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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Towards verifiable cancer digital twins: tissue level modeling protocol for precision medicine

Cancer exhibits substantial heterogeneity, manifesting as distinct morphological and molecular variations across tumors, which frequently undermines the efficacy of conventional oncological treatments. Developments in multiomics and sequencing technologies have paved the way for unraveling this heterogeneity. Nevertheless, the complexity of the data gathered from these methods cannot be fully interpreted through multimodal data analysis alone. Mathematical modeling plays a crucial role in delineating the underlying mechanisms to explain sources of heterogeneity using patient-specific data. Intra-tumoral diversity necessitates the development of precision oncology therapies utilizing multiphysics, multiscale mathematical models for cancer. This review discusses recent advancements in computational methodologies for precision oncology, highlighting the potential of cancer digital twins to enhance patient-specific decision-making in clinical settings. We review computational efforts in building patient-informed cellular and tissue-level models for cancer and propose a computational framework that utilizes agent-based modeling as an effective conduit to integrate cancer systems models that encode signaling at the cellular scale with digital twin models that predict tissue-level response in a tumor microenvironment customized to patient information. Furthermore, we discuss machine learning approaches to building surrogates for these complex mathematical models. These surrogates can potentially be used to conduct sensitivity analysis, verification, validation, and uncertainty quantification, which is especially important for tumor studies due to their dynamic nature.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Automated electrical demand peak leveling in a manufacturing facility with short term energy storage for smart grid participation

Demand side management of energy is a vital function in the smart grid that allows for greater integration of renewable energy resources, and is facilitated with economic incentives in energy and demand pricing schedules. Manufacturing systems can take advantage of these incentives to reduce their energy costs through active energy management. This paper is a simulation analysis on the implementation of a novel algorithm that levelizes the maximum power load of an industrial bakery that operates under an on-peak demand price structure. The algorithm takes advantage of an untapped thermal energy storage resource in the facility, a chilled glycol buffer tank, to level the short intra-day power oscillations that the facility experiences. One of the key advantages of the algorithm is that it does not require precise demand forecasting or complex control algorithms, such as model predictive control. Even with substantial error in peak power estimates (5%), the algorithm is expected to result in at least a 2% peak reduction. Under ideal prediction, the algorithm reduces the on-peak facility power maximum by 7.3% of the possible 9.0% reduction the storage can provide. Further, the algorithm uses very few facility specific inputs, and can readily be adapted for any facility with short intra-day oscillatory power profiles and untapped storage capacity. The key insight of the paper is the employment of a novel algorithm to leverage untapped energy storage in manufacturing facilities to transform them into smart grid participants with no major capital investment.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Asynchronous GPU-based DEM solver embedded in commercial CFD software with polyhedral mesh support

A novel graphical processing unit-based discrete element method solver is introduced to improve stability, performance, and provide seamless integration into commercial or open-source computational fluid dynamics software. A key innovation is eliminating a need for network communication between solvers, which was previously required for cross-platform coupling. This is accomplished by a direct coupling method that employs dynamic-linked libraries. Furthermore, the solver optimizes memory usage by streamlining the particle-cell search algorithm by eliminating the cells' searching grid. This ensures the solver is compatible with a wide range of mesh types, providing high geometric flexibility. The approach simplifies the simulation process by directly incorporating computational fluid dynamics mesh information into the discrete element method solver. The performance analysis indicates about sixteen times boost in computational speed compared to benchmark central processing unit-based solvers. Finally, the solver's compatibility with polyhedral meshes, a vital advantage for complex geometries, is tested against a referenced study regarding the simulation of an immersed-tube fluidized bed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Variance Estimation in Monte Carlo Eigenvalue Simulations Using Spectral Analysis Method

