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NASA NTRS2019

Multi-Band Atmospheric Correction Algorithm for Ocean Color Retrievals

NASA's current Atmospheric Correction (AC) algorithm for ocean color utilizes two bands and their ratio in the Near Infrared (NIR) to estimate aerosol reflectance and aerosol type. The algorithm then extrapolates the spectral dependence of aerosol reflectance to the visible wavelengths based on modeled spectral dependence of the identified aerosol type. Future advanced ocean color sensors, such as the Ocean Color Instrument (OCI) that will be carried on the Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) satellite, will be capable of measuring the hyperspectral radiance from 340 to 890 nm at 5-nm spectral resolution and at 7 discrete Short-wave Infrared (SWIR) channels: 940, 1038,1250, 1378, 1615, 2130, and 2260 nm. To optimally employ this unprecedented instrument capability, we propose an improved AC algorithm that utilizes all atmospheric-window channels in the NIR to SWIR spectral range to reduce the uncertainty in the AC process. A theoretical uncertainty analysis of this, namely Multi-Band AC (MBAC), indicates that the algorithm can reduce the uncertainty in remote sensing reflectance (Rrs) retrievals of the ocean caused by sensor random noise. Furthermore, in optically complex waters, where the NIR signal is affected by contributions from highly-reflective turbid waters, the MBAC algorithm can be adaptively weighted to the strongly-absorbing SWIR channels to enable improved ocean color retrievals in coastal waters. We provide here a description of the algorithm and demonstrate the improved performance in ocean color retrievals, relative to the current NASA standard AC algorithm, through comparison with field measurements and assessment of propagated uncertainties in applying the MBAC algorithm to MODIS and simulated PACE OCI data.

PACE↗

NASA NTRS2019

A New Discrete Wavelength BUV Algorithm for Consistent Volcanic SO2 Retrievals from Multiple Satellite Missions

This paper describes a new discrete wavelength algorithm developed for retrieving volcanic sulfur dioxide (SO2) vertical column density (VCD) from UV observing satellites. The Multi-Satellite SO2 algorithm (MS_SO2) simultaneously retrieves column densities of sulfur dioxide, ozone, and Lambertian effective reflectivity (LER) and its spectral dependence. It is used operationally to process measurements from the heritage Total Ozone Mapping Spectrometer (TOMS) onboard NASA's Nimbus-7 satellite (N7/TOMS: 1978-1993) and from the current Earth Polychromatic Imaging Camera (EPIC) onboard Deep Space Climate Observatory (DSCOVR: 2015-) from the Earth-Sun Lagrange (L1) orbit. Results from MS_SO2 algorithm for several volcanic cases were assessed using the more sensitive principal component analysis (PCA) algorithm. The PCA is an operational algorithm used by NASA to retrieve SO2 from hyperspectral UV spectrometers, such as the Ozone Monitoring Instrument (OMI) onboard NASA's Earth Observing System Aura satellite and Ozone Mapping and Profiling Suite (OMPS) onboard NASA-NOAA Suomi National Polar Partnership (SNPP) satellite. For this comparative study, the PCA algorithm was modified to use the discrete wavelengths of the Nimbus-7/TOMS instrument, described in Sect. S1 of the Supplement. Our results demonstrate good agreement between the two retrievals for the largest volcanic eruptions of the satellite era, such as the 1991 Pinatubo eruption. To estimate SO2 retrieval systematic uncertainties, we use radiative transfer simulations explicitly accounting for volcanic sulfate and ash aerosols. Our results suggest that the discrete-wavelength MS_SO2 algorithm, although less sensitive than hyperspectral PCA algorithm, can be adapted to retrieve volcanic SO2 VCDs from contemporary hyperspectral UV instruments, such as OMI and OMPS, to create consistent, multi-satellite, long-term volcanic SO2 climate data records.

