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DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗

DOE OSTI2024

On the Training and Generalization of Deep Operator Networks

Here, we present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram–Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.

deep operator networks↗

DOE OSTI2026

Multi‐Sensor Trajectory Reconstruction of the 24 April 2025 Alaska Fireball and Implications for Planetary Defense

On 24 April 2025 at 18:30:57 UTC, a bright daytime fireball over Southcentral Alaska was detected by 37 seismic stations, 16 single infrasound sensors, and four infrasound arrays, yielding 30 ballistic and multiple fragmentation arrivals. Here, the unprecedented density of seismoacoustic coverage enabled detailed reconstruction of the event using acoustic signals, with fragmentation source locations further guiding the identification of Doppler weather radar signatures of a meteorite fall. Incorporation of a radar-derived terminal point yielded a final trajectory solution, which agreed closely with an independent optical trajectory solution from video analysis. The reconstructed entry parameters from seismoacoustic analysis indicate a velocity of 25.3 km/s, an entry angle of 19°, and an energy release of ∼38 t TNT equivalent. Assuming a chondritic composition, the pre-entry object diameter was ∼0.7 m. Using orbital parameters from the optical solution, we estimate meteoroid composition as most likely an L-type ordinary chondrite. The event occurred in the sub-Arctic, where space-based optical systems face challenges in detection, demonstrating the critical role of dense ground-based seismoacoustic networks in characterizing high-latitude atmospheric entries. This uniquely well-recorded event demonstrates the capability of dense seismoacoustic networks to constrain bolide trajectories, energetics, and fragmentation, with radar and optical data providing critical confirmation and complementary perspectives. These results bridge the methodological gap between planetary-defense monitoring of natural impactors and space-traffic analyses of artificial reentries, illustrating how multi-sensor integration can deliver calibration-grade trajectories even for unpredicted events.

Fireball↗

DOE OSTI2025

Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

Latent representations↗

DOE OSTI2025

Structural Investigation of Six Quinary Sulfides Synthesized via the Flux-Assisted Boron-Chalcogen Mixture (BCM) Method: Eu 2+ Containing Members of the RE 3 MTQ 7 (M and T = Transition or Main Group Metals, Q = Chalcogens) Family

For this work, a series of six quinary rare-earth sulfides Ce 4+ 1.85 Eu 2+ 1.15 Na 0.30 SiS 7 , Ce 4+ 1.91 Eu 2+ 1.09 K 0.18 SiS 7 , Ce 4+ 1.96 Eu 2+ 1.04 Rb 0.08 SiS 7 , Ce 4+ 1.98 Eu 2+ 1.02 Cs 0.05 SiS 7 , Ce 4+ 1.97 Eu 2+ 1.03 Ag 0.06 SiS 7 , and Ce 4+ 1.50 Eu 2+ 1.50 CuSiS 7 were obtained in an alkali iodide flux using the boron-chalcogen mixture (BCM) method. Single crystal X-ray diffraction was used to determine the structures of the high quality single crystals that were grown; their elemental compositions were confirmed by energy-dispersive spectroscopy (EDS). The compounds crystallize in the hexagonal crystal system in the noncentrosymmetric space group P63. The crystal structure consists of a three-dimensional network composed of mixed cerium and europium bicapped trigonal prisms, isolated SiS4 tetrahedra, and monovalent metals (Na, K, Rb, Cs, Ag, and Cu) located in cavities created by linked Ce/EuS 8 polyhedra. The structures are charge-balanced when Ce and Eu are in their +4 and +2 oxidation states, respectively. The effective magnetic moment of Ce 1.50 4+ Eu 1.50 2+ CuSiS 7 determined from the temperature dependence of the magnetic susceptibility data is consistent with the presence of Ce 4+ and Eu 2+ . Clear correlations between the alkali ion site occupancy, the ionic radius of the alkali cations, and the average bond length of Ce 4+ /Eu 2+ –S, were established. UV–vis diffuse reflectance data were collected for Ce 1.50 4+ Eu 1.50 2+ CuSiS 7 and a band gap of 1.9(1) eV was established.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Scalar bounded-from-below conditions from Bayesian active learning

