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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Ultrafast radiographic imaging and tracking: An overview of instruments, methods, data, and applications

Ultrafast radiographic imaging and tracking (U-RadIT) use state-of-the-art ionizing particle and light sources to experimentally study sub-nanosecond transients or dynamic processes in physics, chemistry, biology, geology, materials science and other fields. These processes are fundamental to modern technologies and applications, such as nuclear fusion energy, advanced manufacturing, communication, and green transportation, which often involve one mole or more atoms and elementary particles, and thus are challenging to compute by using the first principles of quantum physics or other forward models. One of the central problems in U-RadIT is to optimize information yield through, e.g. high-luminosity X-ray and particle sources, efficient imaging and tracking detectors, novel methods to collect data, and large-bandwidth online and offline data processing, regulated by the underlying physics, statistics, and computing power. We review and highlight recent progress in: (a.) Detectors such as high-speed complementary metal-oxide semiconductor (CMOS) cameras, hybrid pixelated array detectors integrated with Timepix4 and other application-specific integrated circuits (ASICs), and digital photon detectors; (b.) U-RadIT modalities such as dynamic phase contrast imaging, dynamic diffractive imaging, and four-dimensional (4D) particle tracking; (c.) U-RadIT data and algorithms such as neural networks and machine learning, and (d.) Applications in ultrafast dynamic material science using XFELs, synchrotrons and laser-driven sources. Hardware-centric approaches to U-RadIT optimization are constrained by detector material properties, low signal-to-noise ratio, high cost and long development cycles of critical hardware components such as ASICs. Interpretation of experimental data, including comparisons with forward models, is frequently hindered by sparse measurements, model and measurement uncertainties, and noise. Alternatively, U-RadIT make increasing use of data science and machine learning algorithms, including experimental implementations of compressed sensing. Machine learning and artificial intelligence approaches, refined by physics and materials information, may also contribute significantly to data interpretation, uncertainty quantification and U-RadIT optimization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Optimal sensor placement for reconstructing wind pressure field around buildings using compressed sensing

Deciding how to optimally deploy sensors in a large, complex, and spatially extended structure is critical to ensure that the surface pressure field is accurately captured for subsequent analysis and design. In some cases, reconstruction of missing data is required in downstream tasks such as the development of digital twins. Here, this paper presents a data-driven sparse sensor selection algorithm, aiming to provide the most information contents for reconstructing aerodynamic characteristics of wind pressures over tall building structures parsimoniously. The algorithm first fits a set of basis functions to the training data, then applies a computationally efficient QR algorithm that ranks existing pressure sensors in order of importance based on the state reconstruction to this tailored basis. The findings of this study show that the proposed algorithm successfully re- constructs the aerodynamic characteristics of tall buildings from sparse measurement locations, generating stable and optimal solutions across a range of conditions. As a result, this study serves as a promising first step toward leveraging the success of data-driven and machine learning algorithms to supplement traditional genetic algorithms currently used in wind engineering.

42 ENGINEERING↗
DOE OSTI2024

Using automated machine learning for the upscaling of gross primary productivity

Estimating gross primary productivity (GPP) over space and time is fundamental for understanding the response of the terrestrial biosphere to climate change. Eddy covariance flux towers provide in situ estimates of GPP at the ecosystem scale, but their sparse geographical distribution limits larger-scale inference. Machine learning (ML) techniques have been used to address this problem by extrapolating local GPP measurements over space using satellite remote sensing data. However, the accuracy of the regression model can be affected by uncertainties introduced by model selection, parameterization, and choice of explanatory features, among others. Recent advances in automated ML (AutoML) provide a novel automated way to select and synthesize different ML models. In this work, we explore the potential of AutoML by training three major AutoML frameworks on eddy covariance measurements of GPP at 243 globally distributed sites. We compared their ability to predict GPP and its spatial and temporal variability based on different sets of remote sensing explanatory variables. Explanatory variables from only Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance data and photosynthetically active radiation explained over 70 % of the monthly variability in GPP, while satellite-derived proxies for canopy structure, photosynthetic activity, environmental stressors, and meteorological variables from reanalysis (ERA5-Land) further improved the frameworks' predictive ability. We found that the AutoML framework Auto-sklearn consistently outperformed other AutoML frameworks as well as a classical random forest regressor in predicting GPP but with small performance differences, reaching an r 2 of up to 0.75. We deployed the best-performing framework to generate global wall-to-wall maps highlighting GPP patterns in good agreement with satellite-derived reference data. This research benchmarks the application of AutoML in GPP estimation and assesses its potential and limitations in quantifying global photosynthetic activity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A deep learning hybrid predictive modeling (HPM) approach for estimating evapotranspiration and ecosystem respiration