Bradford L Fisher↗

NASA NTRSDate not supplied

Post-Flight Performance Analysis of Navigation and Advanced Guidance Algorithms on a Terrestrial Suborbital Rocket Flight

There is currently renewed interest in robotic and crewed landers for a return to the lunar surface. Advanced guidance and navigation algorithms are essential to accurately delivering cargo and crew safely to the moon successfully. This paper reports the overall performance of an integrated set of navigation and guidance algorithms flown on a terrestrial suborbital rocket up to an altitude of approximately 100km. The navigation algorithm consists of an onboard extended Kalman Filter (EKF) that ingests multiple sensor measurements, one of which is the output from a terrain relative navigation (TRN) algorithm that cross-references camera images to on-board satellite imagery to perform feature correlation within the camera image. The guidance algorithm solves for a 6-degree-of-freedom (DoF) optimal trajectory using a successive convexification method during powered descent. The altitude range as well as the landing dynamics experienced during this test flight are realistic for an extraterrestrial landing and provide an invaluable data set to gauge the current development of these landing algorithms in an effort to advance the overall software readiness levels (SRL). This paper will delve into different aspects of each algorithm and present an analysis of the in-flight performance of the algorithms. This flight was conducted under the National Aeronautics and Space Administration (NASA) Safe and Precise Landing Integrated Capabilities Evolution (SPLICE) project focused on technology advancement for landing applications.

Guidance↗

NASA NTRS2021

Adaptive-Sweep Algorithm for Spacecraft Carrier Acquisition and Tracking: System Analysis and Implementation

This paper presents an adaptive-sweep algorithm that can be used in conjunction with a Phased-Lock Loop to acquire and track the carrier of a Binary Phase-shift Keying signal with residual carrier. This algorithm is useful in proximity links where no Doppler pre-compensation is available at the transmitter, and allows the receiver to acquire the incoming carrier even if the experienced Doppler shift is several orders of magnitude larger than the PLL bandwidth. Other applications for this algorithm include Multiple Uplink per Antenna at the Deep Space Network, and generation of observables (Doppler shift, Doppler rate, range rate) for in-situ navigation purposes. This paper enhances a previously presented adaptive-sweep algorithm and its performance analysis in two fronts. First, the algorithm now uses the direction function to automatically estimate the required frequency jump to achieve PLL lock. This enables a fully adaptive-sweep scheme in which system implementer does not need to manually select thresholds. On the other hand, we study the system performance in the presence of Additive White Gaussian Noise and derive necessary conditions for the system to operate at low signal-to-noise conditions. This allows us to create design rules that specify all parameters of the algorithm given a set of system-level requirements. To test the performance of the proposed algorithm, we implement it in GNU Radio, an open-source Software-Defined Radio that interfaces with several commercial radio peripherals. We use this implementation to demonstrate carrier lock and quantify system performance under different noise conditions. We also test the algorithm using open-loop recordings of two downlinks between the Lunar Reconnaissance Orbiter and the Deep Space Network. We show that even after large frequency jumps (tens of kHz), the proposed system is able to rapidly reacquire the carrier and continue operation.

Divsalar, Dariush↗

NASA NTRS2022

Cloud Mask Intercomparison eXercise (CMIX): An evaluation of cloud masking algorithms for Landsat 8 and Sentinel-2

