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At least 55 records · Page 3

A supernodal all-pairs shortest path algorithm

We show how to exploit graph sparsity in the Floyd-Warshall algorithm for the all-pairs shortest path (Apsp) problem. Floyd-Warshall is an attractive choice for Apsp on high-performing systems due to its structural similarity to solving dense linear systems and matrix multiplication. However, if sparsity of the input graph is not properly exploited, Floyd-Warshall will perform unnecessary asymptotic work and thus may not be a suitable choice for many input graphs. To overcome this limitation, the key idea in our approach is to use the known algebraic relationship between Floyd-Warshall and Gaussian elimination, and import several algorithmic techniques from sparse Cholesky factorization, namely, fill-in reducing ordering, symbolic analysis, supernodal traversal, and elimination tree parallelism. When combined, these techniques reduce computation, improve locality and enhance parallelism. We implement these ideas in an efficient shared memory parallel prototype that is orders of magnitude faster than an efficient multi-threaded baseline Floyd-Warshall that does not exploit sparsity. Our experiments suggest that the Floyd-Warshall algorithm can compete with Dijkstra's algorithm (the algorithmic core of Johnson's algorithm) for several classes sparse graphs.

Sao, Piyush↗

A Block-Based Triangle Counting Algorithm on Heterogeneous Environments

Triangle counting is a fundamental building block in graph algorithms. In this article, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

97 MATHEMATICS AND COMPUTING↗

A Block-Based Triangle Counting Algorithm on Heterogeneous Environments

Triangle counting is a fundamental building block in graph algorithms. In this paper, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

97 MATHEMATICS AND COMPUTING↗

Computing the QRPA level density with the finite amplitude method

Here, we describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Accelerating the density-functional tight-binding method using graphical processing units

Acceleration of the density-functional tight-binding (DFTB) method on single and multiple graphical processing units (GPUs) was accomplished using the MAGMA linear algebra library. Herein two major computational bottlenecks of DFTB ground-state calculations were addressed in our implementation: the Hamiltonian matrix diagonalization and the density matrix construction. The code was implemented and benchmarked on two different computer systems: (1) the SUMMIT IBM Power9 supercomputer at the Oak Ridge National Laboratory Leadership Computing Facility with 1–6 NVIDIA Volta V100 GPUs per computer node and (2) an in-house Intel Xeon computer with 1–2 NVIDIA Tesla P100 GPUs. The performance and parallel scalability were measured for three molecular models of 1-, 2-, and 3-dimensional chemical systems, represented by carbon nanotubes, covalent organic frameworks, and water clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solving the electronic structure problem for over 100000 atoms in real space

Using a real-space high-order finite-difference approach, we investigate the electronic structure of large spherical silicon nanoclusters. Within Kohn-Sham density functional theory and using pseudopotentials, we report the self-consistent field convergence of a system with over 100000 atoms: a Si 107,641 ⁢H 9,084 nanocluster with a diameter of 16 nm. Our approach uses Chebyshev-filtered subspace iteration to speed up the convergence of the eigenspace, and blockwise Hilbert space-filling curves to speed up sparse matrix-vector multiplications, all of which are implemented in the parsec code. For the largest system, we utilized 2048 nodes (114 688 cores) on the Frontera machine in the Texas Advanced Computing Center. Our quantitative analysis of the electronic structure shows how it gradually approaches its bulk counterpart as a function of nanocluster size. The band gap is enlarged due to quantum confinement in nanoclusters, but decreases as the system size increases, as expected. In conclusion, our work serves as a proof of concept for the capacity of the real-space approach in efficiently parallelizing very large calculations using high-performance computer platforms, which can straightforwardly be replicated in other systems with more than 10 5 atoms.

0-dimensional systems↗

Discrete Fracture Network Modeling to Estimate Upscaled Parameters for the Topopah Spring, Lava Flow, and Tiva Canyon Aquifers at Pahute Mesa, Nevada National Security Site