Climate change is reshaping vulnerable ecosystems, leading to uncertain effects on ecosystem dynamics, including evapotranspiration (ET) and ecosystem respiration (R eco ). However, accurate estimation of ET and R eco still remains challenging at sparsely monitored watersheds, where data and field instrumentation are limited. In this study, we developed a hybrid predictive modeling approach (HPM) that integrates eddy covariance measurements, physically based model simulation results, meteorological forcings, and remote-sensing datasets to estimate ET and R eco in high space–time resolution. HPM relies on a deep learning algorithm and long short-term memory (LSTM) and requires only air temperature, precipitation, radiation, normalized difference vegetation index (NDVI), and soil temperature (when available) as input variables. We tested and validated HPM estimation results in different climate regions and developed four use cases to demonstrate the applicability and variability of HPM at various FLUXNET sites and Rocky Mountain SNOTEL sites in Western North America. To test the limitations and performance of the HPM approach in mountainous watersheds, an expanded use case focused on the East River Watershed, Colorado, USA. The results indicate HPM is capable of identifying complicated interactions among meteorological forcings, ET, and R eco variables, as well as providing reliable estimation of ET and R eco across relevant spatiotemporal scales, even in challenging mountainous systems. The study documents that HPM increases our capability to estimate ET and R eco and enhances process understanding at sparsely monitored watersheds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Probing eddy size and its effective mixing length in stably stratified roughness sublayer flows

Stably stratified roughness sublayer flows are ubiquitous yet remain difficult to represent in models and to interpret using field experiments. Here, continuous high-frequency potential temperature profiles from the forest floor up to 6.5 times the canopy height observed with distributed temperature sensing (DTS) are used to link eddy topology to roughness sublayer stability correction functions and coupling between air layers within and above the canopy. The experiments are conducted at two forest stands classified as hydrodynamically sparse and dense. Near-continuous profiles of eddy sizes (length scales) and effective mixing lengths for heat are derived from the observed profiles using a novel conditional sampling approach. The approach utilizes potential temperature isoline fluctuations from a statically stable background state. The transport of potential temperature by an observed eddy is assumed to be conserved (adiabatic movement) and we assume that irreversible heat exchange between the eddy and the surrounding background occurs along the (vertical) periphery of the eddy. This assumption is analogous to Prandtl's mixing-length concept, where momentum is transported rapidly vertically and then equilibrated with the local mean velocity gradient. A distinct dependence of the derived length scales on background stratification, height above ground, and canopy characteristics emerges from the observed profiles. Implications of these findings for (1) the failure of Monin–Obukhov similarity in the roughness sublayer and (2) above-canopy flow coupling to the forest floor are examined. The findings have practical applications in terms of analysing similar DTS data sets with the proposed approach, modelling roughness sublayer flows, and interpreting nocturnal eddy covariance measurements above tall forested canopies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Evaluation of Graph Analytics Frameworks Using the GAP Benchmark Suite