Cloud cover is a major limiting factor in exploiting time-series data acquired by optical spaceborne remote sensing sensors. Multiple methods have been developed to address the problem of cloud detection in satellite imagery and a number of cloud masking algorithms have been developed for optical sensors but very few studies have carried out quantitative intercomparison of state-of-the-art methods in this domain. This paper summarizes results of the first Cloud Masking Intercomparison eXercise (CMIX) conducted within the Committee Earth Observation Satellites (CEOS) Working Group on Calibration & Validation (WGCV). CEOS is the forum for space agency coordination and cooperation on Earth observations, with activities organized under working groups. CMIX, as one such activity, is an international collaborative effort aimed at intercomparing cloud detection algorithms for moderate-spatial resolution (10–30 m) spaceborne optical sensors. The focus of CMIX is on open and free imagery acquired by the Landsat 8 (NASA/USGS) and Sentinel-2 (ESA) missions. Ten algorithms developed by nine teams from fourteen different organizations representing universities, research centers and industry, as well as space agencies (CNES, ESA, DLR, and NASA), are evaluated within the CMIX. Those algorithms vary in their approach and concepts utilized which were based on various spectral properties, spatial and temporal features, as well as machine learning methods. Algorithm outputs are evaluated against existing reference cloud mask datasets. Those datasets vary in sampling methods, geographical distribution, sample unit (points, polygons, full image labels), and generation approaches (experts, machine learning, sky images). Overall, the performance of algorithms varied depending on the reference dataset, which can be attributed to differences in how the reference datasets were produced. The algorithms were in good agreement for thick cloud detection, which were opaque and had lower uncertainties in their identification, in contrast to thin/semi-transparent clouds detection. Not only did CMIX allow identification of strengths and weaknesses of existing algorithms and potential areas of improvements, but also the problems associated with the existing reference datasets. The paper concludes with recommendations on generating new reference datasets, metrics, and an analysis framework to be further exploited and additional input datasets to be considered by future CMIX activities.

Sergii Skakun↗

NASA NTRSDate not supplied

Biomass Harmonization and SAR Analysis with the Multi-mission Algorithm and Analysis Platform (MAAP)

The Multi‐mission Algorithm and Analysis Platform (MAAP) is a collaborative effort between NASA and the European Space Agency (ESA) to support above ground biomass (AGB) research in an open science framework. MAAP brings together relevant data, algorithms, and computing capabilities in a common cloud environment to address the challenges of sharing and processing data from field, airborne and satellite measurements. MAAP was publicly released in October 2021, providing computing capabilities co-located with the data, a collaborative coding and analysis environment, and a set of interoperable tools and algorithms developed to support the estimation and visualization of data. MAAP has allowed scientists from both North America and Europe to collaborate on the generation and analysis/visualization of data derived from multiple, discipline-adjacent missions in an open, collaborative environment that has reached beyond traditional scientific investigation. MAAP has been used to support multiple scientific activities. To date, existing LiDAR data from multiple platforms has been calibrated with field measurements and combined for more comprehensive and accurate estimates of above ground biomass AGB; these LiDAR platforms include airborne (e.g. LVIS), the International Space Station (NASA’s Global Ecosystem Dynamics Investigation (GEDI), and satellites (e.g. ICESat-2). The current challenge is to effectively and seamlessly combine the aforementioned LiDAR-based data with new data sources such as P-band RADAR from ESA’s upcoming BIOMASS mission, existing ESA Sentinel-1 C-band SAR, and the 30 PB/yr of high cadence global coverage L-band SAR data from the upcoming NASA-ISRO SAR (NISAR) mission. Recent analysis using MAAP merged ICESat-2 and optical data (Harmonized Landsat Sentinel) produced the most comprehensively precise estimate of boreal-wide AGB to date. Another effort using MAAP is the production and open distribution of global comparisons of AGB map estimates, including from ICESat-2 and GEDI, to bolster stakeholder uptake for policy applications. These map estimates will feed into the Intergovernmental Panel on Climate Change (IPCC) database, likely aiding the next Global Carbon Stocktake of the UNFCCC. Furthermore, the biomass retrieval intercomparison exercise BRIX-2 could benefit from the MAAP providing standardized test cases (based on airborne campaign and spaceborne data) allowing the community to develop and apply retrieval algorithms based on these test cases, while forthcoming SAR data training curricula could also use the MAAP as a teaching and learning platform. The MAAP is meeting the challenges inherent in international, open science collaboration and large scale computing with a platform that is entirely open source and cloud native, using open standards for data access, manipulation, protocols, and formats. The MAAP data system consists of a dedicated data store whose data is indexed in an online catalog conforming to established metadata, application programmatic interfaces (APIs), and service interface standards, using an implementation of the open sourced NASA Common Metadata Repository. Federation of user identities allows users from either NASA or ESA to access and consume services from the other using a unified metadata catalog for the data utilized across the ESA and NASA MAAP platforms. Similarly, we are exploring how to increase interoperability to achieve a common approach to packaging, orchestrating and executing algorithms, with interoperable access to data for subsetting, fast browse, and cloud-optimized access, all using interoperable standards such as those from the Open Geospatial Consortium (OGC). Designed for interoperability, ESA and NASA utilize a common architecture for the software platform. It provides a cloud-based algorithm development environment (ADE) that enables scientists to develop algorithms collaboratively with access to the MAAP data catalog as well as other data archives. MAAP provides an Eclipse Che-based ADE supporting both Python and R languages, popular in this biomass community. Algorithms developed and containerized within the ADE can be deployed to run to thousands of computational nodes in the MAAP’s data processing system (DPS), dramatically speeding up processing and giving scientists a rapid, iterative turnaround of results. NASA’s implementation of the DPS is based on the Hybrid Science Data System (HySDS) framework, used by NASA flight projects to produce Earth science standard products.