Monte Carlo (MC) simulation is widely used to solve the eigenvalue form of the Boltzmann transport equation that mathematically represents the neutron transport process through complex multiplying (fissionable) systems. Monte Carlo eigenvalue simulation starts with an assumed fission source distribution and uses the fission sites from the previous iteration (cycle) as the starting source in the current iteration. Important system parameters (MC tallies) such as fuel pin-power distribution are estimated over several cycles after the convergence of the fission source distribution to a stationary distribution. However, the MC fission source iteration algorithm that uses fission source sites from the previous cycle introduces a cycle-to-cycle correlation. Monte Carlo simulations that do not account for the cycle-to-cycle correlation systematically underestimate the variance of the estimated system parameters (sample mean). This paper presents the relationship between the spectral density in the frequency domain at frequency zero and the variance of the sample mean. This paper introduces a novel method in the frequency domain for the MC variance estimation. For the three test problems used in this paper, researchers have observed that the new method results in an improvement of more than one order of magnitude to the standard deviation of the sample mean. The new method also compares favorably with the previously introduced batch, bootstrap, and covariance-adjusted methods when applied to the three test problems investigated in this paper. This new method does not require modification of the MC eigenvalue algorithm (power iteration), is code agnostic, and is therefore easy to use when implementing in any existing MC code. In conclusion, the new estimate can be calculated without saving tally results of all active/stationary cycles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Theory of Trotter Error with Commutator Scaling

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, nearly matching or even outperforming the best previous results. Our applications include: (i) a simulation of second-quantized plane-wave electronic structure, nearly matching the interaction-picture algorithm of Low and Wiebe; (ii) a simulation of $k$-local Hamiltonians almost with induced one-norm scaling, faster than the qubitization algorithm of Low and Chuang; (iii) a simulation of rapidly decaying power-law interactions, outperforming the Lieb-Robinson-based approach of Tran et al.; (iv) a hybrid simulation of clustered Hamiltonians, dramatically improving the result of Peng, Harrow, Ozols, and Wu; and (v) quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets, tightening previous analyses of Bravyi and Gosset. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound nearly matching a recent result of Tran et al. Our analysis reproduces known tight bounds for first- and second-order formulas. We further investigate the tightness of our bounds for higher-order formulas. For quantum simulation of a one-dimensional Heisenberg model with an even-odd ordering of terms, our result overestimates the complexity by only a factor of $5$. Our bound is also close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both the asymptotic scaling and the constant prefactor.

quantum computing, numerical analysis↗
DOE OSTI2024

An open source knowledge graph ecosystem for the life sciences

Translational research requires data at multiple scales of biological organization. Advancements in sequencing and multi-omics technologies have increased the availability of these data, but researchers face significant integration challenges. Knowledge graphs (KGs) are used to model complex phenomena, and methods exist to construct them automatically. However, tackling complex biomedical integration problems requires flexibility in the way knowledge is modeled. Moreover, existing KG construction methods provide robust tooling at the cost of fixed or limited choices among knowledge representation models. PheKnowLator (Phenotype Knowledge Translator) is a semantic ecosystem for automating the FAIR (Findable, Accessible, Interoperable, and Reusable) construction of ontologically grounded KGs with fully customizable knowledge representation. The ecosystem includes KG construction resources (e.g., data preparation APIs), analysis tools (e.g., SPARQL endpoint resources and abstraction algorithms), and benchmarks (e.g., prebuilt KGs). We evaluated the ecosystem by systematically comparing it to existing open-source KG construction methods and by analyzing its computational performance when used to construct 12 different large-scale KGs. With flexible knowledge representation, PheKnowLator enables fully customizable KGs without compromising performance or usability.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2020

OPTIMAL CONTROL AND ENERGY-SAVING ANALYSIS OF COMMON PRESSURE RAIL ARCHITECTURES: HHEA & STEAM

In recent years several novel hydraulic architectures have been proposed with the intention of significantly increasing system efficiency. Two of these architectures, Steigerung der Energieeffizienz in der Arbeitshydraulik mobiler Arbeitsmaschinen (STEAM), and the Hybrid Hydraulic-Electric Architecture (HHEA), use a system of multiple common pressure rails (CPRs) to serve the multiple degrees-of-freedom of the machine. The key difference is that STEAM throttles hydraulic power from these rails while HHEA combines electric and hydraulic power to meet actuator demands. As a throttle-less architecture, HHEA is expected to save more energy than STEAM at the expense of added complexity. Therefore, it is useful to quantify this additional energy saving. Both systems have discrete operational choices corresponding to how the CPRs are utilized for each actuator. It is necessary to determine optimal operation for each of these architectures for analysis and fair comparison. Techniques for optimal operation of the HHEA have been developed previously from the Langrange multiplier method. Applying the same optimal control method to STEAM encountered some technical challenge leading to the optimal control algorithm not being able to satisfy certain constraints. The issue is analyzed and solved by adding noise to the optimization. Using this proposed algorithm, case studies are performed to compare the energy-saving potentials of STEAM and HHEA for two sizes of excavators and a wheel-loader performing representative duty cycles. The baseline is a standard load-sensing architecture. Results show that STEAM and HHEA can reduce energy consumption between 35-65% and 50-80% respectively