The analysis of connected data is an increasingly important application in high-performance computing. Such analyses can reveal fraudulent patterns in financial transactions, optimize telecommunications networks, predict information flow in social networks, etc. However, the landscape of graph analytics is highly diverse. Graph algorithms stress processor architectures differently, and no one graph can represent all topologies. Consequently, no single approach or framework is expected to be optimal for all graph analytics problems. To help make sense of this diverse landscape, we evaluated four approaches to graph analytics: GraphBLAS, Galois, BGL17, GraphIt; and compare them against hand-tuned implementations that take advantage of hardware features on our test platform. Graph- BLAS formulates graph analytics as sparse linear algebra. Galois provides syntactic constructs for data parallelism over irregular data structures. BGL17 is a generic C++ template library for implementing graph algorithms. GraphIt provides a domain- specific language to describe and optimize graph algorithms. We use the GAP Benchmark Suite to establish baseline performance and guide the side-by-side evaluation of each framework. GAP consists of 30 tests: six graph analytics algorithms (breadth- first search, single-source shortest path, PageRank, betweenness centrality, connected components, and triangle counting) run on five graphs, each with different topological characteristics (e.g., high diameter, skewed degree distribution, high average degree). High-performance reference implementations are included for each benchmark algorithm. Because a graph can be loaded into memory a number of ways (e.g., flat file on disk, compressed sparse format, data frames, retrieved from SQL or NoSQL databases), our evaluation focused on computational performance rather than I/O. Our results show the relative strengths of each framework.

Graph algorithms, Benchmarking, shared-memory prog↗
DOE OSTI2022

Dynamic signal recovery in distribution grids using compressive lossy measurements

Distribution system state estimation requires reliable aggregation of the measured data. However, the large volume of the measured data imposes a significant stress on the underlying communication infrastructure. With the challenges associated with measurement availability, current distribution systems are typically unobservable. To cope with the unobservability issue, compressive sensing theory allows us to recover system state information from a small number of measurements provided the states of the distribution system exhibit sparsity. In this paper, we evaluate the robustness of an updated Kalman filtered modified compressive sensing (KF-ModCS) technique that dynamically estimates the grid states using a small fraction of measured data. In practice, measurements used for sparsity based state estimation may also be intermittent due to communication network induced losses. Further, to understand the effect of packet losses on KF-ModCS, we provide an upper bound for the expected variances of the state estimation error for a given rate of information loss. This upper bound is further improved if the support set of the sparse signal that characterizes the state dynamics does not change over time and/or the reduced model is observable. Simulations based on two practical data sets collected from actual customers in a distribution grid validate the theoretical results.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Assessing the limitations of commercial sensors and models for supporting marine carbon dioxide removal monitoring: a case study

Several unknowns remain surrounding marine Carbon Dioxide Removal (mCDR) monitoring, reporting, and verification (MRV) practices and capabilities. Current in-situ sensor technology is limited (primarily pH and pCO 2 ), requiring calculations and assumptions to estimate changes in carbonate chemistry parameters, including total alkalinity (TA). Considering that cost, energy consumption, and accuracy of commercial sensors can vary by orders of magnitude, understanding how well existing sensors perform in an mCDR context is important for this emerging community. Likewise, documenting sensor limitations and how relatively simple models can optimize sensor deployments will improve MRV efforts and support protocol development. Here we (1) compare performance a variety of commercially available sensors in a blind mesocosm experiment simulating ocean alkalinity enhancement (OAE), and how sensor performance impacted carbonate chemistry estimates; (2) evaluate if sensors can distinguish the OAE signal from natural variability during a small scale OAE field test in Sequim Bay, WA, USA, and (3) use an idealized ocean biogeochemistry model to explore optimal sensor network design based on (1) and (2). Our mesocosm results indicate that correctly constraining pH uncertainty will be critical for accurate TA estimates with current sensor technology compared to the less impactful variation caused by uncertainty in pCO 2 (pH data that are presented throughout are reported on the total scale (pH T ) unless otherwise noted). Our pilot field test demonstrated that sensors were capable of distinguishing mCDR signatures from natural variability under optimal real-world conditions. Idealized modeling simulations of the field test showed that a range of sparse and dense (3 to 100) sensors sampling areas of detectable increases will underestimate the net change in surface pH by at least 35–55%, at both realistic and highly elevated alkalinity input levels. We also highlight the limitations of current sensing technology for MRV, and the importance of ocean biogeochemistry models as critical tools for predicting when and where mCDR signals will be detectable using available sensors. Overall, our findings suggest that commercially available pCO 2 sensors and some pH sensors will form an important backbone for mCDR MRV tasks, though complete MRV characterization will require these data to be used in combination with other tools.