cloud computing↗

NASA NTRSDate not supplied

Demand-Capacity Balancing Algorithms for Urban Air Mobility Operations

This paper proposes new Demand/Capacity Balancing (DCB) algorithms that resolve imbalances at enroute waypoints, such as crossing, merging, and UAM corridor entry or exit waypoints, in addition to vertiports; we refer to this algorithm as DCB-Waypoint, still using pre-departure delay as the sole resolution mechanism. Like DCB-Vertiport, DCB-Waypoint takes one flight at a time and resolves imbalances one waypoint at a time, starting from the origin vertiport followed by the sequence of constrained waypoints and, finally, the destination vertiport. The next advancement assigns airborne delays, in addition to pre-departure delays at vertiports. This algorithm, called DCB-Airborne-Delays, uses information on flight speeds to ensure that the assigned delays are feasible, meaning that variations in flight speeds are within feasible aircraft speed ranges. The proposed algorithms are being implemented in a new fast-time simulation tool developed especially for simulating UAM operations. The full paper will provide additional details of the new DCB algorithms that have been developed, as well as the results from simulations using these algorithms. Finally, the DCB algorithms will be compared against one another to obtain insights and recommendations for the future development of more advanced DCB algorithms.

urban air mobility, demand-capacity balancing↗

NASA NTRSDate not supplied

Demand-Capacity Balancing Algorithms for Urban Air Mobility Operations

urban air mobility↗

NASA NTRS2014

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial-optimization problems that encompasses, among many others, the problem of generating optimal space-data communications schedules.

ground stations↗

DOE OSTI2024

DyG-DPCD: A Distributed Parallel Community Detection Algorithm for Large-Scale Dynamic Graphs

Dynamic (Temporal) graphs capture the valuable evolution of real-world systems, from the continuously evolving patterns of social interactions and genetic pathways to the dynamic fluctuations of economic forces. Detecting communities for such evolving networks poses unique challenges. Detecting and analyzing the evolution of communities within dynamic graphs unlocks valuable insights into the underlying structural and temporal patterns of real-world systems. However, the sheer volume of modern graph data and the inherent complexity of the temporal dimension pose significant challenges to scalable community detection algorithms. Addressing this gap, our work explores the limited landscape of scalable distributed-memory parallel methods specifically designed for dynamic network community detection. We propose a novel parallel algorithm, DyG-DPCD (Dynamic Graph Distributed Parallel Community Detection), to detect communities in dynamic networks using the Message Passing Interface (MPI) framework. We present a vertex-centric approach, allowing us to detect communities through local optimization. Furthermore, we enhance our baseline algorithm by incorporating three heuristics, which improve the algorithm’s performance significantly while maintaining the quality of the solutions. We demonstrate the efficiency of our algorithm by experimenting on several real-world large-scale networks with hundreds of millions of edges spanning diverse domains. Notably, DyG-DPCD achieves speedups between 25× and 30× for large networks that we experimented on using NERSC compute nodes. In conclusion, our algorithm outperforms the STINGER parallel re-agglomeration algorithm by 30×.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Study of 201 Non-Small Cell Lung Cancer Patients Given Stereotactic Ablative Radiation Therapy Shows Local Control Dependence on Dose Calculation Algorithm