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Gradient-based optimization for regression in the functional tensor-train format

Predictive analysis of complex computational models, such as uncertainty quantification (UQ), must often rely on using an existing database of simulation runs. In this paper we consider the task of performing low-multilinear-rank regression on such a database. Specifically we develop and analyze an efficient gradient computation that enables gradient-based optimization procedures, including stochastic gradient descent and quasi-Newton methods, for learning the parameters of a functional tensor-train (FT). We compare our algorithms with 22 other nonparametric and parametric regression methods on 10 real-world data sets and show that for many physical systems, exploiting low-rank structure facilitates efficient construction of surrogate models. Here, we use a number of synthetic functions to build insight into behavior of our algorithms, including the rank adaptation and group-sparsity regularization procedures that we developed to reduce overfitting. Finally we conclude the paper by building a surrogate of a physical model of a propulsion plant on a naval vessel.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Automated Hybrid Variance Reduction on Advanced Architectures in the Shift Monte Carlo Code

Monte Carlo transport methods are the most accurate schemes for solving problems with complex energy and spatial features, but they come with a high computational cost. Although hybrid methods have enabled the use of Monte Carlo transport for a large class of problems, they still require significant computing resources. Modern multicore CPUs with large numbers of compute cores and graphical processing units (GPUs) provide opportunities to optimize the memory and run-time costs of hybrid Monte Carlo methods. This paper documents the development and analysis of three Monte Carlo transport algorithms that support hybrid transport using the consistent adjoint-driven importance sampling (CADIS) and forward-weighted CADIS methods in the Shift Monte Carlo code: history-based transport using static and dynamic threading on multicore CPUs and event-based transport enabling weight window tracking on GPUs. The results are shown for two challenging hybrid problems on the Frontier supercomputer at the Oak Ridge Leadership Computing Facility. The results show that all three methods yield good performance and enable solutions of difficult fixed-source transport problems in less than 2 min on 20 nodes of Frontier. Dynamic threading was observed to give up to 20% better scaling behavior than static threading. Moreover, the AMD Instinct 250X GPU was found to give 9 to 11 times greater throughput per graphics compute die than the best CPU performance. In conclusion, additional opportunities for optimization of hybrid transport on GPUs are discussed.

Denovo↗
DOE OSTI2020

Fast Evaluation of Aircraft Icing Severity Using Machine Learning Based on XGBoost

Aircraft icing represents a serious hazard in aviation which has caused a number of fatal accidents over the years. In addition, it can lead to substantial increase in drag and weight, thus reducing the aerodynamics performance of the airplane. The process of ice accretion on a solid surface is a complex interaction of aerodynamic and environmental variables. The complex relationship makes machine learning-based methods an attractive alternative to traditional numerical simulation-based approaches. In this study, we introduce a purely data-driven approach to find the complex pattern between different flight conditions and aircraft icing severity prediction. The supervised learning algorithm Extreme Gradient Boosting (XGBoost) is applied to establish the prediction framework which makes prediction based on any set of observations. The input flight conditions for the proposed prediction framework are liquid water content, droplet diameter and exposure time. The proposed approach is demonstrated in three cases: maximum ice thickness prediction, icing area prediction and icing severity level evaluation. Performance comparison studies and error analysis are also conducted to verify the effectiveness and performance of the proposed method. Results show that the proposed method has reasonable capability in evaluating aircraft icing severity.

