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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Machine learned potential for high-throughput phonon calculations of metal—organic frameworks

Metal–organic frameworks (MOFs) are highly porous and versatile materials studied extensively for applications such as carbon capture and water harvesting. However, computing phonon-mediated properties in MOFs, like thermal expansion and mechanical stability, remains challenging due to the large number of atoms per unit cell, making traditional Density Functional Theory (DFT) methods impractical for high-throughput screening. Recent advances in machine learning potentials have led to foundation atomistic models, such as MACE-MP-0, that accurately predict equilibrium structures but struggle with phonon properties of MOFs. In this work, we developed a workflow for computing phonons in MOFs within the quasi-harmonic approximation with a fine-tuned MACE model, MACE-MP-MOF0. The model was trained on a curated dataset of 127 representative and diverse MOFs. The fine-tuned MACE-MP-MOF0 improves the accuracy of phonon density of states and corrects the imaginary phonon modes of MACE-MP-0, enabling high-throughput phonon calculations with state-of-the-art precision. The model successfully predicts thermal expansion and bulk moduli in agreement with DFT and experimental data for several well-known MOFs. These results highlight the potential of MACE-MP-MOF0 in guiding MOF design for applications in energy storage and thermoelectrics.

Elena, Alin Marin↗
DOE OSTI2026

ZENN: A thermodynamics-inspired computational framework for heterogeneous data–driven modeling

Traditional entropy-based methods—such as cross-entropy loss in classification problems—have long been essential tools for representing the information uncertainty and physical disorder in data and for developing artificial intelligence algorithms. However, the rapid growth of data across various domains has introduced new challenges, particularly the integration of heterogeneous datasets with intrinsic disparities. To address this, we introduce a zentropy-enhanced neural network (ZENN), extending zentropy theory into the data science domain via intrinsic entropy, enabling more effective learning from heterogeneous data sources. ZENN simultaneously learns both energy and intrinsic entropy components, capturing the underlying structure of multisource data. To support this, we redesign the neural network architecture to better reflect the intrinsic properties and variability inherent in diverse datasets. We demonstrate the effectiveness of ZENN on classification tasks and energy landscape reconstructions, showing its superior generalization capabilities and robustness-particularly in predicting high-order derivatives. In image and text classification tasks, ZENN demonstrates superior generalization by introducing a learnable temperature variable that models latent multisource heterogeneity, allowing it to surpass state-of-the-art models on CIFAR-10/100, BBC News, and AG News. As a practical application in materials science, we employ ZENN to reconstruct the Helmholtz energy landscape of Fe3Pt using data generated from density functional theory and capture key material behaviors, including negative thermal expansion and the critical point in the temperature–pressure space. Overall, this work presents a zentropy-grounded framework for data-driven machine learning, positioning ZENN as a versatile and robust approach for scientific problems involving complex, heterogeneous datasets.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Novel ceramic capacitors with ultrahigh energy density and efficiency (Final Technical Report)

Antiferroelectric ceramics are a special class of material that have shown great potential as the dielectric in electrical capacitors due to their high energy- and power-density. During each charge-discharge cycle, the ceramic undergoes transformation to a ferroelectric phase and resumes its antiferroelectric phase. The hysteresis associated with the transitions leads to a mediocre energy efficiency and service lifetime of antiferroelectric capacitors and, hence, their almost absence in commercial products. Under the support of this research project, we first formulated a universal lattice-compatibility theory that included electrostatic polarization energy along with elastic energy and thermal energy to understand the origin of the hysteresis in antiferroelectric oxides. Guided by this compatibility theory, we conducted high-throughput density functional theory (DFT) calculations to assess chemical modifiers and their effect on crystal structures of 400+ PbZrO 3 -based compositions. Down-selected compositions were experimentally validated for their suppressed hysteresis and higher energy efficiency. The verified low-hysteresis compositions were then expanded to an antiferroelectric ceramic library with nearly 500 new compositions (more than 1,500 samples) using high-throughput experiments involving ceramic synthesis and property screening. The large quantity of data generated (theory and experimental) in these tasks were processed by machine-learning techniques and identified trends were fed to the next iteration. In the end, we successfully discovered four compositions with near-zero hysteresis, yielding a world-record energy efficiency of 98.2% at an energy density of 3.0 J/cm 3 . Furthermore, our antiferroelectric ceramic capacitor reaches 79.5 million charge-discharge cycles lifetime, a factor of 80 enhancement over previous antiferroelectric ceramics with large hysteresis. These research accomplishments have not only met the milestones set in the SOPO, but also led to two patent filings, three journal publications (one of them was in Advanced Materials, impact factor 29.4), and nine oral presentations at various venues. Through the course of the project, three postdocs, four Ph.D. students, and one M.S. student were trained. In short, our project established a new methodology in searching next-generation functional ceramics on the fundamental side and discovered several high-efficiency antiferroelectric compositions for capacitors on the applied side. Once fabricated into the multilayer form for commercial applications, these ceramic capacitors can potentially enable the high temperature high power density DC-link capacitors that are critical for the next generation inverters in electric vehicles. The project also significantly contributed to the nation’s workforce development in the STEM fields.