Purpose: Pencil beam (PB) and collapsed cone convolution (CCC) dose calculation algorithms differ significantly when used in the thorax. However, such differences have seldom been previously directly correlated with outcomes of lung stereotactic ablative body radiation (SABR). Methods and Materials: Data for 201 non-small cell lung cancer patients treated with SABR were analyzed retrospectively. All patients were treated with 50 Gy in 5 fractions of 10 Gy each. The radiation prescription mandated that 95% of the planning target volume (PTV) receive the prescribed dose. One hundred sixteen patients were planned with BrainLab treatment planning software (TPS) with the PB algorithm and treated on a Novalis unit. The other 85 were planned on the Pinnacle TPS with the CCC algorithm and treated on a Varian linac. Treatment planning objectives were numerically identical for both groups. The median follow-up times were 24 and 17 months for the PB and CCC groups, respectively. The primary endpoint was local/marginal control of the irradiated lesion. Gray's competing risk method was used to determine the statistical differences in local/marginal control rates between the PB and CCC groups. Results: Twenty-five patients planned with PB and 4 patients planned with the CCC algorithms to the same nominal doses experienced local recurrence. There was a statistically significant difference in recurrence rates between the PB and CCC groups (hazard ratio 3.4 [95% confidence interval: 1.18-9.83], Gray's test P=.019). The differences (Δ) between the 2 algorithms for target coverage were as follows: ΔD99{sub GITV} = 7.4 Gy, ΔD99{sub PTV} = 10.4 Gy, ΔV90{sub GITV} = 13.7%, ΔV90{sub PTV} = 37.6%, ΔD95{sub PTV} = 9.8 Gy, and ΔD{sub ISO} = 3.4 Gy. GITV = gross internal tumor volume. Conclusions: Local control in patients receiving who were planned to the same nominal dose with PB and CCC algorithms were statistically significantly different. Possible alternative explanations are described in the report, although they are not thought likely to explain the difference. We conclude that the difference is due to relative dosimetric underdosing of tumors with the PB algorithm.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2015

Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Benchmarking Coordination Number Prediction Algorithms on Inorganic Crystal Structures

Coordination numbers and geometries form a theoretical framework for understanding and predicting materials properties. Algorithms to determine coordination numbers automatically are increasingly used for machine learning and automatic structural analysis. In this work, we introduce MaterialsCoord, a benchmark suite containing 56 experimentally-derived crystal structures (spanning elements, binaries, and ternary compounds) and their corresponding coordination environments as described in the research literature. We also describe CrystalNN, a novel algorithm for determining near neighbors. We compare CrystalNN against 7 existing near-neighbor algorithms on the MaterialsCoord benchmark, finding CrystalNN to perform similarly to several well-established algorithms. For each algorithm, we also assess computational demand and sensitivity towards small perturbations that mimic thermal motion. Finally, we investigate the similarity between bonding algorithms when applied to the Materials Project database. Finally, we expect that this work will aid the development of coordination prediction algorithms as well as improve structural descriptors for machine learning and other applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Models and Algorithms for Equilibrium Analysis of Mixed-Material Nucleic Acid Systems