This report describes the results of Discrete Fracture Network (DFN) simulations for the Topopah Spring Aquifer (TSA), Lava Flow Aquifer, and Tiva Canyon Aquifer (TCA), at Pahute Mesa on the Nevada National Security Site (NNSS), formerly the Nevada Test Site. The research focuses on calculating upscaled groundwater flow and contaminant transport parameters using DFNs generated according to fracture characteristics observed in the TSA, LFA and TCA at Pahute Mesa. The highly fractured and heterogeneous nature of these aquifers makes them candidates for stochastic DFN modeling of radionuclide transport on a small scale with subsequent upscaling. One hundred independent DFN realizations are generated for each aquifer, and the upscaled parameters for continuum simulations of subsurface flow and transport in fractured media at Pahute Mesa are calculated. Our goal is to implement a modeling approach that can translate parameters to larger-scale models that account for local-scale flow and transport processes, such as channelization of flow and transport along a few well connected, large fractures. Additionally, to simulate advective and advective-diffusive transport through the fracture networks, the Time Domain Random Walk (TDRW) approach is applied to account for matrix diffusion into a finite half-space. Moreover, a novel approach to calculate dynamic (active) fracture surface area to reflect flow channeling is implemented. This work will improve the representation of radionuclide transport processes in largescale, regulatory-focused models by providing estimates of hard-to-measure flow and contaminant transport parameters at large scales. In this report, we (1) show recent results of flow and transport simulations on multiple DFN realizations of the TSA, LFA, TCA; (2) discuss the resulting distributions of estimated upscaled parameters; (3) describe the estimation of upscaled parameters for an equivalent parallel-plate continuum model and (4) present a comparison between simulated transport from the equivalent continuum model and an actual DFN.

54 ENVIRONMENTAL SCIENCES↗

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗

GSoFa: Scalable Sparse Symbolic LU Factorization on GPUs

Decomposing a matrix $\mathbf {A}$ into a lower matrix $\mathbf {L}$ and an upper matrix $\mathbf {U}$, which is also known as LU decomposition, is an essential operation in numerical linear algebra. For a sparse matrix, LU decomposition often introduces more nonzero entries in the $\mathbf {L}$ and $\mathbf {U}$ factors than in the original matrix. A symbolic factorization step is needed to identify the nonzero structures of $\mathbf {L}$ and $\mathbf {U}$ matrices. Attracted by the enormous potentials of the Graphics Processing Units (GPUs), an array of efforts have surged to deploy various LU factorization steps except for the symbolic factorization, to the best of our knowledge, on GPUs. This article introduces gSoFa, the first GPU-based symbolic factorization design with the following three optimizations to enable scalable LU symbolic factorization for nonsymmetric pattern sparse matrices on GPUs. First, here we introduce a novel fine-grained parallel symbolic factorization algorithm that is well suited for the Single Instruction Multiple Thread (SIMT) architecture of GPUs. Second, we tailor supernode detection into a SIMT friendly process and strive to balance the workload, minimize the communication and saturate the GPU computing resources during supernode detection. Third, we introduce a three-pronged optimization to reduce the excessive space consumption problem faced by multi-source concurrent symbolic factorization. Taken together, gSoFa achieves up to 31× speedup from 1 to 44 Summit nodes (6 to 264 GPUs) and outperforms the state-of-the-art CPU project, on average, by 5×. Notably, gSoFa also achieves up to 47 percent of the peak memory throughput of a V100 GPU in the Summit Supercomputer.

97 MATHEMATICS AND COMPUTING↗

TUMME: Tsinghua University Minnesota Master Equation program

We report that TUMME is a program for assembling and solving master equations for gas-phase chemical kinetics based on chemically significant eigenmodes. TUMME has interfaces to the Gaussian, Polyrate, and/or MSTor output files that allow the master equation code to obtain the microcanonical flux coefficients needed for the coefficient matrix of the master equation. The flux coefficients for reactions with barriers can be calculated by multi-structural variational transition state theory with small-curvature tunneling (MS-VTST/SCT) or by simpler approximations to this such as conventional transition state theory without tunneling (also called RRKM theory). The flux coefficients for barrierless reactions are provided by a hard-sphere model. TUMME is written in double precision with Python 3; quadruple and octuple precision are also available for some subtasks in C++. The Python code can run in serial or parallel (MP or MPI), and the C++ code can run on a single processor or on multiple processors with OpenMP.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accelerating Binarized Neural Networks via Bit-Tensor-Cores in Turing GPUs

Despite foreseeing tremendous speedups over conventional deep neural networks, the performance advantage of binarized neural networks (BNNs) has merely been showcased on general-purpose processors such as CPUs and GPUs. In fact, due to being unable to leverage bit-level-parallelism with a word-based architecture, GPUs have been criticized for extremely low utilization (1%) when executing BNNs. Consequently, the latest tensorcores in NVIDIA Turing GPUs start to experimentally support bit computation. In this work, we look into this brand new bit computation capability and characterize its unique features. We show that the stride of memory access can significantly affect performance delivery and a data-format co-design is highly desired to support the tensorcores for achieving superior performance than existing software solutions without tensorcores. We realize the tensorcore-accelerated BNN design, particularly the major functions for fully-connect and convolution layers — bit matrix multiplication and bit convolution. Evaluations on two NVIDIA Turing GPUs show that, with ResNet-18, our BTC-BNN design can process ImageNet at a rate of 5.6K images per second, 77% faster than state-of-the-art. Our BNN approach is released on https://github.com/pnnl/TCBNN.