36 MATERIALS SCIENCE↗
DOE OSTI2025

First-Principles Assessment of ZnTe and CdSe as Prospective Tunnel Barriers at the InAs/Al Interface

Majorana zero modes are predicted to emerge in semiconductor/ superconductor interfaces, such as InAs/Al. Majorana modes could be utilized for fault tolerant topological qubits. However, their realization is hindered by materials challenges. The coupling between the superconductor and the semiconductor may be too strong for Majorana modes to emerge, due to effective doping of the semiconductor by the metallic contact. This could be mediated by adding a tunnel barrier of controlled thickness. We use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO), to assess ZnTe and CdSe as prospective tunnel barriers for the InAs/Al interface. The results of DFT +U(BO) for ZnTe are validated by comparison to angle resolved photoemission spectroscopy (ARPES). We then study bilayer interfaces of the three semiconductors with each other and with Al, as well as trilayer interfaces with a varying number of ZnTe or CdSe layers inserted between InAs and Al. We find that 16 atomic layers of either material completely insulate the InAs from metal induced gap states (MIGS). However, ZnTe and CdSe differ significantly in their band alignment, such that ZnTe forms an effective barrier for electrons, whereas CdSe forms a barrier for holes. Because of Fermi level pinning in the conduction band at the interface, only electron transport is relevant for InAs-based Majorana devices. Therefore, ZnTe is the better choice. Based on the results of our simulations, we suggest conducting experiments with ZnTe barriers in the thickness range of 6–18 atomic layers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Quantum computing universal thermalization dynamics in a (2 + 1)D Lattice Gauge Theory

Simulating non-equilibrium phenomena in strongly-interacting quantum many-body systems, including thermalization, is a promising application of near-term and future quantum computation. By performing experiments on a digital quantum computer consisting of fully-connected optically-controlled trapped ions, we study the role of entanglement in the thermalization dynamics of a Z 2 lattice gauge theory in 2+1 spacetime dimensions. Using randomized-measurement protocols, we efficiently learn a classical approximation of non-equilibrium states that yields the gap-ratio distribution and the spectral form factor of the entanglement Hamiltonian. These observables exhibit universal early-time signals for quantum chaos, a prerequisite for thermalization. Our work, therefore, establishes quantum computers as robust tools for studying universal features of thermalization in complex many-body systems, including in gauge theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Developing reliable machine learning interatomic potential for Fe–Cr–Ni austenitic alloys

Gaining atomistic understanding of mechanical behavior of heat-resistant structural materials such as Fe–Cr–Ni-based alloys requires an approach with an accuracy close to density functional theory (DFT) that considers the intrinsic properties of the bulk lattice and important defects such as stacking faults, grain boundaries, and surfaces. This work aims to develop reliable machine learning interatomic potential (MLIAP) at cross-scale for Fe–Cr–Ni ternary alloys with a focus on the face-centered-cubic (fcc) solid solution structure. Leveraging the advantages of moment tensor potentials, which typically necessitate a relatively small training dataset and enable rapid calculations using the large-scale atomic/molecular massively parallel simulator package, we ensure the stability and accuracy of the trained potentials. Important defects such as stacking faults, grain boundaries, and surfaces for wide-range compositions are investigated. Structural, thermal, elastic, and defect properties are determined from molecular dynamics simulations comprising several thousand atoms, generated via canonical Monte Carlo simulations guided by the trained potential. The trained potential allows efficient atomic simulations of structural, thermal, and mechanical properties of fcc Fe–Cr–Ni solid solution alloys as a function of composition and temperature. Therefore, the MLIAP approach represents a major advancement from DFT calculations that are limited to small simulation sizes and traditional molecular dynamics simulations using relatively low accuracy potentials. Furthermore, this work outlines a practical foundation for further investigating the structural evolution and mechanical behavior of austenitic stainless steel and nickel-based alloys in a wide array of applications in extreme environments.

