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DOE OSTI2025

Deep Learning for Subsurface Flow: A Comparative Study of U‐Net, Fourier Neural Operators, and Transformers in Underground Hydrogen Storage

Subsurface flow research is essential for the sustainable management of natural resources and the environment. Deep learning (DL) has significantly advanced this field by developing efficient and accurate surrogate models to replace computationally expensive physics‐based simulations. These surrogate models are commonly used to predict the spatiotemporal evolution of state variables, such as gas saturation and reservoir pressure, in heterogeneous geological formations. Despite the various DL models applied to this task, there is a lack of studies systematically comparing their performance. This absence of comparative analysis leads to somewhat arbitrary DL model selection in subsurface flow research, resulting in suboptimal performance and potentially inaccurate predictions. To bridge this gap, we conduct a systematic comparison study of three popular DL architectures—U‐Net, Fourier Neural Operators (FNO), and Segmentation Transformer (SETR)—in surrogate modeling of underground hydrogen storage (UHS). We focus on UHS due to its promise of enhancing clean energy resilience and its cyclic operational conditions that represent common scenarios in various subsurface applications. We evaluate the models based on accuracy, training cost, and inference speed. The comparison shows that U‐Net achieves the highest accuracy, followed by SETR and FNO. Despite its lower accuracy, FNO has the highest inference speed. SETR offers competitive accuracy with the least training memory usage, demonstrating the potential of transformers in learning subsurface flow. Our results provide guidance for selecting DL models for surrogate modeling in a wide range of subsurface flow problems.

42 ENGINEERING↗

DOE OSTI2024

Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits

Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers.

42 ENGINEERING↗

DOE OSTI2024

Rethinking materials simulations: Blending direct numerical simulations with neural operators

Abstract Materials simulations based on direct numerical solvers are accurate but computationally expensive for predicting materials evolution across length- and time-scales, due to the complexity of the underlying evolution equations, the nature of multiscale spatiotemporal interactions, and the need to reach long-time integration. We develop a method that blends direct numerical solvers with neural operators to accelerate such simulations. This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism to enable accurate extrapolation and efficient time-to-solution predictions of the dynamics. We demonstrate the effectiveness of this hybrid framework on simulations of microstructure evolution via the phase-field method. Such simulations exhibit high spatial gradients and the co-evolution of different material phases with simultaneous slow and fast materials dynamics. We establish accurate extrapolation of the coupled solver with large speed-up compared to DNS depending on the hybrid strategy utilized. This methodology is generalizable to a broad range of materials simulations, from solid mechanics to fluid dynamics, geophysics, climate, and more.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Virtual sensing-enabled digital twin framework for real-time monitoring of nuclear systems leveraging deep neural operators

Abstract Real-time monitoring is a foundation of nuclear digital twin technology, crucial for detecting material degradation and maintaining nuclear system integrity. Traditional physical sensor systems face limitations, particularly in measuring critical parameters in hard-to-reach or harsh environments, often resulting in incomplete data coverage. Machine learning-driven virtual sensors offer a transformative solution by complementing physical sensors in monitoring critical degradation indicators. This paper introduces the use of Deep Operator Networks (DeepONet) to predict key thermal-hydraulic parameters in the hot leg of pressurized water reactor. DeepONet acts as a virtual sensor, mapping operational inputs to spatially distributed system behaviors without requiring frequent retraining. Our results show that DeepONet achieves low mean squared and Relative L2 error, making predictions 1400 times faster than traditional CFD simulations . These characteristics enable DeepONet to function as a real-time virtual sensor, synchronizing with the physical system to track degradation conditions and provide insights within the digital twin framework for nuclear systems.

Hossain, Raisa↗

DOE OSTI2026

Challenges, Technological Pathways and Trade-Offs of Perovskite Solar Modules for Long-Term Operation

Perovskite solar modules (PSMs) have emerged as a promising photovoltaic technology due to their high efficiency, low fabrication cost and compatibility with lightweight and flexible applications. However, ensuring long-term reliable performance under real-world conditions remains a critical barrier to commercialization. PSMs degrade through mechanisms that differ substantially from those affecting established technologies such as silicon, particularly under environmental stressors like ultraviolet light, oxygen, temperature cycling and reverse bias. Here we provide an analysis of the degradation pathways specific to perovskite modules and discuss why standard accelerated tests often fail to predict outdoor performance. We conceptualize challenges across material, device and module levels and evaluate strategies to mitigate ion migration, interfacial breakdown and encapsulation failure. By highlighting the need for realistic testing protocols and durable materials, we propose a framework highlighting key challenges, technological pathways and the trade-offs required to extend perovskite module lifetimes towards long-term operation, aiming to guide the development of PSMs capable of a 30-year operational lifetime.

14 SOLAR ENERGY↗

DOE OSTI2025

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Dynamic operation and reaction network coupling in solid oxide electrochemical reactors

Solid oxide cells have traditionally been confined to operation as standalone electrolyzers or fuel cells, with research predominantly focused on materials performance. Here, this Comment highlights opportunities to leverage integrated faradaic and non-faradaic reactions alongside dynamic operation in these electrochemical membrane reactors to maximize energy utilization and expand product scope.