Li, Ang↗

Enabling the Broader Use of MOOSE for Nuclear Energy and Other Simulation

This Final Scientific and Technical Report summarizes work performed under the Phase IIA SBIR project “Enabling the Broader Use of MOOSE for Nuclear Energy and Other Simulation” (DE-SC0020906) from August 2023 through August 2025. The objective of the Phase IIA effort was to mature and harden capabilities developed during Phase II, with the goal of enabling practical interoperability between Coreform’s isogeometric analysis (IGA) technologies and the Multiphysics Object-Oriented Simulation Environment (MOOSE), while improving robustness, performance, and scalability for complex, nuclear-relevant geometries. Over the course of Phase IIA, the project established and validated an extraction-based interoperability pathway between Coreform tools and MOOSE. A combined mesh and matrix format was defined collaboratively with MOOSE developers and integrated into the solver, enabling standard MOOSE workflows to operate on data exported from Coreform’s IGA and Flex Representation Method (FRM) pipelines. Early demonstrations validated architectural compatibility using linear solid mechanics problems, while later efforts focused on benchmark testing and external use. By the end of the project period, engineers at BWXT were able to independently set up and execute a simulation using the Coreform–MOOSE workflow and provide direct feedback that informed further refinement. In parallel, substantial effort was devoted to improving the robustness of trimmed U-spline construction for complex CAD geometries. A growing test suite of nuclear-relevant models was compiled through collaboration with multiple stakeholders and used to drive extensive bug fixing and reliability improvements. These efforts resulted in improved robustness and performance, including the addition of fallback capabilities that enhance reliability when the underlying commercial CAD kernel fails. Performance-oriented work progressed later in the project, with the development and demonstration of methods to decompose complex geometries into structured subregions and updated data representations to support more efficient solver processing. Additionally, extensive enhancements to threadsafe parallel data structures and trimming operations established a foundation for scalable processing of large assemblies. Collaboration with Sandia National Laboratories on the SGM geometric modeling kernel advanced to a functioning interface test case, positioning the workflow for future kernel integration. Overall, the Phase IIA effort successfully transitioned the project from architectural proof-of-concept to externally exercised, solver-integrated capability, while clarifying remaining technical challenges related to standardization, performance optimization, and kernel integration.

42 ENGINEERING↗

Propulsion Electrification Architecture Selection Process and Cost of Carbon Abatement Analysis for Heavy-Duty Off-Road Material Handler

The heavy-duty off-road industry continues to expand efforts to reduce fuel consumption and CO 2 e (carbon dioxide equivalent) emissions. Many manufacturers are pursuing electrification to decrease fuel consumption and emissions. Future policies will likely require electrification for CO2e savings, as seen in light-duty on-road vehicles. Electrified architectures vary widely in the heavy-duty off-road space, with parallel hybrids in some applications and series hybrids in others. The diverse applications for different types of equipment mean different electrified configurations are required. Companies must also determine the value in pursuing electrified architectures; this work analyzes a range of electrified architectures, from micro hybrids to parallel hybrids to series hybrids to a BEV, looking at the total cost, total CO 2 e, and cost per CO 2 e (cost of carbon abatement, or cost of carbon reduction) using data for the year 2021. This study is focused on a heavy-duty off-road material handler, the Pettibone Cary-Lift 204i. This machine’s specialty application, including events like unloading large oil pipes from a railcar, requires a unique electrified architecture that suits its specific needs. However, the results from this study may be extrapolated to similar machinery to inform fuel savings options across the heavy-duty off-road industry. In this study, a unique electrified architecture is determined for the Cary-Lift. This architecture is informed by multiple rounds of a Pugh matrix decision analysis to select a shortened list of desirable electrified architectures. The shortened list is modeled and simulated to determine CO 2 e, cost, and cost per CO 2 e. A final architecture is determined as a plug-in series hybrid that reduces fuel consumption by 65%, targeting the large fuel and CO 2 e savings that are likely to be required for the future of the heavy-duty off-road industry.