We present a procedure leveraging Bayesian deep active learning to rapidly produce highly accurate approximate bounded-from-below conditions for arbitrary renormalizable scalar potentials, in the form of a neural network which may be saved and exported for use in arbitrary parameter space scans. We explore the performance of our procedure on three different scalar potentials with either highly nontrivial or unknown symbolic bounded-from-below conditions (the most general two-Higgs doublet model, the three-Higgs doublet model, and a version of the Georgi-Machacek model without custodial symmetry). We find that we can produce fast and highly accurate binary classifiers for all three potentials. Furthermore, for the potentials for which no known symbolic necessary and sufficient conditions on boundedness-from-below exist, our classifiers substantially outperform some common approximate analytical methods, such as producing tractable sufficient but not necessary conditions or evaluating boundedness-from-below conditions for scenarios in which only a subset of the theory’s fields achieve vacuum expectation values. Our methodology can be readily adapted to any renormalizable scalar field theory. For the community’s use, we have developed a package, BFBrain, which allows for the rapid implementation of our analysis procedure on user-specified scalar potentials with a high degree of customizability. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2025

Advancing Multiscale Simulation of Plasma-Surface Interfaces

We report the development of an atomistic-informed, surface-state-dependent predictive model for particle exchange in a carbon-tungsten plasma-surface interface. The predictive model uses machine learning (ML) techniques to learn the energy and angular distributions for particle exchange and rate functions for surface state evolution from molecular dynamics simulations of cumulative bombardment of tungsten by energetic carbon ions. Each predictive component is sensitive to the energy and trajectory of incident plasma species and the surface state. The surface state is represented by a set of surface state descriptors, which were derived from the atomistic surface state for each independent carbon bombardment event. These descriptors are representative of the composition and degree of amorphization of the outermost angstrom of surface material and were chosen to optimize predictive performance for particle exchange at the interface. The distributions for particle exchange (reflection/sputtering) are demonstrated to vary with each surface state descriptor, motivating the development of surface-state-dependent particle exchange models for plasma simulations. The performance of various ML methods was compared, including polynomial quantile regression, artificial neural networks, k-nearest neighbors, and random forest algorithms, with polynomial regression performing the best for interpolation and extrapolation of learned relationships. In addition to the particle exchange model, a neutral network was developed and used to identify data sufficiency throughout surface descriptor space, which will enable real-time feedback during future data production to ensure data is produced where it is most needed, and we provide commentary on improvements to the data production workflow for future endeavors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Comprehensive Neural Posterior Estimation for Galaxy-Galaxy Strong Lensing

We present a deep learning model based on neural posterior estimation (NPE) for comprehensive extraction of astrophysical parameters from galaxy-scale strong gravitational lenses. The unprecedentedly large amount of galaxy-scale strong lenses expected in future cosmological surveys (${\cal O}(10^5)$) promises to enable valuable statistical constraints in various studies ranging from galaxy formation to the nature of dark matter, but it also poses a significant challenge for traditional modelling pipelines. To this end, our automated model includes several new, state-of-the-art features and approaches leveraging the framework of simulation-based inference (SBI). We infer a total of 20 parameters describing the mass and light profiles of both lens and source galaxies, using simulated raw multi-band data modelled under noise and observing conditions expected by the Legacy Survey of Space and Time (LSST), with its summary statistics generated by a residual network. We examine the efficacy of multi-band data in extracting nearly 20 model parameters simultaneous from strong lensing images including lens light. Finally, We perform a comprehensive set of diagnostics for SBI models, evaluating the model's prediction accuracy, stability, and uncertainty quantification.