Cho, Yoon Jin [University of Michigan, Ann Arbor, ↗

DOE OSTI2025

HEPCloud Operations at Fermilab—The First Five Years

The HEPCloud Facility at Fermilab has now been in production operation for five years. This facility is a unified provisioning gateway to US high performance computing centers, including NERSC, OLCF, and ALCF, other large supercomputers run by the NSF, and commercial clouds. HEPCloud delivers hundreds of millions of core-hours yearly for CMS. HEPCloud also serves other Fermilab experiments including DUNE, Mu2e, Muon g-2, and NOvA. In this paper we present the practical considerations of operating a distributed facility such as HEPCloud. We also mention some of the interesting research and development that HEPCloud has been used for including GPU-based machine learning inference servers, and tests of Quantum Computing.

Timm, Steven [Fermilab]↗

DOE OSTI2024

Cryogen-free modular scanning tunneling microscope operating at 4-K in high magnetic field on a compact ultra-high vacuum platform

One of the daunting challenges in modern low temperature scanning tunneling microscopy (STM) is the difficulty of combining atomic resolution with cryogen-free cooling. Further functionality needs, such as ultra-high vacuum (UHV), high magnetic field (HF), and compatibility with μm-sized samples, pose additional challenges to an already ambitious build. We present the design, construction, and performance of a cryogen-free, UHV, low temperature, and high magnetic field system for modular STM operation. An internal vibration isolator reduces vibrations in this system, allowing for atomic resolution STM imaging while maintaining a low base temperature of ∼4 K and magnetic fields up to 9 T. Samples and tips can be conditioned in situ utilizing a heating stage, an ion sputtering gun, an e-beam evaporator, a tip treater, and sample exfoliation. In situ sample and tip exchange and alignment are performed in a connected UHV room temperature stage with optical access. Multisite operation without breaking vacuum is enabled by a unique quick-connect STM head design. A novel low-profile vertical transfer mechanism permits transferring the STM between room temperature and the low temperature cryostat.

Instruments & Instrumentation↗

DOE OSTI2024

Novel deuterium–tritium (DT) neutron activation diagnostics for increased neutron yield operations at Sandia’s Z-facility (invited)

As inertial confinement fusion experiments at Sandia National Laboratories’ Z-facility begin using deuterium–tritium (DT) fuels, the expected DT-neutron yields are expected to increase many orders of magnitude. This brings about the need for diagnostics that have a significantly higher dynamic range of operation and ability to obtain yields where there will be significant radiation holds. Using the current activation diagnostic infrastructure at the Z-facility, a pair of activation diagnostics are being developed. Here, the first is fluorine activation, which will be used in a similar manner to current copper activation diagnostics that are fielded in a rabbit for quick removal from the experiments without opening the vacuum experiment containment. The second is a prompt DT-neutron detector that exploits the activation of oxygen with similar operation characteristics as the current Be-probes fielded at Z. We will discuss the design of this pair of instruments, along with calibration work performed at Sandia’s Ion Beam Laboratory in support of the development and anticipated instrument performance.

Mangan, Michael Antony↗

DOE OSTI2026

Neural operator transformers capture bifurcating drift-wave turbulence in fusion plasma simulations

Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Closed-form expressions for unitaries of spin-adapted fermionic operators

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while naïve Trotterization schemes break spin symmetry. Here, in this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalised single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.

fermionic algebra↗

DOE OSTI2025

SAM Two-Phase Flow Model Development and Applications for Operational Transients in Advanced Reactors

As advanced nuclear technologies continue to develop, the need for the flexible operation and generation of these advanced reactors becomes necessary to maximize economic potential. As large-scale experiments are not always feasible, modeling and simulations of advanced reactors play a crucial role in design optimization and analysis. The SAM (System Analysis Module) code developed at Argonne National Laboratory is a state-of-the-art system-level thermal-hydraulic code aimed at simulating advanced reactor systems. Recent code developments have implemented two-phase flow modeling using the homogeneous equilibrium model, and a new steam generator component has been developed to utilize the two-phase flow implementation. In addition to verification tests, a load-following simulation was performed to model a realistic load-following transient in a proposed integrated system consisting of a conceptual advanced reactor known as the Advanced Burner Test Reactor (ABTR) and thermal energy storage (TES) tanks. The integrated system model uses two large TES tanks designed for sodium and a model helical coil steam generator to simulate the operational load-following transient. The flow rates of the feedwater and secondary loops are regulated to meet a prescribed steam generator load consistent with the electricity demand over a 24-h period. In conclusion, the results found the ABTR system was able to maintain stable reactor conditions and primary- and secondary-side characteristics over the course of the load-following transient.

