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NASA NTRS2021

Status of the Moderate-resolution Imaging Spectroradiometer Level 1B Algorithm

The Moderate-resolution Imaging Spectroradiometer (MODIS) instruments are on-board the Aqua and Terra spacecraft, launched in 2002 and 1999, respectively. Since beginning operation, they have continued to collect valuable remote sensing data of the Earth in 36 spectral bands ranging in wavelengths from 0.41 to 14.5 μm. The Level 1B (L1B) algorithm produces calibrated top of the atmosphere (TOA) radiances for each Earth-view (EV) pixel and calibrated TOA reflectances for the reflective solar bands using geo-located, uncalibrated instrument data and calibration look up tables (LUTs) produced regularly by the MODIS Characterization Support Team (MCST). The L1B algorithm also calculates an uncertainty value for each EV pixel. The calibrated radiance and reflectance products are used to generate higher-level science products. A separate L1B code version is maintained for both MODIS instruments so that sensor specific issues can be handled individually. The current L1B algorithm version produces the Collection 6.1 (C6.1) products and was released in 2017. An overview of the C6.1 algorithm is provided together with improvements made since its release. Also discussed briefly are the planned improvements in the Collection 7 L1B algorithm.

MODIS↗

NASA NTRS2021

One- and Two-Band Sensors and Algorithms to Derive aCDOM(440) from Global Above- and In-Water Optical Observations

The colored (or chromophoric, depending on the literature) dissolved organic matter (CDOM) spectral absorption coefficient, aCDOM(λ), is a variable of global interest that has broad application in the study of biogeochemical processes. Within the funding for scientific research, there is an overarching trend towards increasing the scale of observations both temporally and spatially, while simultaneously reducing the cost per sample, driving a systemic shift towards autonomous sensors and observations. Legacy aCDOM(λ) measurement techniques can be cost-prohibitive and do not lend themselves toward autonomous systems. Spectrally rich datasets carefully collected with advanced optical systems in diverse locations that span a global range of water bodies, in conjunction with appropriate quality assurance and processing, allow for the analysis of methods and algorithms to estimate aCDOM(440) from spectrally constrained one- and two-band subsets of the data. The resulting algorithms were evaluated with respect to established fit-for-purpose criteria as well as quality assured archival data. Existing and proposed optical sensors capable of exploiting the algorithms and intended for autonomous platforms are identified and discussed. One-band in-water algorithms and two-band above-water algorithms showed the most promise for practical use (accuracy of 3.0% and 6.5%, respectively), with the latter demonstrated for an airborne dataset.

ocean color↗

NASA NTRSDate not supplied

Path-Adaptive Guidance Algorithm Trades for a Two-Stage Lunar Descent Vehicle

For the next generation of NASA’s missions, explicit, path-adaptive descent guidance algorithms must provide the stability and customizability required for a safe and efficient descent to the lunar surface, while also meeting program and vehicle constraints. Several descent algorithms have been flown and tested for single-stage landers through the Apollo and Altair programs, but thus far little analysis has been conducted involving the application of these algorithms to a two-stage descent vehicle. Due to payload mass and fairing constraints of the existing fleet of launch vehicles, multi-stage descent architectures are a unique option for achieving the greatest possible mass to lunar surface. This paper seeks to compare the performance of guidance configurations of a lunar lander system consisting of two stages, one of which separates partway through descent. Through development of this paper, an optimization suite has been written that is specifically designed for optimizing planetary non-atmospheric two-stage descent trajectories, and is used as a baseline to compare the guidance algorithms tested. Time-to-go computational methods and ignition logic routines that may be employed in a lunar environment are also discussed. Preliminary results are presented that show relative performance metrics for a range of different guidance algorithm configurations.