Crystal structure↗
DOE OSTI2026

Mass of 101 Sn and Bayesian extrapolations to the proton drip line

The favorable energy configurations of nuclei at magic numbers of 𝑁 neutrons and 𝑍 protons are fundamental for understanding the evolution of nuclear structure. The 𝑍 = 50 (tin) isotopic chain is a frontier for such studies, with particular interest at and around the doubly magic 100 Sn isotope, for which the mass is a topic of debate. Precise mass values for neutron-deficient isotopes provide necessary anchor points for mass models to test extrapolations near the proton drip line, where experimental studies remain out of reach. In this work, we report a Penning trap mass measurement of 101 Sn . The determined mass excess of −59889.89⁢(96) keV for 101 Sn represents a factor-of-300 improvement over the current precision and indicates that 101 Sn is less bound than previously thought. Mass predictions from a recently developed Bayesian model combination framework employing statistical machine learning and nuclear masses computed within seven global models based on nuclear density functional theory agree within 1⁢𝜎 with experimental masses from the 48 ≤ 𝑍 ≤ 52 isotopic chains. The framework's resilience to new mass data gave confidence in the extrapolation of tin masses down to 𝑁 = 46. Our calculations suggest that 96 Sn is a two-proton drip line nucleus and predict a mass excess of −58090⁢(800) keV for 100 Sn , showing a preference within 1⁢𝜎 for the mass of 100 Sn derived from the 𝛽-delayed 𝑄 value measured at GSI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Hybrid Quantum Mechanical, Molecular Mechanical, and Machine Learning Potential for Computing Aqueous-Phase Adsorption Free Energies on Metal Surfaces

Performing reliable computer simulations of elementary processes occurring at metal–water interfaces is pivotal for novel catalyst design in sustainable energy applications. Computational catalyst design hinges on the ability to reliably and efficiently compute the potential energy surface (PES) of the system. Here, due to the large system sizes needed for studying processes at liquid water–metal interfaces, these systems can currently not be described using density functional theory (DFT). In this work, we used a hybrid quantum mechanical, molecular mechanical, and machine learning potential for studying the adsorption behavior of phenol, atomic hydrogen, 2-butanol, and 2-butanone on the (0001) facet of Ru under reducing conditions when Ru is not oxidized. Specifically, we describe the adsorbate and the surrounding metal atoms at the DFT level of theory. Here, we also considered the electrostatic field effect of the water molecules on adsorbate–metal interactions. Next, for the water–water and water–adsorbate interactions, we used established classical force fields. Finally, for the water–Ru surface interaction, for which no reliable force fields have been published, we used Behler–Parrinello high-dimensional neural network potentials (HDNNPs). Employing this setup, we used our explicit solvation for metal surface (eSMS) approach to compute the aqueous-phase effect on the low-coverage adsorption of selected molecules and atoms on the (0001) facet of Ru. In agreement with previous experimental and computational studies of oxygenated molecules over transition metal facets, we found that liquid water destabilizes the tested adsorbates on Ru(0001). Interestingly, our findings indicate that adsorbates on Ru are less affected by the presence of an aqueous phase than on other transition metals (e.g., Pt), highlighting the necessity of experimental investigations of Ru-based catalytic systems in liquid water.

Adsorption↗
DOE OSTI2024

Accelerating the Discovery of New, Single Phase High Entropy Ceramics via Active Learning

High-entropy ceramics have garnered interest due to their remarkable hardness, compressive strength, thermal stability, and fracture toughness; yet the discovery of new high-entropy ceramics (out of a tremendous number of possible elemental permutations) still largely requires costly, inefficient, trial-and-error experimental and computational approaches. The entropy forming ability (EFA) factor was recently proposed as a computational descriptor that positively correlates with the likelihood that a 5-metal high-entropy carbide (HECs) will form the desired single phase, homogeneous solid solution; however, discovery of new compositions is computationally expensive. If you consider 8 candidate metals, the HEC EFA approach uses 49 optimizations for each of the 56 unique 5-metal carbides, requiring a total of 2744 costly density functional theory calculations. Here, we describe an orders-of-magnitude more efficient active learning (AL) approach for identifying novel HECs. To begin, we compared numerous methods for generating composition-based feature vectors (e.g., magpie and mat2vec), deployed an ensemble of machine learning (ML) models to generate an average and distribution of predictions, and then utilized the distribution as an uncertainty. Here we then deployed an AL approach to extract new training data points where the ensemble of ML models predicted a high EFA value or was uncertain of the prediction. Our approach has the combined benefit of decreasing the amount of training data required to reach acceptable prediction qualities and biases the predictions toward identifying HECs with the desired high EFA values, which are tentatively correlated with the formation of single phase HECs. Using this approach, we increased the number of 5-metal carbides screened from 56 to 15,504, revealing 4 compositions with record-high EFA values that were previously unreported in the literature. Our AL framework is also generalizable and could be modified to rationally predict optimized candidate materials/combinations with a wide range of desired properties (e.g., mechanical stability, thermal conductivity).