33 ADVANCED PROPULSION SYSTEMS↗

Porting fragmentation methods to GPUs using an OpenMP API: Offloading the resolution-of-the-identity second-order Møller–Plesset perturbation method

Here, using an OpenMP Application Programming Interface, the resolution-of-the-identity second-order Møller–Plesset perturbation (RI-MP2) method has been off-loaded onto graphical processing units (GPUs), both as a standalone method in the GAMESS electronic structure program and as an electron correlation energy component in the effective fragment molecular orbital (EFMO) framework. First, a new scheme has been proposed to maximize data digestion on GPUs that subsequently linearizes data transfer from central processing units (CPUs) to GPUs. Second, the GAMESS Fortran code has been interfaced with GPU numerical libraries (e.g., NVIDIA cuBLAS and cuSOLVER) for efficient matrix operations (e.g., matrix multiplication, matrix decomposition, and matrix inversion). The standalone GPU RI-MP2 code shows an increasing speedup of up to 7.5× using one NVIDIA V100 GPU with one IBM 42-core P9 CPU for calculations on fullerenes of increasing size from 40 to 260 carbon atoms using the 6-31G(d)/cc-pVDZ-RI basis sets. A single Summit node with six V100s can compute the RI-MP2 correlation energy of a cluster of 175 water molecules using the correlation consistent basis sets cc-pVDZ/cc-pVDZ-RI containing 4375 atomic orbitals and 14 700 auxiliary basis functions in ~0.85 h. In the EFMO framework, the GPU RI-MP2 component shows near linear scaling for a large number of V100s when computing the energy of an 1800-atom mesoporous silica nanoparticle in a bath of 4000 water molecules. The parallel efficiencies of the GPU RI-MP2 component with 2304 and 4608 V100s are 98.0% and 96.1%, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Generalizing mkFit and its Application to HL-LHC

mkFit is an implementation of the Kalman filter-based track reconstruction algorithm that exploits both thread- and data-level parallelism. In the past few years the project transitioned from the R&D phase to deployment in the Run-3 offline workflow of the CMS experiment. The CMS tracking performs a series of iterations, targeting reconstruction of tracks of increasing difficulty after removing hits associated to tracks found in previous iterations. mkFit has been adopted for several of the tracking iterations, which contribute to the majority of reconstructed tracks. When tested in the standard conditions for production jobs, speedups in track pattern recognition are on average of the order of 3.5x for the iterations where it is used (3-7x depending on the iteration). Multiple factors contribute to the observed speedups, including vectorization and a lightweight geometry description, as well as improved memory management and single precision. Efficient vectorization is achieved with both the icc and the gcc (default in CMSSW) compilers and relies on a dedicated library for small matrix operations, Matriplex, which has recently been released in a public repository. While the mkFit geometry description already featured levels of abstraction from the actual Phase-1 CMS tracker, several components of the implementations were still tied to that specific geometry. We have further generalized the geometry description and the configuration of the run-time parameters, in order to enable support for the Phase-2 upgraded tracker geometry for the HL-LHC and potentially other detector configurations. The implementation strategy and high-level code changes required for the HL-LHC geometry are presented. Speedups in track building from mkFit imply that track fitting becomes a comparably time consuming step of the tracking chain.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Versatile soil gas concentration and isotope monitoring: optimization and integration of novel soil gas probes with online trace gas detection