Jason M Everett↗

NASA NTRSDate not supplied

Performance and Accuracy Assessment of Line Marching Algorithm Computations Utilizing GPUs Within a Predictive GNSS Quality Service

This paper presents a detailed analysis of the accuracy and performance of line marching algorithms executing on a GPU. In the context of an accurate Global Navigation Satellite System(GNSS) quality of service simulation, horizon sky-plots are a useful tool to determine satellite visibility in the presence of obstructions from objects, such as buildings or dense foliage. In order to accurately model satellite visibility at a point of interest on a map, a horizon plot can identify the viewing angles at which objects are blocking the sky. This computation requires traversing a line starting at the point of interest on a 2D altitude map, moving outward for every azimuth angle. To explore the performance of this computation, we propose a new dynamic stopping condition for the traversal of the line, benefiting from objects close to the point of interest. We compare the accuracy of common line marching algorithms, and consider their parallel performance when developed in CUDA. We find that our proposed stopping condition for line marching provides a significant improvement in performance in urban canyon sky-plots, as compared to previous work. Additionally, these results show that simpler algorithms, such as the digital differential analyzer line algorithm, are better suited for GPUs than more sophisticated schemes such as Bresenham’s algorithm, specifically in the context of sky-plothorizon computations. The trade-off between accuracy and performance is analyzed and providing guidance that depends on the targeted goal of the GNSS application.

GNSS↗

NASA NTRSDate not supplied

Implementation of a Six Degree of Freedom Precision Lunar Landing Algorithm Using Dual Quaternion Representation

In this study, a powered descent guidance algorithm using a unit dual quaternion represen- tation of the vehicle dynamics is implemented in a high-fidelity simulation and on representative flight hardware. This Dual-Quaternion Guidance (DQG) algorithm is applied to the precision lunar landing problem which levies complex constraints upon the trajectory, including state triggered attitude constraints to enable terrain-relative navigation and hazard detection as well as real-time requirements for landing site re-designation. The investigation explores DQG’s usefulness as a mission design tool as well as a real-time guidance algorithm and defines real-time performance requirements for the hazard detection and avoidance (HDA) re-targeting phase of precision lunar landing. The experiment is presented in two parts. First, DQG is implemented within a high-fidelity Monte Carlo simulation to tune the algorithm’s parameters for the simulated vehicle, to refine the mission design, and to develop guidance update timing requirements to perform the HDA maneuver. DQG generates trajectories online for the divert which are tracked by the vehicle’s inner-loop controllers to the targeted landing site. Second, DQG is run on representative hardware to demonstrate real-time operation through a divert maneuver. These results allow for rapid, flexible, optimal mission design satisfying complex constraints, and for the definition of real-time performance requirements for the HDA operations inherent in precision lunar landing. The HDA divert maneuver is found to require guidance trajectory updates in less than three seconds. DQG is found to be too slow to meet this update timing on the descent and landing computer (DLC) in its current implementation. DQG running on alternative hardware can meet the update rate requirement. Algorithm implementation improvements are also recommended which are expected to speed up computation sufficiently to meet requirements on the DLC.

GN&C↗

NASA NTRS2020

ICESat 2/ATLAS Onboard Flight Science Receiver Algorithms: Purpose, Process, and Performance

The Advanced Topographic Laser Altimetry System (ATLAS) is the sole instrument on the Ice, Cloud, and land Elevation Satellite 2 (ICESat-2). Without some method of reducing the transmitted data, the volume of ATLAS telemetry would far exceed the normal X-band downlink capability or require many more ground station contacts. The ATLAS Onboard Flight Science Receiver Algorithms (hereinafter Receiver Algorithms or Algorithms) control the amount of science data that is telemetered from the instrument, limiting the data volume by distinguishing surface echoes from background noise, and allowing the instrument to telemeter data from only a small vertical region about the signal. This is accomplished through the transfer of the spacecraft's location and attitude to the instrument every second, use of an onboard Digital Elevation Model, implementation of signal processing techniques, and use of onboard relief and surface type reference maps. Extensive ground testing verified the performance of the Algorithms. On-orbit analysis shows that the Algorithms are working as expected from the ground testing; they are performing well and meeting the mission requirements.

Algoritms, Signal Processing, Optimization, Flight↗

NASA NTRSDate not supplied

Self-consistent Quantum Iteratively Sparsified Hamiltonian Algorithm (SQuISH)

Due to coherence time limitations, reducing the resources required to run quantum algorithms and simulate physical systems on a quantum computer is crucial. With regards to Hamiltonian simulation, a significant effort has focused on building efficient algorithms using various factorizations and truncations, typically derived from the Hamiltonian alone. We introduce a new paradigm for improving Hamiltonian simulation and reducing the cost of ground state problems based on ideas recently developed for classical chemistry simulations. The key idea is that one can find efficient ways to reduce resources needed by quantum algorithms by making use of two key pieces of information: the Hamiltonian operator and an approximate ground state wavefunction. We refer to our algorithm as the self-consistent quantum iteratively sparsified Hamiltonian (SQuISH). By performing our scheme iteratively, one can drive SQuISH to create an accurate wavefunction using a truncated, resource-efficient Hamiltonian. By utilizing this more compact Hamiltonian, our algorithm provides an approach to reduce the gate complexity of ground state calculations on quantum hardware. As proof of principle, we implement SQuISH using configuration interaction for small molecules and coupled cluster for larger systems. Through our combination of approaches, we demonstrate how it performs on a range of systems, the largest of which would require more than 200 qubits to run on quantum hardware.