Zhao, Roy J. [Chicago U., KICP]↗

DOE OSTI2024

Machine-learning based approach to examine ecological processes influencing the diversity of riverine dissolved organic matter composition

Dissolved organic matter (DOM) assemblages in freshwater rivers are formed from mixtures of simple to complex compounds that are highly variable across time and space. These mixtures largely form due to the environmental heterogeneity of river networks and the contribution of diverse allochthonous and autochthonous DOM sources. Most studies are, however, confined to local and regional scales, which precludes an understanding of how these mixtures arise at large, e.g., continental, spatial scales. The processes contributing to these mixtures are also difficult to study because of the complex interactions between various environmental factors and DOM. Here we propose the use of machine learning (ML) approaches to identify ecological processes contributing toward mixtures of DOM at a continental-scale. We related a dataset that characterized the molecular composition of DOM from river water and sediment with Fourier-transform ion cyclotron resonance mass spectrometry to explanatory physicochemical variables such as nutrient concentrations and stable water isotopes ( 2 H and 18 O). Using unsupervised ML, distinctive clusters for sediment and water samples were identified, with unique molecular compositions influenced by environmental factors like terrestrial input and microbial activity. Sediment clusters showed a higher proportion of protein-like and unclassified compounds than water clusters, while water clusters exhibited a more diversified chemical composition. We then applied a supervised ML approach, involving a two-stage use of SHapley Additive exPlanations (SHAP) values. In the first stage, SHAP values were obtained and used to identify key physicochemical variables. These parameters were employed to train models using both the default and subsequently tuned hyperparameters of the Histogram-based Gradient Boosting (HGB) algorithm. The supervised ML approach, using HGB and SHAP values, highlighted complex relationships between environmental factors and DOM diversity, in particular the existence of dams upstream, precipitation events, and other watershed characteristics were important in predicting higher chemical diversity in DOM. Our data-driven approach can now be used more generally to reveal the interplay between physical, chemical, and biological factors in determining the diversity of DOM in other ecosystems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

On infinite tensor networks, complementary recovery and type II factors

We initiate a study of local operator algebras at the boundary of infinite tensor networks, using the mathematical theory of inductive limits. In particular, we consider tensor networks in which each layer acts as a quantum code with complementary recovery, a property that features prominently in the bulk-to-boundary maps intrinsic to holographic quantum error-correcting codes. In this case, we decompose the limiting Hilbert space and the algebras of observables in a way that keeps track of the entanglement in the network. As a specific example, we describe this inductive limit for the holographic Harlow-Pastawski-Preskill-Yoshida code model and relate its algebraic and error-correction features. We find that the local algebras in this model are given by the hyperfinite type II$_\infty$ factor. Next, we discuss other networks that build upon this framework and comment on a connection between type II factors and stabilizer circuits. We conclude with a discussion of multiscale entanglement renormalization ansatz networks in which complementary recovery is broken. We argue that this breaking possibly permits a limiting type III von Neumann algebra, making them more suitable ansätze for approximating subregions of quantum field theories.

holographic dualities↗

DOE OSTI2024

A tri-level optimization model for interdependent infrastructure network resilience against compound hazard events

Resilient operation of interdependent infrastructures against compound hazard events is essential for maintaining societal well-being. To address consequence assessment challenges in this problem space, we propose a novel policy-guided tri-level optimization model applied to a proof-of-concept case study with fuel distribution and transportation networks – encompassing one realistic network; one fictitious, yet realistic network; as well as networks drawn from three synthetic distributions. Mathematically, our approach takes the form of a defender-attacker-defender (DAD) model—a multi-agent tri-level optimization, comprised of a defender, attacker, and an operator acting in sequence. Here, in this study, our notional operator may choose proxy actions to operate an interdependent system comprised of fuel terminals and gas stations (functioning as supplies) and a transportation network with traffic flow (functioning as demand) to minimize unmet demand at gas stations. A notional attacker aims to hypothetically disrupt normal operations by reducing supply at the supply terminals, and the notional defender aims to identify best proxy defense policy options which include hardening supply terminals or allowing alternative distribution methods such as trucking reserve supplies. We solve our DAD formulation at a metropolitan scale and present practical defense policy insights against hypothetical compound hazards. We demonstrate the generalizability of our framework by presenting results for a realistic network; a fictitious, yet realistic network; as well as for three networks drawn from synthetic distributions. Additionally, we demonstrate the scalability of the framework by investigating runtime performance as a function of the network size. Steps for future research are also discussed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Make the Fastest Faster: Importance Mask Synthesis for Interactive Volume Visualization using Reconstruction Neural Networks