Advanced Burner Test Reactor (ABTR)↗

DOE OSTI2025

Challenges and Opportunities Specific to Microreactors: Compact and Light-Weight Shielding During Operation and Transportation

The problem of designing a shield for a mobile microreactor has been addressed. The principal challenges encountered in this endeavor are the dual goals of increasing radiation protection and decreasing weight. It is recognized that these two goals are contradictory. Increasing shielding naturally increases weight. Conversely, decreasing weight naturally calls for decreasing material inventory, including possibly decreasing shield mass. The operational and regulatory drivers for shielding and transportation constraints are identified and summarized. The main constraints pertain to volume, mass, radiation dose, material feasibility and availability, and decommissioning expectations. The latter are limits on residual contamination and dose rates after the reactor is removed. Progress toward solving the challenge of shielding a transportable microreactor is made by considering a tungsten tetraboride (WB4) shell surrounding the reactor vessel. The shield and a generic microreactor were modeled using the MCNP code. It was determined that the presence of a 16-cm-thick WB4 shield reduces the dose equivalent rate during operations to 3.6 mrem/h just outside of a concrete vault and dome and soil berm surrounding the reactor, which is very near the occupational dose rate limits. Without the WB4 layer, the dose rate at the same location outside the berm would be 120 mrem/h. Most importantly, the presence of the WB4 shield substantially protects the surrounding concrete and soil from activation, thus decreasing the duration of administrative control for the site following removal of the reactor from 16 to 3.4 years. At that point, the site may be decommissioned and returned to unrestricted public access. A limitation on the incorporation of a WB4 shield as an intrinsic component of a microreactor is that it results in a design that is transportable only by using the largest road conveyances and that the load would require special permits for transit through the U.S. highway system. New directions for further improvements and possibly more effective solutions to the shielding problem of a mobile microreactor are discussed in the conclusion section.

Microreactor↗

DOE OSTI2026

Commissioning and operation of a real-time multi-point Thomson scattering evaluation system at Wendelstein 7-X

A real-time multi-point Thomson scattering (rtMPTS) evaluation system has recently been installed and commissioned at the Wendelstein 7-X (W7-X) stellarator during the 2024 -2025 operational phases. This system has demonstrated successful evaluation of Thomson scattered spectra on millisecond timescales. We discuss initial results from this system, consisting of a comparison of different evaluation techniques, assessment of system evaluation times, and proof-of-principle control experiments carried out with the W7-X poloidal correlation reflectometer (PCR) system. This diagnostic represents the first step towards the development of a density profile controller at W7-X, which can be leveraged to support steady-state operation.

Mohammed, Ameer [Princeton Plasma Physics Laborato↗

DOE OSTI2024

Ripple-induced neoclassical toroidal viscous torque in Augmented-First Plasma operation phase in ITER

Abstract A systematic calculation is performed on the ripple-induced neoclassical toroidal viscous (NTV) torque for new ITER scenarios designed for the Augmented-First Plasma (A-FP) operation phase with the full tungsten wall, where the plasma-wall gap is varied in view of mitigating the impact of tungsten wall-plasma interactions. The torque calculation includes drift kinetic response of the plasma thermal and energetic particles to the n = 18 ( n is the toroidal harmonic number) ripple field. For the plasma scenario with ~45 cm plasma-wall gap at the outboard mid-plane and considering the corrected ripple level of 0.17% by the ferritic steel inserts, the computed net NTV torque acting on the plasma column is in the sub-Nm level. However, with decreasing the plasma-wall gap, the computed net NTV torque can reach a level comparable to that produced by the neutral-beam momentum injection in ITER. Ripple correction by ferritic inserts reduces the net torque by a factor of 3.3 for all the three A-FP scenarios considered. The n ω d = l ω b (with ω d and ω b being the toroidal precession and bounce frequencies of trapped particles, respectively, and l an integer number) type of resonance-enhancement of the NTV torque, due to thermal particles, is found to be weak in ITER despite high- n of 18. The same also holds for the ITER 10 MA steady state scenario from the D-T operation phase, where the aforementioned resonance associated with fusion-born alphas is also included. The ripple-induced NTV torque is well below that produced by the resonant magnetic perturbation applied for controlling the type-I edge-localized mode in ITER.

ITER↗

DOE OSTI2024

Tearing Stable Stationary ITER Baseline Operation in DIII-D

We present a tearing stable, stationary and reproducible operating solution for DIII-D plasmas characterized by the ITER Baseline Scenario normalized parameter set and shape. In these plasmas low differential rotation (Δf1,2) between the core and edge is identified as the single root cause of the onset of the primary limiting instability, the 2,1 Neoclassical Tearing Mode (NTM), while a group of other examined parameters have a much weaker impact on the stability. Explanation is offered by drift kinetic simulations, which show a six-fold reduction in the NTM onset threshold due to diminished stabilizing ion polarization currents when the seed island drift frequency ceases in the local plasma frame. Based on the experimental observation and the explanation provided by the theory, a new method is developed to sustain Δf1,2 by modifying the edge neoclassical potential through neutral gas fueling. This method enables stationary ITER baseline operation free of disruptive 2,1 tearing modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