Diana Chamaki↗

NASA NTRS2023

High-Order Coronagraphic Wavefront Control With Algorithmic Differentiation: First Experimental Demonstration

Future space-based coronagraphs will rely critically on focal-plane wavefront sensing and control with deformable mirrors to reach deep contrast by mitigating optical aberrations in the primary beam path. Until now, most focal-plane wavefront control algorithms have been formulated in terms of Jacobian matrices, which encode the predicted effect of each deformable mirror actuator on the focal-plane electric field. A disadvantage of these methods is that Jacobian matrices can be cumbersome to compute and manipulate, particularly when the number of deformable mirror actuators is large. Recently, we proposed a new class of focal-plane wavefront control algorithms that utilize gradient-based optimization with algorithmic differentiation to compute wavefront control solutions while avoiding the explicit computation and manipulation of Jacobian matrices entirely. In simulations using a coronagraph design for the proposed Large UV/Optical/Infrared Surveyor (LUVOIR), we showed that our approach reduces overall CPU time and memory consumption compared to a Jacobian-based algorithm. Here, we expand on these results by implementing the proposed algorithm on the High Contrast Imager for Complex Aperture Telescopes (HiCAT) testbed at the Space Telescope Science Institute (STScI) and present initial experimental results, demonstrating contrast suppression capabilities equivalent to Jacobian-based methods.

wavefront control↗

NASA NTRSDate not supplied

Do Better Satellite Precipitation Algorithms Improve Landslide Hazard Assessment?

Satellites make it possible to estimate precipitation in near real time. Given the challenges of achieving global coverage by other means, these data are used widely. However, few systems for landslide hazard assessment rely on satellite precipitation estimates. This could be due in part to perceptions of accuracy, although latency, spatial resolution, and other factors may also be important. We test whether recent changes to data streams from the Global Precipitation Measurement mission (GPM) have improved its potential for use in landslide prediction. Specifically, we examine data produced by the Integrated Multi-satellitERetrievals for the GPM (IMERG) algorithm, which was upgraded to version 7 this year. IMERG relies upon other algorithms, including the Goddard Profiling Algorithm (GPROF) and the GPM Combined Radar-Radiometer Algorithm (CORRA). Many changes have been made during the switch from IMERG version 6 to version 7. These include upgrading CORRA and GPROF to version 7, to improve the accuracy of precipitation in frozen, mountainous, and coastal areas. The measured intensity of some storms has been enhanced with a new algorithm, the Scheme for Histogram Adjustment with Ranked Precipitation Estimates in the Neighborhood. Combined with many others, these changes to IMERG should improve its utility for landslide hazard assessment in a variety of contexts. To test this idea, we retrain the global Landslide Hazard Assessment for Situational Awareness (LHASA) model twice—first with data from IMERG version 6B and second with 7B. Since current daily rainfall is the most important variable in determining outcomes predicted by LHASA, it should reflect changes made to that input. First, we grid the landslides at a daily, thirty-arcsecond resolution. This serves as the response variable. At each of these sites current and antecedent rainfall are extracted, along with antecedent snow mass and soil moisture, slope, and PGA. In addition, one million grid cells are selected at random points to represent conditions under which landslides (probably) do not occur. After merging these data, we hold back 20% of the dataset for validation purposes and train a machine-learning model with the rest. We assess both the model’s overall ability to identify landslides and its ability to predict specific large landslide disasters.

Thomas A Stanley↗

NASA NTRS2024

A Computationally Efficient Algorithm for Sampling the Rudd Differential Cross Section

Monte Carlo radiation transport codes such as RITRACKS or Geant4 are used to simulate the interaction of ions with matter. These codes rely on sampling algorithms to determine interactions and various physical properties of particles involved in the simulations. It is crucial to develop efficient sampling algorithms since Monte Carlo radiation transport simulations can be time consuming. This work presents an efficient sampling algorithm to determine the energy of secondary electrons following ion-water interactions. The applicability and intended use of the algorithm are discussed in detail, and it is shown that the new algorithm is up to 6X10 4 times faster than the method currently used in Geant4-DNA.