Li, Sibo (ORCID:000000021705844X)↗
DOE OSTI2019

Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems

This study presents a topology optimization method to design assemblies of periodic cellular materials with controllable geometric complexity. The framework is based on a novel multi-scale and multi-material design model in which the structure, the layout of the material subdomains, and their micro-structures are optimized concurrently. To allow a tight control over its geometrical complexity, the layout at the macro-scale is described by level-set fields, parameterized by geometric primitives. The micro-scale geometry is represented through a density approach. A nonlinear programming algorithm drives the optimization process using design sensitivities computed by the discrete adjoint method. The proposed design framework is studied with heat transfer problems. Practical design problems, such as a heat sink and a thermal storage unit with phase change are discussed. The macro-scale analysis model relies on a generalized transient diffusion equation. At the micro-scale, homogenization is used to compute equivalent material properties. The numerical examples in this study show that the optimized multi-scale multi-material layouts outperform the corresponding mono-scale structures while maintaining geometric simplicity at the macro-scale level.

42 ENGINEERING↗
DOE OSTI2019

Enhancing Network Visibility and Security through Tensor Analysis

The increasing size, variety, rate of growth and change, and complexity of network data has warranted advanced network analysis and services. Tools that provide automated analysis through traditional or advanced signature-based systems or machine learning classifiers suffer from practical difficulties. These tools fail to provide comprehensive and contextual insights into the network when put to practical use in operational cyber security. In this paper, we present an effective tool for network security and traffic analysis that uses high-performance data analytics based on a class of unsupervised learning algorithms called tensor decompositions. The tool aims to provide a scalable analysis of the network traffic data and also reduce the cognitive load of network analysts and be network-expert-friendly by presenting clear and actionable insights into the network. With this being said, In this paper, we demonstrate the successful use of the tool in two completely diverse operational cyber security environments, namely, (1) security operations center (SOC) for the SCinet network at the SuperComputing (SC) Conference in 2016 and 2017 and (2) Reservoir Labs’ Local Area Network (LAN). In each of these environments, we produce actionable results for cyber security specialists including (but not limited to) (1) finding malicious network traffic involving internal and external attackers using port scans, SSH brute forcing, and NTP amplification attacks, (2) uncovering obfuscated network threats such as data exfiltration using DNS port and using ICMP traffic, and (3) finding network misconfiguration and performance degradation patterns.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence (AI) and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. Advances in data collection and numerical simulation have changed the dynamics of scientific research and motivate the need for randomized algorithms. For instance, advances in imaging technologies such as X-ray ptychography, electron microscopy, electron energy loss spectroscopy, or adaptive optics lattice light-sheet microscopy collect hyperspectral imaging and scattering data in terabytes, at breakneck speed enabled by state-of-the-art detectors. The data collection is exceptionally fast compared with its analysis. Likewise, advances in high-performance architectures have made exascale computing a reality and changed the economies of scientific computing in the process. Floating-point operations that create data are essentially free in comparison with data movement. Thus far, most approaches have focused on creating faster hardware. Ironically, this faster hardware has exacerbated the problem by making data still easier to create. Under such an onslaught, scientists often resort to heuristic deterministic sampling schemes (e.g., low-precision arithmetic, sampling every nth element) and sacrifice potentially valuable accuracy. Dramatically better results can be achieved via randomized algorithms, reducing the data size as much as or more than naive deterministic subsampling can achieve, while retaining the high accuracy of computing on the full data set. By randomized algorithms we mean those algorithms that employ some form of randomness in internal algorithmic decisions to accelerate time to solution, increase scalability, or improve reliability. Examples include matrix sketching for solving large-scale least-squares problems (see Figure 1) and stochastic gradient descent for training machine learning models. We are not recommending heuristic methods but rather randomized algorithms that have certificates of correctness and probabilistic guarantees of optimality and near-optimality. Such approaches can be useful beyond acceleration, for example, in understanding how to avoid measure zero worst-case scenarios that plague methods such as QR matrix factorization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multi-Objective Optimization of Uranium Target Assembly–3: A Comparison of Genetic and Traditional Methods