Abstract. Gas concentrations and isotopic signatures can unveil microbial metabolisms and their responses to environmental changes in soil. Currently, few methods measure in situ soil trace gases such as the products of nitrogen and carbon cycling or volatile organic compounds (VOCs) that constrain microbial biochemical processes like nitrification, methanogenesis, respiration, and microbial communication. Versatile trace gas sampling systems that integrate soil probes with sensitive trace gas analyzers could fill this gap with in situ soil gas measurements that resolve spatial (centimeters) and temporal (minutes) patterns. We developed a system that integrates new porous and hydrophobic sintered polytetrafluoroethylene (sPTFE) diffusive soil gas probes that non-disruptively collect soil gas samples with a transfer system to direct gas from multiple probes to one or more central gas analyzer(s) such as laser and mass spectrometers. Here, we demonstrate the feasibility and versatility of this automated multiprobe system for soil gas measurements of isotopic ratios of nitrous oxide (δ18O, δ15N, and the 15N site preference of N2O), methane, carbon dioxide (δ13C), and VOCs. First, we used an inert silica matrix to challenge probe measurements under controlled gas conditions. By changing and controlling system flow parameters, including the probe flow rate, we optimized recovery of representative soil gas samples while reducing sampling artifacts on subsurface concentrations. Second, we used this system to provide a real-time window into the impact of environmental manipulation of irrigation and soil redox conditions on in situ N2O and VOC concentrations. Moreover, to reveal the dynamics in the stable isotope ratios of N2O (i.e., 14N14N16O, 14N15N16O, 15N14N16O, and 14N14N18O), we developed a new high-precision laser spectrometer with a reduced sample volume demand. Our integrated system – a tunable infrared laser direct absorption spectrometry (TILDAS) in parallel with Vocus proton transfer reaction mass spectrometry (PTR-MS), in line with sPTFE soil gas probes – successfully quantified isotopic signatures for N2O, CO2, and VOCs in real time as responses to changes in the dry–wetting cycle and redox conditions. Broadening the collection of trace gases that can be monitored in the subsurface is critical for monitoring biogeochemical cycles, ecosystem health, and management practices at scales relevant to the soil system.

54 ENVIRONMENTAL SCIENCES↗

Exploring the Use of Novel Spatial Accelerators in Scientific Applications

Driven by the need to find alternative accelerators which can viably replace GPUs in next-generation Supercomputing systems, this paper proposes a methodology to enable agile application/hardware co-design. The application-first methodology provides the ability to come up with design of accelerators while working with real-world workloads, available accelerators, and system software. The iterative design process targets a set of kernels in a workload for performance estimates that can prune the design space for later phases of detailed architectural evaluations. To this effect, in this paper, a novel data-parallel device model is introduced that simulates the latency of performance-sensitive operations in an accelerator including data transfers and kernel computation using multi-core CPUs. The use of off-the-shelf simulators, such as pre-RTL simulator Aladdin or multiple tools available for exploring the design of deep neural network accelerators (e.g., Timeloop) is demonstrated for evaluation of various accelerator designs using applications with realistic inputs. Examples of multiple device configurations that are instantiable in a system are explored to evaluate the performance benefit of deploying novel accelerators. The proposed device is integrated with a programming model and system software to potentially explore the impacts of high-level programming languages/compilers and low-level effects such as task scheduling on multiple accelerators. We analyze our methodology for a set of applications that represent high-performance computing (HPC) and graph analytics. The applications include a computational chemistry kernel realized using tensor contractions, triangle counting, GraphSAGE and Breadth-first Search. These applications include kernels such as dense matrix-dense matrix multiplication, sparse matrix-spare matrix multiplication, and sparse matrix-dense vector multiplication. Our results indicate potential performance benefits and insights for system design by including accelerators that realize these kernels along-side general purpose accelerators.

AI, codesign, Accelerated Computing, Modeling and ↗

Sensitivity and reliability of key electrochemical markers for detecting lithium plating during extreme fast charging

Lithium plating is one of the key challenges for enabling extreme fast charging (XFC, ≤10 to 15 min charging at ≥6C) in graphite-based lithium-ion batteries. Significant R&D effort has been focused on how to mitigate Li plating. Parallel effort is also being devoted to developing methods to detect Li plating when and if it happens during fast charging. In that regard, electrochemical (EC) signature-based detection techniques are less resource intensive, more convenient, and more practical from an end-user application perspective. However, a comprehensive understanding of key plating related EC signatures for extreme fast charging is presently unavailable. In particular, there exist distinct issues of unreliability with key plating-related EC signatures—e.g., incremental capacity (dQ.dV -1 ), differential OCV (dOCV.dt -1 ), end of lithiation (EOL) rest voltage—at XFC conditions, and the underlying reasons have not been explored and identified methodically. Using a comprehensive test matrix and XFC conditions with Li/graphite half cells, this article highlights the unreliability issues associated with the EC Li plating diagnostics and explains the underlying root cause. This study finds distinct sensitivity and unreliability issues with plating related dQ.dV -1 , dOCV.dt -1 , and EOL rest voltage signatures with charging rates. Furthermore, the complex interaction between graphite and plated Li that happens through multiple competing mechanisms —Li stripping and chemical intercalation— at different charging rates is at the core of the sensitivity and unreliability issue.

25 ENERGY STORAGE↗