36 MATERIALS SCIENCE↗
DOE OSTI2024

Understanding Twinning and Deformation in High Entropy Alloys

A combination of high strength and high ductility has been observed in multi-principal element alloys due to twin formation attributed to low stacking fault energy (SFE). In the pursuit of low SFE alloys, a key bottleneck is the lack of understanding of the composition–SFE cor- relations that would guide tailoring SFE via alloy composition. Using density functional theory (DFT), we show that dopant radius, which have been postulated as a key descriptor for SFE in dilute alloys, does not fully explain SFE trends across different host metals. Instead, charge density is a much more central descriptor. It allows us to (1) explain contrasting SFE trends in Ni and Cu host metals due to various dopants in dilute concentrations, (2) explain the large SFE variations observed in the literature even within a given alloy composition due to the nearest neighbor environments in “model” concentrated alloys, and (3) develop a machine learning model that can be used to predict SFEs in multi-elemental alloys. This model opens a possibility to use charge density as a descriptor for predicting SFE in alloys. Furthermore, a descriptor-less machine learning (ML) model based only on charge density images extracted from density functional theory (DFT) is developed to predict stacking fault energies (SFE) in concentrated alloys. The model is based on convolutional neural networks (CNNs) as one of the promising ML techniques for dealing with complex images and data. Identification of correct descriptors is a key bottleneck to develop ML models for predicting materials properties. Often, in most ML models, textbook physical descriptors such as atomic radius, valence charge and electronegativity are used as descriptors which have limitations because these properties change in concentrated alloys when multiple elements are mixed to form a solid solution. We illustrate that, within the scope of DFT, the search for descriptors can be circumvented by electronic charge density, which is the backbone of the Kohn-Sham DFT and describes the system completely. The performance of our model is demonstrated by predicting SFE of concentrated alloys with an RMSE and R2 of 6.18 mJ/m2 and 0.87, respectively, validating the accuracy of the proposed approach.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Machine Learning Thermodynamics And Kinetics of Defects For Accelerated Materials Discovery

Atomistic defects play a pivotal role in functional and structural materials’ performance across a myriad of technology applications. Quantitative prediction of the thermodynamics and kinetics of defect formation and migration, respectively, typically requires accurate but expensive first-principles approaches, such as density functional theory (DFT). Their computational expense limits the throughput needed to perform high-throughput materials discovery/screening exercises or to perform materials modeling tasks relying on extensive sampling techniques. Therefore, in this Sandia National Laboratories Laboratory Directed Research and Development (LDRD) project (Project #229366), we developed a variety of machine learning techniques, trained on density functional theory calculations, to accelerate the discovery and modeling of materials in which vacancy and interstitial defects primarily dictate material performance. These include applications such as metal oxides for water-splitting or mixed ionic-electronic conduction, metal hydrides for hydrogen storage, and transition metal dichalcogenides for electronics, and the approaches developed herein can further be applied to many other domains that similarly depend on materials’ thermodynamic and kinetic defect properties for their desired functionality.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Towards AI-assisted neutrino flavor theory design

Particle physics theories, such as those which explain neutrino flavor mixing, arise from a vast landscape of model-building possibilities. A model’s construction typically relies on the intuition of theorists. It also requires considerable effort to identify appropriate symmetry groups, assign field representations, and extract predictions for comparison with experimental data. We develop Autonomous Model Builder (AMBer), a framework in which a reinforcement learning agent interacts with a streamlined physics software pipeline to search these spaces efficiently. AMBer selects symmetry groups, particle content, and group representation assignments to construct models while minimizing the number of free parameters introduced. We validate our approach in well-studied regions of theory space and extend the exploration to a previously unexamined symmetry group. While demonstrated in the context of neutrino flavor theories, this approach of reinforcement learning with physics software feedback may be extended to other theoretical model-building problems in the future.