OAE↗
DOE OSTI2026

Data for A Hybrid Biophysical-Machine Learning Framework for Diurnal Surface Energy Flux Estimation Using Proximal Sensing

Thermal infrared-based remote sensing of surface energy fluxes has traditionally relied on high spatial resolution satellite data with revisit frequencies on the order of weeks. In this study, we evaluate a biophysics-based analytical surface energy balance model for predicting latent energy (LE) and sensible heat (H) fluxes using proximal sensing observations. The Surface Temperature Initiated Closure (STIC1.2) model has been extensively validated across a wide range of spatial and temporal scales using various satellite-derived thermal infrared data sets. Here we extend this validation by applying STIC at sub-hourly temporal resolution over multiple growing seasons for four distinct agricultural systems. We further develop and evaluate novel STIC variants that incorporate machine learning (ML) techniques to eliminate the need for surface energy balance observations, specifically net radiation and soil heat flux, thereby enhancing model applicability in data-sparse settings. The integration of a ML component to estimate surface available energy is shown to have strong predictive performance for both LE (R2 = 0.81–0.94) and H (R2 = 0.46–0.72) across all agricultural systems examined here, demonstrating the potential of hybrid biophysical-machine learning approaches for surface energy balance modeling with minimal data requirements. This study concludes with a novel application of explainable machine learning (exML) to diagnose sources of model error. This exML framework attributes residual prediction errors to both model input variables and environmental drivers not explicitly included in the simulation experiments. This approach provides a new pathway for improving model design and integrating previously overlooked yet influential variables into future model iterations.

AI/ML↗
DOE OSTI2023

MetaFlux: Meta-learning global carbon fluxes from sparse spatiotemporal observations

We provide a global, long-term carbon flux dataset of gross primary production and ecosystem respiration generated using meta-learning, called MetaFlux. The idea behind meta-learning stems from the need to learn efficiently given sparse data by learning how to learn broad features across tasks to better infer other poorly sampled ones. Using meta-trained ensemble of deep models, we generate global carbon products on daily and monthly timescales at a 0.25-degree spatial resolution from 2001 to 2021, through a combination of reanalysis and remote-sensing products. Site-level validation finds that MetaFlux ensembles have lower validation error by 5–7% compared to their non-meta-trained counterparts. In addition, they are more robust to extreme observations, with 4–24% lower errors. We also checked for seasonality, interannual variability, and correlation to solar-induced fluorescence of the upscaled product and found that MetaFlux outperformed other machine-learning based carbon product, especially in the tropics and semi-arids by 10–40%. Overall, MetaFlux can be used to study a wide range of biogeochemical processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Assimilation of citizen science data in snowpack modeling using a new snow data set: Community Snow Observations

A physically based snowpack evolution and redistribution model was used to test the effectiveness of assimilating crowd-sourced snow depth measurements collected by citizen scientists. The Community Snow Observations project gathers, stores, and distributes measurements of snow depth recorded by recreational users and snow professionals in high mountain environments. These citizen science measurements are valuable since they come from terrain that is relatively undersampled and can offer in situ snow information in locations where snow information is sparse or nonexistent. The present study investigates (1) the improvements to model performance when citizen science measurements are assimilated, and (2) the number of measurements necessary to obtain those improvements. Model performance is assessed by comparing time series of observed (snow pillow) and modeled snow water equivalent values, by comparing spatially distributed maps of observed (remotely sensed) and modeled snow depth, and by comparing fieldwork results from within the study area. The results demonstrate that few citizen science measurements are needed to obtain improvements in model performance, and these improvements are found in 62 % to 78 % of the ensemble simulations, depending on the model year. Model estimations of total water volume from a subregion of the study area also demonstrate improvements in accuracy after CSO measurements have been assimilated. These results suggest that even modest measurement efforts by citizen scientists have the potential to improve efforts to model snowpack processes in high mountain environments, with implications for water resource management and process-based snow modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