Visualizing a large-scale volumetric dataset with high resolution is challenging due to the substantial computational time and space complexity. Recent deep learning-based image inpainting methods significantly improve rendering latency by reconstructing a high-resolution image for visualization in constant time on GPU from a partially rendered image where only a portion of pixels go through the expensive rendering pipeline. However, existing solutions need to render every pixel of either a predefined regular sampling pattern or an irregular sample pattern predicted from a low-resolution image rendering. Both methods require a significant amount of expensive pixel-level rendering. In this work, we provide Importance Mask Learning (IML) and Synthesis (IMS) networks, which are the first attempts to directly synthesize important regions of the regular sampling pattern from the user’s view parameters, to further minimize the number of pixels to render by jointly considering the dataset, user behavior, and the downstream reconstruction neural network. Our solution is a unified framework to handle various types of inpainting methods through the proposed differentiable compaction/decompaction layers. Experiments show our method can further improve the overall rendering latency of state-of-the-art volume visualization methods using reconstruction neural network for free when rendering scientific volumetric datasets. Our method can also directly optimize the off-the-shelf pre-trained reconstruction neural networks without elongated retraining.

Large-scale data↗

DOE OSTI2025

Tomography of longitudinal phase space linearization for the generation of attosecond electron bunches

The generation of electron bunches on the attosecond timescale is important for a multitude of accelerator-based applications. Here, we report on a tomographic measurement of the (pre)linearized longitudinal phase space of a low charge 3 MeV electron bunch generated with the 1.6 cell Pegasus photoinjector for the generation of attosecond bunches. The nonlinear correlations in the longitudinal phase space induced by space charge at the photocathode, radiofrequency field curvature of the gun, and vacuum dispersion are compensated using a compact X-band linearizer. Then, the initial and compensated phase of the picosecond electron bunch is precisely reconstructed by neural network assisted tomographic reconstruction from momentum spectra at varying buncher linac phase. Finally, we combine the measured phase space shape with particle tracking simulations to show that electron bunches as short as 941 as develop downstream the beamline.

Beam control↗

DOE OSTI2024

NuGraph2: A Graph Neural Network for Neutrino Event Reconstruction

Neutrino experiments are set to probe some of the most important open questions in physics, from CP violation and the nature of dark matter. The technology of choice for many of these experiments is the liquid argon time projection chamber (LArTPC). In current LArTPC experiments, reconstruction performance often represents a limiting factor for the sensitivity. New developments are therefore needed to unlock the full potential of LArTPC experiments. NuGraph2 is a state of the art Graph Neural Network for reconstruction of data in LArTPC experiments. NuGraph2 utilizes a heterogeneous graph structure, with separate subgraphs of 2D nodes (hits in each plane) connected across planes via 3D nodes (space points). The model provides a consistent description of the neutrino interaction across all planes. NuGraph2 is a multi-purpose network, with a common message-passing attention engine connected to multiple decoders with different classification or regression tasks. These include the classification of detector hits according to the particle type that produced them (semantic segmentation) and the separation of hits from the neutrino interaction from hits due to noise or cosmic-ray background. Additional decoders are being developed, performing tasks such as the regression of the neutrino interaction vertex position. Performance results will be presented based on publicly available samples from MicroBooNE. These include both physics performance metrics, achieving 95% accuracy for semantic segmentation and 98% classification of neutrino hits, as well as computational metrics for training and for inference on CPU or GPU. The status of the NuGraph integration in the LArSoft software framework will be presented, as well as initial studies about model interpretability and injection of domain knowledge.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