Commonly produced as a byproduct of uranium fission, 99 Mo is a key medical isotope that is in high demand in the United States. An international goal is to switch from medical isotope production technologies that require highly enriched uranium to medical isotope production technologies that require only low-enriched uranium. Niowave Inc. is contributing to this goal by developing an accelerator-driven subcritical assembly called the Uranium Target Assembly (UTA). This work compares the performance of Dakota’s Multi-Objective Genetic Algorithm (MOGA) against traditional sensitivity analysis in the neutronic optimization of the UTA-3 system. The design objectives are k-eigenvalue (k eff ) and natural uranium fission power, which are directly correlated with the amount of 99 Mo produced. Dakota:MOGA did not perform as well as human engineering ingenuity in optimization studies with high numbers of input parameters, such as fuel rod type selection and fuel rod placement. However, Dakota:MOGA did outperform traditional sensitivity analysis in optimization studies with fewer than 20 parameters and revealed the degree to which each parameter influences the optimal design space for k eff and natural uranium fission power (to a lesser extent). As the design model became more complex in the final stage of design, the computational resources required to calculate the design objective values in the Monte Carlo N-Particle transport code from selected input parameter combinations limited Dakota:MOGA’s performance, and, unfortunately, human intervention was required to discern the optimal design space. In conclusion, future work will attempt to reduce computational resource constraints by incorporating areduced-order neutronics model into the optimization cycle.

Accelerator-driven systems↗
DOE OSTI2022

Performance of New Near-Real-Time PERSIANN Product (PDIR-Now) for Atmospheric River Events over the Russian River Basin, California

Most heavy precipitation events and extreme flooding over the U.S. Pacific coast can be linked to prevalent atmospheric river (AR) conditions. Thus, reliable quantitative precipitation estimation with a rich spatiotemporal resolution is vital for water management and early warning systems of flooding and landslides over these regions. At the same time, high-quality near-real-time measurements of AR precipitation remain challenging due to the complex topographic features of land surface and meteorological conditions of the region: specifically, orographic features occlude radar measurements while infrared-based algorithms face challenges, differentiating between both cold brightband (BB) precipitation and the warmer nonbrightband (NBB) precipitation. It should be noted that the latter precipitation is characterized by greater orographic enhancement. In this study, we evaluate the performance of a recently developed near-real-time satellite precipitation algorithm: Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) Dynamic Infrared–Rain Rate-Now (PDIR-Now). This model is primarily dependent on infrared information from geostationary satellites as input; consequently, PDIR-Now has the advantage of short data latency, 15–60-min delay between observation to precipitation product delivery. The performance of PDIR-Now is analyzed with a focus on AR-related events for cases dominated by NBB and BB precipitation over the Russian River basin. In our investigations, we utilize S-band (3-GHz) precipitation profilers with Joss/Parsivel disdrometer measurements at the Middletown and Santa Rosa stations to classify BB and NBB precipitation events. In general, our analysis shows that PDIR-Now is more skillful in retrieving precipitation rates over both BB and NBB events across the topologically complex study area as compared to PERSIANN-Cloud Classification System (CCS). Also, we discuss the performance of well-known operational near-real-time precipitation products from 2017 to 2019. Conventional categorical and volumetric categorical indices, as well as continuous statistical metrics, are used to show the differences between various high-resolution precipitation products such as Multi-Radar Multi-Sensor (MRMS).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

In Silico Identification of Microbial Partners to Form Consortia with Anaerobic Fungi

Lignocellulose is an abundant and renewable resource that holds great promise for sustainable bioprocessing. However, unpretreated lignocellulose is recalcitrant to direct utilization by most microbes. Current methods to overcome this barrier include expensive pretreatment steps to liberate cellulose and hemicellulose from lignin. Anaerobic gut fungi possess complex cellulolytic machinery specifically evolved to decompose crude lignocellulose, but they are not yet genetically tractable and have not been employed in industrial bioprocesses. Here, we aim to exploit the biomass-degrading abilities of anaerobic fungi by pairing them with another organism that can convert the fermentable sugars generated from hydrolysis into bioproducts. By combining experiments measuring the amount of excess fermentable sugars released by the fungal enzymes acting on crude lignocellulose, and a novel dynamic flux balance analysis algorithm, we screened potential consortia partners by qualitative suitability. Microbial growth simulations reveal that the fungus Anaeromyces robustus is most suited to pair with either the bacterium Clostridia ljungdahlii or the methanogen Methanosarcina barkeri—both organisms also found in the rumen microbiome. By capitalizing on simulations to screen six alternative organisms, valuable experimental time is saved towards identifying stable consortium members. This approach is also readily generalizable to larger systems and allows one to rationally select partner microbes for formation of stable consortia with non-model microbes like anaerobic fungi.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications

We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.

Barnafi, Nicolas [University of Chile, Santiago]↗