The Value of Information From Horizontal Distributed Acoustic Sensing Compared to Multicomponent Geophones Via Machine Learning

Abstract Faults play an important role in recharging many geothermal reservoirs, and seismic information can image the locations of these faults. The value of information (VOI) metric is used to objectively quantify and compare the value of two types of seismic receiver data via a machine learning approach. The demonstrated VOI methodology is novel by including spatial models from seismic data and obtaining the information statistics from machine learning. Our two-dimensional numerical experiments compare images created from sparsely spaced (80 m), two-component geophone sampling to high spatial resolution (1 m), single-component DAS. We used a three-fold cross validation of a U-Net convolutional neural networks to achieve average classification statistics. The results suggest that when horizontal sources are utilized, geophones and DAS identify reflectors and non-reflectors at roughly the same rate. The average F1 score for horizontal DAS is 0.939 and 0.931 for geophones. For images created from a vertical source, DAS performed marginally better (F1 = 0.919) than geophones (F1 = 0.877). Our transferrable methodology can provide guidance on which acquisition scenarios can improve images of important structures in the subsurface and present an efficient method for obtaining reliability statistics from high-dimensional, spatial data.

Energy & Fuels↗
DOE OSTI2024

Minimization of Measurement Uncertainty in Optical Frequency Domain Reflectometry

Optical frequency domain reflectometry (OFDR) is a technique for interrogating optical fiber sensors to generate relative, quasi-distributed measurements. Although Optical frequency domain reflectometry (OFDR) is increasingly being adopted for aerospace, energy production, and structural monitoring applications, the quantification of uncertainty for OFDR measurements has not been developed beyond sparse empirical relationships. To address this knowledge gap, an uncertainty metric for OFDR measurements was developed. This uncertainty metric was applied to weight the edges between OFDR measurements on directed correlation graphs and analyzed to minimize the cumulative uncertainty. In conclusion, this work is the first to propose an uncertainty metric for OFDR and provides a generalized mathematical framework for optimizing OFDR hardware selection, optical fiber sensor selection, and postprocessing strategy.

42 ENGINEERING↗
DOE OSTI2026

A Hybrid Biophysical‐Machine Learning Framework for Diurnal Surface Energy Flux Estimation Using Proximal Sensing

Thermal infrared-based remote sensing of surface energy fluxes has traditionally relied on high spatial resolution satellite data with revisit frequencies on the order of weeks. In this study, we evaluate a biophysics-based analytical surface energy balance model for predicting latent energy ( LE ) and sensible heat ( H ) fluxes using proximal sensing observations. The Surface Temperature Initiated Closure (STIC1.2) model has been extensively validated across a wide range of spatial and temporal scales using various satellite-derived thermal infrared data sets. Here we extend this validation by applying STIC at sub-hourly temporal resolution over multiple growing seasons for four distinct agricultural systems. We further develop and evaluate novel STIC variants that incorporate machine learning (ML) techniques to eliminate the need for surface energy balance observations, specifically net radiation and soil heat flux, thereby enhancing model applicability in data-sparse settings. The integration of a ML component to estimate surface available energy is shown to have strong predictive performance for both LE (R 2 = 0.81–0.94) and H (R 2 = 0.46–0.72) across all agricultural systems examined here, demonstrating the potential of hybrid biophysical-machine learning approaches for surface energy balance modeling with minimal data requirements. This study concludes with a novel application of explainable machine learning (exML) to diagnose sources of model error. This exML framework attributes residual prediction errors to both model input variables and environmental drivers not explicitly included in the simulation experiments. This approach provides a new pathway for improving model design and integrating previously overlooked yet influential variables into future model iterations.

