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DOE OSTI2025

A novel transformation of the ice sheet Stokes equations and some of its properties and applications

We introduce a novel transformation of the Stokes equations into a form closely resembling the shallow Blatter–Pattyn equations. The two forms differ by only a few additional terms, while their variational formulations differ only by a single term in each horizontal direction. Specifically, the variational formulation of the Blatter–Pattyn model drops the vertical velocity in the second invariant of the strain rate tensor. Here we make use of the new transformation in two ways. First, we consider incorporating the transformed equations into a code that can be very easily converted from a Stokes to a Blatter–Pattyn model, and vice versa, by switching these terms on or off. This may be generalized so that the Stokes model is switched on adaptively only where the Blatter–Pattyn model loses accuracy. Second, the key role played by the vertical velocity in the Blatter–Pattyn approximation motivates new approximations. Two examples are presented. These require a mesh that enables the discrete continuity equation to be invertible for the vertical velocity in terms of the horizontal velocity components. Examples of such meshes, such as the first-order P1–E0 mesh and the second-order P2–E1 mesh, are given in both 2D and 3D. However, the transformed Stokes model has the same type of gravity forcing as the Blatter–Pattyn model, determined by the ice surface slope, thereby forgoing some of the mesh generality of the traditional formulation of the Stokes model.

58 GEOSCIENCES↗

DOE OSTI2021

Experimental results of wake steering using fixed angles

In this article, the authors present a test of wake steering at a commercial wind farm. A single fixed yaw offset, rather than an optimized offset schedule, is alternately applied to an upstream wind turbine, and the effect on downstream turbines is analyzed. This experimental design allows for comparison with engineering wake models independent of the controller's ability to track a varying offset and correctly measure wind direction. Additionally, by applying the same offset in beneficial and detrimental conditions, we are able to collect important data for assessing second-order wake model predictions. Results of the article from collected data show good agreement with the FLOw Redirection and Induction in Steady State (FLORIS) engineering model and offer support for the asymmetry of wake steering predicted by newer models, such as the Gauss–curl hybrid model.

17 WIND ENERGY↗

DOE OSTI2025

JVP Flash Attention (jvp_flash_attention) v0.0.4

A Flash Attention Triton kernel with support for second-order derivatives, such as Jacobian-Vector Products (JVPs) and Hessian-Vector Products (HVPs).

Morehead, Alex [Lawrence Berkeley National Laborat↗

DOE OSTI2021

Portage: A Modular Data Remap Library for Multiphysics Applications on Advanced Architectures

Portage is a scalable and extensible remap library for numerical simulations. It supports state-of-the-art remap schemes for meshes and particles in 2D and 3D up to a second-order accuracy. Portage ensures critical properties such as local/global conservation and bounds preservation for mesh remap. It enables multi-material field remap through a dedicated plugin, and leverages the hybrid parallelism exposed by advanced architectures using multi-processing and multi-threading.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Data-Driven Operator Theoretic Methods for Global Phase Space Learning

In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant subsets of a phase space from the spectral properties of the associated Koopman operator constructed from time-series data. Moreover, in the case when the system evolution is known locally in various invariant subspaces, then a phase space stitching result is proposed that can be applied to identify a global Koopman operator. A biological system, bistable toggle switch and a second-order nonlinear system example are considered to illustrate the proposed results. The construction of this global Koopman operator is very helpful in experimental works as multiple experiments can't be run at the same time starting from several initial conditions.