NuGraph2: A Graph Neural Network for Neutrino Event Reconstruction

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Toward machine-learning-assisted PW-class high-repetition-rate experiments with solid targets

We present progress in utilizing a machine learning (ML) assisted optimization framework to study the trends in a parameter space defined by spectrally shaped, high-intensity, petawatt-class (8 J, 45 fs) laser pulses interacting with solid targets and give the first simulation-based overview of predicted trends. A neural network (NN) incorporating uncertainty quantification is trained to predict the number of hot electrons generated by the laser–target interaction as a function of pulse shaping parameters. The predictions of this NN serve as the basis function for a Bayesian optimization framework to navigate this space. For post-experimental evaluation, we compare two separate neural network (NN) models. One is based solely on data from experiments, and the other is trained only on ensemble particle-in-cell simulations. Reviewing the predicted and observed trends across the experiment-capable laser parameter search space, we find that both ML models predict a maximal increase in hot electron generation at a level of approximately 12%–18%; however, no statistically significant enhancement was observed in experiments. On direct comparison of the NN models, the average discrepancy is 8.5%, with a maximum of 30%. Since shot-to-shot fluctuations in experiments affect the observations, we evaluate the behavior of our optimization framework by performing virtual experiments that vary the number of repeated observations and the noise levels. Here, we discuss the implications of such a framework for future autonomous exploration platforms in high-repetition-rate experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Learning PDFs through interpretable latent representations in Mellin space

Representing the parton distribution functions (PDFs) of the proton and other hadrons through flexible, high-fidelity parametrizations has been a long-standing goal of particle physics phenomenology. This is particularly true since the chosen parametrization methodology can play an influential role in the ultimate PDF uncertainties as extracted in QCD global analyses; these, in turn, are often determinative of the reach of experiments at the LHC and other facilities to nonstandard physics, including at large 𝑥, where parametrization effects can be significant. In this study, we explore a series of encoder-decoder machine-learning (ML) models with various neural-network topologies as efficient means of reconstructing PDFs from meaningful information stored in an interpretable latent space. Given recent effort to pioneer synergies between QCD analyses and lattice-gauge calculations, we formulate a latent representation based on the behavior of PDFs in Mellin space, i.e., their integrated moments, and test the ability of various models to decode PDFs from this information faithfully. We introduce a numerical package, PDFdecoder, which implements several encoder-decoder models to reconstruct PDFs with high fidelity and use this end-to-end tool to explore how such neural-network-based models might connect PDF parametrizations to underlying properties like their Mellin moments. We additionally dissect patterns of learned correlations between encoded Mellin moments and reconstructed PDFs that suggest opportunities for further improvements to ML-based approaches to PDF parametrizations and uncertainty quantification.

Machine learning↗

DOE OSTI2026

Neural-Network Inverse Design of SRF Cavities and Transmons for Bosonic Quantum Computation

Three-dimensional superconducting radio-frequency (SRF) cavities provide exceptionally long-lived electromagnetic modes and, when coupled to nonlinear elements such as transmon qubits, become promising architectures for bosonic quantum information processing. The inverse design of such systems, i.e., recovering device geometries that produce specified electromagnetic and coupling targets, is generally a one-to-many problem. The qubit-cavity coupling strength depends sensitively on both the transmon geometry and its position within the cavity's electromagnetic field. As these systems scale up and their design parameter spaces grow, the cost of conventional iterative simulation becomes prohibitive. We present two deep neural network (DNN) approaches that address this inverse-design problem at complementary levels of the design stack. The first proposes SRF cavity geometries that produce target cavity observables. The second proposes transmon qubit designs that produce target qubit-cavity parameters - the coupling rate, qubit frequency, and anharmonicity $(g, ν_q, α)$. The recovered candidate designs match the targets to within ~5% (cavity) and ~2% (transmon), confirmed by end-to-end re-simulation. Both approaches map desired device behavior directly to candidate designs, a fast alternative to the iterative simulation studies usually required.

Yaker, Joseph [Fermilab; Northwestern U.]↗