evapotranspiration↗
DOE OSTI2025

Automatic Image Point Matching

Sparse Image Point Matching (SIPM) is a foundational technology for photo triangulation, structure from motion (SfM), Simultaneous Location and Mapping (SLAM), and data fusion. The goal of the matching is to automatically generate sets of image coordinates that identify the same feature across images. Ideally, the process should be robust to lighting, scale, perspective, and modality changes. The scope of the image matching topic in the field of remote sensing (RS) is enormous because of the variety of collection platforms, modalities, sensor types, applications, and subjects. In this work, we report the history of and assess the state of the art of visible-spectrum (panchromatic and color) image matching of the Earth’s surface. Work specific to large-format images (LFI) (e.g., metric aerial cameras and Earth-observing satellites) will be highlighted. However, the state of the art in this century will mostly be traced through machine vision research and benchmarks because research specific to LFI is rare.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

High-throughput spin-bath characterization of spin defects in semiconductors

Detailed knowledge of the local environments of spin defects in semiconductors, such as nitrogenvacancy (NV) centers in diamond or divacancies in silicon carbide, is crucial for optimizing control and entanglement protocols in quantum sensing and information applications. However, at present a direct experimental characterization of individual defect environments is not scalable, as conventional spin-bath measurements are time consuming and difficult to automate. Achieving high-throughput characterization requires short experiments to probe the spin bath. However, with fewer and noisier measurements, the inverse problem of recovering spin-bath properties from measured data becomes ill posed, with multiple spin baths having a high likelihood of yielding the same data. In this work, we present a set of computational tools to resolve the ill-posed inverse problem of recovering the atomic positions and hyperfine couplings of random nuclei surrounding spin defects from sparse, noisy experimental coherence data, which can be obtained in hours. Here, we use a trans-dimensional Bayesian approach that incorporates ab initio data to yield full posterior distributions over nuclear spin environments, enabling robust recovery from limited data. We also provide practical tools and guidelines to determine the limits of detectability for hyperfine couplings under specific dynamical decoupling sequences and sampling conditions. In addition, we demonstrate how the tools developed here, in combination with ab initio simulations of spin baths, can guide the design of efficient experimental protocols for application-specific high-throughput screening. To showcase the utility of our approach, we apply it to design fast dynamical decoupling experiments to characterize the spin baths often individual NV centers in diamond. While the primary focus is on accelerating spin-bath characterization of spin defects, this Bayesian approach also lays the foundation for digital-twin studies of spin defects, where a virtual model of the spin-defect system evolves in real time with ongoing experimental measurements. Together, the set of tools we designed and applied paves the way for scalable deployment of spin defects in semiconductors for quantum sensing and information applications.

Bayesian methods↗
DOE OSTI2026

Data for: A hybrid biophysical-machine learning framework for diurnal surface energy flux estimation using proximal sensing

Thermal-based remote sensing of surface energy fluxes has traditionally relied on high spatial resolution satellite data with revisit frequencies on the order of weeks. In this study, we evaluate a biophysics-based analytical surface energy balance model for predicting latent energy (LE) and sensible heat (H) fluxes using proximal sensing observations. The Surface Temperature Initiated Closure (STIC1.2) model has been extensively validated across a wide range of spatial and temporal scales using various satellite-derived thermal datasets. Here we extend this validation by applying STIC at sub-hourly temporal resolution over multiple growing seasons for four distinct agricultural systems. We further develop and evaluate novel STIC variants that incorporate machine learning (ML) techniques to eliminate the need for specific surface energy balance observations, specifically net radiation and soil heat flux, thereby enhancing model applicability in data-sparse settings. The integration of an ML component to estimate surface available energy is shown to have strong predictive performance for both LE (R2 = 0.81-0.94) and H (R2 = 0.46-0.72) across all agricultural systems examined here, demonstrating the potential of hybrid biophysical – machine learning approaches for surface energy balance modeling with minimal data requirements. This study concludes with a novel application of explainable machine learning (exML) to diagnose sources of model error. This exML framework attributes residual prediction errors to both model input variables and environmental drivers not explicitly included in the simulation experiments. This approach provides a new pathway for improving model design and integrating previously overlooked yet influential variables into future model iterations.

Agricultural Sciences↗
DOE OSTI2025

Ansatz-Free Hamiltonian Learning with Heisenberg-Limited Scaling

Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.

machine learning↗