Nandanoori, Sai Pushpak↗

DOE OSTI2020

Impact of Aggregated PV on Subsynchronous Torsional Interaction

This paper investigates induced oscillation (specifically subsynchronous torsional interactions) in power systems arising from photovoltaic (PV) power modulation. Time domain simulations of a modified IEEE first-benchmark system are presented and analyzed. In the IEEE benchmark system, a PV generator was added at the same bus where the synchronous generator is connected. The impact of different parameters of the PV inverters’ volt-volt-ampere reactive (volt-var) curve on SSTI is examined. The most severe impact found arises from the time response of the inverter’s reactive power change. A second-order time response with natural frequency matching the rotor speed deviation oscillation frequency and low-damping ratio quickly drives the system to an unstable region. Although it is highly unlikely that conditions necessary for distributed energy resource-induced oscillations would occur in the field, with knowledge of this vulnerability in mind, inverters' control parameters can be designed to avoid it.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2022

Lattice QCD and the Computational Frontier

The search for new physics requires a joint experimental and theoretical effort. Lattice QCD is already an essential tool for obtaining precise model-free theoretical predictions of the hadronic processes underlying many key experimental searches, such as those involving heavy flavor physics, the anomalous magnetic moment of the muon, nucleon-neutrino scattering, and rare, second-order electroweak processes. As experimental measurements become more precise over the next decade, lattice QCD will play an increasing role in providing the needed matching theoretical precision. Achieving the needed precision requires simulations with lattices with substantially increased resolution. As we push to finer lattice spacing we encounter an array of new challenges. They include algorithmic and software-engineering challenges, challenges in computer technology and design, and challenges in maintaining the necessary human resources. In this white paper we describe those challenges and discuss ways they are being dealt with. Overcoming them is key to supporting the community effort required to deliver the needed theoretical support for experiments in the coming decade.

Boyle, Peter↗

DOE OSTI2022

Preparation for a Measurement of Charge Asymmetry in the Bethe-Heitler Process

We have prepared a measurement of the energy asymmetry in wide- and medium-angle electron/positron pair production off protons and heavy targets. This asymmetry is caused by the interference between the first- and second-order Born diagrams and the Compton scattering diagram. It directly probes aspects of QED, as well as providing a direct measurement of the real part of the Compton amplitude. It will be conducted at the HI??S facility at Duke University, using a 60 MeV photon beam. This dissertation serves as documentation of the preparation stage of the Bethe-Heitler experiment. The major was the recommissioning of the vertical drift chambers previously used in the Q-weak experiment at the Jefferson Lab. Cosmic test runs were conducted, drift time data were collected and efficiency plateaus were measured. We made modifications to the JLAB Hall A analyzer to suit the geometry and drift characteristics of these wire chambers. The analyzer was used for the reconstruction of the trajectories of cosmic ray test runs with the results confirmed by direct measurement of trigger geometry. Spatial and angular resolution is estimated to ~300?? and 0.17° respectively. Geant 4 simulations with generated Bethe-Heitler pairs satisfying theoretical differential cross sections. It was used to check detector acceptance, optimize apparatus layout, and estimate measurable energy asymmetry. The measurable asymmetries from electron/positron pairs with polar angles around between approximately 5° and 8°, azimuthal angles differing by 180°, and energy differing by approximately 9 MeV to 15 MeV are predicted to be above 10%. The kinematics of primary vertices are reconstructed using the data from wire chambers in the simulation. The energy resolution is determined to be better than 1MeV.

Chen, Haoyu↗

DOE OSTI2022

A Study on Surface Texture and Wettability of Femtosecond Laser Treated Aluminum Alloys