Dynamic programming algorithms within the NUPACK software suite enable analysis of equilibrium base-pairing properties for complex and test tube ensembles containing arbitrary numbers of interacting nucleic acid strands. Currently, calculations are limited to single-material systems that are either all-RNA or all-DNA. Here, to enable analysis of mixed-material systems that are critical for modern applications in vitro, in situ, and in vivo, we develop physical models and dynamic programming algorithms that allow the material of the system to be specified at nucleotide resolution. Free energy parameter sets are constructed for both RNA/DNA and RNA/2'OMe-RNA mixed-material systems by combining available empirical mixed-material parameters with single-material parameter sets to enable treatment of the full complex and test tube ensembles. New dynamic programming recursions account for the material of each nucleotide throughout the recursive process. For a complex with N nucleotides, the mixed-material dynamic programming algorithms maintain the O(N 3 ) time complexity of the single-material algorithms, enabling efficient calculation of diverse physical quantities over complex and test tube ensembles (e.g., complex partition function, equilibrium complex concentrations, equilibrium base-pairing probabilities, minimum free energy secondary structure(s), and Boltzmann-sampled secondary structures) at a cost increase of roughly 2.0-3.5×. The results of existing single-material algorithms are exactly reproduced when applying the new mixed-material algorithms to single-material systems. Accuracy is significantly enhanced using mixed-material models and algorithms to predict RNA/DNA and RNA/2'OMe-RNA duplex melting temperatures from the experimental literature as well as RNA/DNA melt profiles from new experiments. In conclusion, mixed-material analyses can be performed online using the NUPACK web app (www.nupack.org) or locally using the NUPACK Python module.

2′OMe-RNA↗

DOE OSTI2014

A Nth-order linear algorithm for extracting diffuse correlation spectroscopy blood flow indices in heterogeneous tissues

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD{sub B}). The purpose of this study is to extend the capability of the Nth-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different types of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD{sub B} in the brain layer with a step decrement of 10% while maintaining αD{sub B} values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order (N ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The Nth-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Quantum Algorithms for Representation-Theoretic Multiplicities

Kostka, Littlewood-Richardson, Plethysm, and Kronecker coefficients are the multiplicities of irreducible representations in the decomposition of representations of the symmetric group that play an important role in representation theory, geometric complexity, and algebraic combinatorics. We give quantum algorithms for computing these coefficients whenever the ratio of dimensions of the representations is polynomial. We show that there is an efficient classical algorithm for computing the Kostka numbers under this restriction and conjecture the existence of an analogous algorithm for the Littlewood-Richardson coefficients. We argue why such classical algorithm does not straightforwardly work for the Plethysm and Kronecker coefficients and conjecture that our quantum algorithms lead to superpolynomial speedups. The conjecture about Kronecker coefficients was disproved by Panova [Polynomial time classical versus quantum algorithms for representation theoretic multiplicities, arXiv:2502.20253] with a classical algorithm which, if optimal, points to a 𝒪⁡(𝑛 4+2⁢𝑘 ) vs $\tilde{Ω}$⁡(𝑛 4⁢𝑘 2 +1 ) polynomial gap in quantum vs classical computational complexity for an integer parameter 𝑘.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms

Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD algorithms have focused on solving the eigenpair problem for ground, excited-state, and thermal observable estimation, there has been a lot less work in considering QSD algorithms for the problem of quantum dynamical simulation. In this work, we propose several quantum Krylov fast-forwarding (QKFF) algorithms capable of predicting long-time dynamics well beyond the coherence time of current quantum hardware. Our algorithms use real-time evolved Krylov basis states prepared on the quantum computer and a multi-reference subspace method to ensure convergence towards high-fidelity, long-time dynamics. In particular, we show that the proposed multi-reference methodology provides a systematic way of trading off circuit depth with classical post-processing complexity. Further, we also demonstrate the efficacy of our approach through numerical implementations for several quantum chemistry problems including the calculation of the auto-correlation and dipole moment correlation functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. Further, this method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

97 MATHEMATICS AND COMPUTING↗