer simulation technology plays a crucial role in processing the field data. The precision of the full-waveform inversion (FWI) essentially depends on the quality of the direct problem solver. This paper introduces a new approach to the numerical simulation of wave processes in complex heterogeneous media. The linear elasticity theory is applied to simulate the dynamic behavior of curvilinear geological layers. In contrast to the conventional approach, the producing oil formation is described in the frame of a porous fluid-filled model. It allows us to explicitly take into account the porosity, oil density, and other physical parameters. The method of setting the physically correct contact conditions between the reservoir and the geological massif based on the transport equation solution for Riemann invariants was successfully implemented. The grid-characteristic method, previously thoroughly verified on acoustic and elastic problems, was adopted. The explicit time-stepping procedure was derived for a two-dimensional case with a method of splitting along coordinate axes. This method guarantees the preservation of the scheme approximation order. The potential application of the new method to a complex model based on the data from the famous Russian oil deposit — the Bazhen Formation — is demonstrated. The seismic responses were registered on the wave fields and synthetic seismograms. The novelty of this paper relates to a uniform approach to the wave propagation simulation in the heterogeneous medium containing contacting subdomains with different rheology types.

A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. This work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive and decision-relevant models.

Time-parallel simulation of the Schrödinger Equation

The numerical simulation of the time-dependent Schrödinger equation for quantum systems is a very active research topic. Yet, resolving the solution sufficiently in space and time is challenging and mandates the use of modern high-performance computing systems. While classical parallelization techniques in space can reduce the runtime per time step, novel parallel-in-time integrators expose parallelism in the temporal domain. They work, however, not very well for wave-type problems such as the Schrödinger equation. One notable exception is the rational approximation of exponential integrators. In this paper we derive an efficient variant of this approach suitable for the complex-valued Schrödinger equation. Using the Faber–Carathéodory–Fejér approximation, this variant is already a fast serial and in particular an efficient time-parallel integrator. It can be used to augment classical parallelization in space and we show the efficiency and effectiveness of our method along the lines of two challenging, realistic examples.