Floriane Poignant↗

DOE OSTI2024

An Accelerated Clip Algorithm for Unstructured Meshes: A Batch-Driven Approach

The clip technique is a popular method for visualizing complex structures and phenomena within 3D unstructured meshes. Meshes can be clipped by specifying a scalar isovalue to produce an output unstructured mesh with its external surface as the isovalue. Similar to isocontouring, the clipping process relies on scalar data associated with the mesh points, including scalar data generated by implicit functions such as planes, boxes, and spheres, which facilitates the visualization of results interior to the grid. In this paper, we introduce a novel batch-driven parallel algorithm based on a sequential clip algorithm designed for high-quality results in partial volume extraction. Our algorithm comprises five passes, each progressively processing data to generate the resulting clipped unstructured mesh. The novelty lies in the use of fixed-size batches of points and cells, which enable rapid workload trimming and parallel processing, leading to a significantly improved memory footprint and run-time performance compared to the original version. On a 32-core CPU, the proposed batch-driven parallel algorithm demonstrates a run-time speed-up of up to 32.6x and a memory footprint reduction of up to 4.37x compared to the existing sequential algorithm. The software is currently available under an open-source license in the VTK visualization system.

Tsalikis, Spiros↗

DOE OSTI2025

Randomized Adiabatic Quantum Linear Solver Algorithm with Optimal Complexity Scaling and Detailed Running Costs

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number 𝜅 of the linear system and the target error 𝜖. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling 𝑂⁡(𝜅⁢log (1/𝜖))—an exponential improvement in 𝜖, and a shaving of a log 𝜅 scaling factor in 𝜅. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is 837⁢𝜅 at 𝜖 = 10 −10 for Hermitian matrices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms

Non-thermal advanced fuel fusion trades the requirement of a large amount of recirculating tritium in the system for that of large recirculating power. Phase space engineering technologies utilizing externally injected electromagnetic fields can be applied to meet the challenge of maintaining non-thermal particle distributions at a reasonable cost. The physical processes of the phase space engineering are studied from a theoretical and algorithmic perspective. It is emphasized that the operational space of phase space engineering is limited by the underpinning symplectic dynamics of charged particles. The phase space incompressibility according to the Liouville theorem is just one of many constraints, and Gromov's non-squeezing theorem determines the minimum footprint of the charged particles on every conjugate phase space plane. In this sense and level of sophistication, the mathematical abstraction of phase space engineering is symplectic topology. To simulate the processes of phase space engineering, such as the Maxwell demon and electromagnetic energy extraction, and to accurately calculate the minimum footprints of charged particles, recently developed structure-preserving geometric algorithms can be used. The family of algorithms conserves exactly, on discretized spacetime, symplecticity and thus incompressibility, non-squeezability, and symplectic capacities. The algorithms apply to the dynamics of charged particles under the influence of external electromagnetic fields as well as the charged particle–electromagnetic field system governed by the Vlasov–Maxwell equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Feedback-based quantum algorithm inspired by counterdiabatic driving

In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗

DOE OSTI2024

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗

DOE OSTI2026

Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping

We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $η$ particles and $N$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O(η^2\sqrt{N})$ $T$-gates, outperforming alternative algorithms when $η ≲ \sqrt{N}$. To achieve such scaling, we require $O(\sqrt{N})$ dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford $+T$ gates and study the impact of noise on the prepared state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1991

An algorithm for converting a virtual-bond chain into a complete polypeptide backbone chain

A systematic analysis is presented of the algorithm for converting a virtual-bond chain, defined by the coordinates of the alpha-carbons of a given protein, into a complete polypeptide backbone. An alternative algorithm, based upon the same set of geometric parameters used in the Purisima-Scheraga algorithm but with a different "linkage map" of the algorithmic procedures, is proposed. The global virtual-bond chain geometric constraints are more easily separable from the loal peptide geometric and energetic constraints derived from, for example, the Ramachandran criterion, within the framework of this approach.

NASA Discipline Exobiology↗