Baretz, Jason Benjamin↗
DOE OSTI2024

Surface Segregation Studies in Ternary Noble Metal Alloys: Comparing DFT and Machine Learning with Experimental Data

Abstract Surface segregation, whereby the surface composition of an alloy differs systematically from the bulk, has historically been hard to study, because it requires experimental and modeling methods that span alloy composition space. In this work, we study surface segregation in catalytically relevant noble and platinum‐group metal alloys with a focus on three ternary systems: AgAuCu, AuCuPd, and CuPdPt. We develop a data set of 2478 fcc slabs with those compositions including all three low‐index crystallographic orientations relaxed with Density Functional Theory using the PBEsol functional with D3 dispersion corrections. We fine‐tune a machine learning model on this data and use the model in a series of 1800 Monte Carlo simulations spanning ternary composition space for each surface orientation and ternary chemical system. The results of these simulations are validated against prior experimental surface segregation data collected using composition spread alloy films for AgAuCu and AuCuPd. Our findings reveal that simulations conducted using the (110) orientation most closely match experimentally observed surface segregation trends, and while predicted trends qualitatively match observation, biases in the PBEsol functional limit numeric accuracy. This study advances understanding of surface segregation and the utility of computational studies and highlights the need for further improvements in simulation accuracy.

Chemistry↗
DOE OSTI2024

Scientific machine learning for closure models in multiscale problems: A review

Here, closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Accelerated Selectrion of Optimal Perovskite Alloys for Solar PV using a Combined Quantum and Machine Learning Hierachiral Approach

The project aims to: (i) accelerate the discovery of “Missing HP alloys” by combining quantum mechanics and artificial intelligence machine learning approaches, and (ii) analyze the stabilities of candidate alloys, including those that do not pass selection filters (and are thus expected to degrade over time) to decipher the nature of the instabilities to guide the development of durable solar cell materials. Successful candidates will be subjected to validation experiments at NREL's state-of-the-art facilities. The discoveries this effort will provide will be directly testable and implementable and will greatly impact U.S. progress in HP PV as they will provide clear direction and motivation for experimental studies including specific material synthetic targets, device optimization, and device stability protocols. A key advantage of this effort is the feedback and guidance provided by the Industry Collaborative Work Group that we established to coordinate academic and national lab research with industry needs. The proposed work will provide a basis for and direct the development of robust and reliable HP PV. It will also provide a timely, valuable and extensive roadmap to the experimental HP PV community to enable it to focus its efforts on improving and fine-tuning promising HP compositions that this effort predicts will likely be the best performers rather than wandering in the vast chemical space for decades spending enormous resources mostly evaluating unpromising candidate materials.

14 SOLAR ENERGY↗
DOE OSTI2025

Learning local and semi-local density functionals from exact exchange-correlation potentials and energies

Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, attaining general purpose chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functional by using the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN)–based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies and densities. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA on various thermochemistry datasets. These results underscore the promise of using the XC potential in modeling XC functionals and can pave the way for systematic learning of increasingly accurate XC functionals.

Science & Technology - Other Topics↗
DOE OSTI2025

Unraveling Adsorbate-Induced Structural Evolution of Iron Carbide Nanoparticles

Iron carbide (Fe x C y ) nanoparticles (NPs) are promising candidates for replacing platinum group metals in industrial applications, such as high-temperature Fischer–Tropsch synthesis. However, due to their amorphous nature, characterization of the active sites has been challenging experimentally and computationally. Here, using a combined density functional theory (DFT), neural network interatomic potential-assisted global optimization, and ensemble learning study, we evaluate dynamic surface changes associated with syngas (H and CO) interactions. For this purpose, we have developed a general procedure that we use to model an experimentally relevant 270-atom Fe 182 C 88 NP using the neural network-assisted stochastic surface walk global optimization algorithm (SSW-NN). Once generated, the Fe 182 C 88 NP active sites and particle morphology are thoroughly characterized before the effects of syngas adsorbate interactions are explored by using DFT and molecular dynamics simulations. Lastly, we explore correlations between geometric and electronic features of the active sites and the adsorption of H (H ads ), using a regularized random forest machine learning algorithm. In doing so, we identified the Fe–C coordination number and p orbital occupancy as the most important descriptors affecting H ads . Furthermore, using a combined ML and quantum chemistry approach, our work demonstrates a general and efficient procedure for generating and probing complex surface phenomena on binary nanoparticles.

Adsorption↗
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↗