This research aims to study the effects of femtosecond laser treatment on surface texture and wettability properties. The first portion of this research studies 2024-T3 aluminum alloy concerning surface texture (e.g., roughness), wettability, and surface free energy. SEM images help aid the researchers in detecting minuscule changes in surface texture. Profilometry extracts topographical data from the surface. A contact angle goniometer measures contact angle, which follows the sessile drop method. Owens, Wendt, Rabel, and Kaelble's method calculates the surface free energy in conjunction with the contact angle. Femtosecond laser modification produces relatively uniform surface morphology at the macroscale. When looking at the microscale, surface morphology differs depending on the interplay between material melting and self-assembly, where the surface becomes rougher after laser treatment. Contact angle results show that all but the control sample and sample 7 exhibit hydrophobic behavior, i.e., contact angle >90°, with Sample 1 having the most significant angle of 115°. The effects of laser parameters on surface energy is apparent. More work is needed to establish correlations among these three quantities: contact angle, surface energy, and laser parameters. The second portion of this research studies aluminum alloy 6061 as the subject material with the primary goal of creating a superhydrophobic surface. A central composite design creates the laser surface texturing design of experiments. SEM images help aid the researchers in detecting minuscule changes in surface texture. A 3D optical profiler extracts topographical data from the surface. The sessile drop method incorporates a contact angle goniometer to measure the contact angle. The response surface method builds a second-order polynomial model for the contact angle and obtains optimized parameters to maximize the contact angle. This research shows that laser surface texturing can generate a wide range of surface profiles and roughness values with geometric features ranging from hundreds of μm to submicron. All three laser parameters (pulse energy, pulse duration, repetition rate) affect surface roughness and contact angle to some degree. To quantify the relationship between the contact angle, pulse energy, and pulse repetition rate, a response surface model for Al 6061 is identified and used to find the optimal conditions of E=214 μJ, tp=10 ps, and fp=2427 Hz with a predicted maximum contact angle of 161°. A confirmation experiment produces a contact angle of 168°, in good agreement with the predicted value.

Angell, Dakota↗

DOE OSTI2024

Validation of Local Structural Loads Computed by OpenFAST Against Measurements From the Focal Experimental Campaign: Preprint

This work presents the validation of the local structural load modeling capability in OpenFAST for floating substructures based on data from the FOCAL experimental campaign. Previously, OpenFAST could only represent the floating substructure as a rigid body, and though this approach can model the global response of the floater in most cases, it is not able to capture the structural loads within its individual members. Consideration of local substructure loads is important for some floating designs, as the pursuit of cost reduction often results in lighter and more flexible structures. To address this limitation, the HydroDyn (hydrodynamics) and SubDyn (substructure dynamics) modules of OpenFAST have been recently extended to account for the flexibility of floating substructures. To validate this new capability, we compare the results obtained by OpenFAST with data measured during the FOCAL experimental campaign, which analyzed a 1:70 scale performance-matched model of the IEA 15-MW reference turbine atop a modified University of Maine VolturnUS-S semisubmersible in a wave basin under the action of both wind and waves. For the purposes of the present work, the most important feature of the experiment is the presence of load cells at the root of each pontoon, and our objective is to assess how well those loads are reproduced by OpenFAST. To model the distributed hydrodynamic and hydrostatic loads along the floating substructure, we adopt a strip-theory approach based on the Morison equation, and we discuss the impact of different hydrodynamic modeling options (wave stretching, MacCamy-Fuchs correction, and second-order wave kinematics) on both motions and loads. For simplicity, we focus on wave-only conditions, both regular and irregular. The results demonstrate good overall agreement for the loads at the root of the pontoons for the waves analyzed in this work, especially given the assumptions and simplifications inherent to a simple strip-theory model.

floating offshore wind turbine↗

DOE OSTI2024

Challenges in Training PINNs: A Loss Landscape Perspective

This paper explores challenges in training Physics Informed Neural Networks (PINNs), emphasizing the role of the loss landscape in the training process. We examine difficulties in minimizing the PINN loss function, particularly due to ill conditioning caused by differential operators in the residual term. We compare gradient-based optimizers Adam, L-BFGS, and their combination Adam+L-FGS, showing the superiority of Adam+L-BFGS, and introduce a novel secondorder optimizer, NysNewton-CG (NNCG), which significantly improves PINN performance. Theoretically, our work elucidates the connection between ill-conditioned differential operators and ill-conditioning in the PINN loss and shows the benefits of combining first- and second-order optimization methods. Our work presents valuable insights and more powerful optimization strategies for training PINNs, which could improve the utility of PINNs for solving difficult partial differential equations.

Rathore, Pratik↗

DOE OSTI2024

Resolution requirements for high-speed droplet impact along a rigid wall

The mechanical and thermal loads that are produced on high-speed projectiles from a droplet are key in the projectile development.To accurately predict the pressure produced along the wall surface during impact, it is important to correctly model the air/water interface of the droplet. Novel modeling approaches such as the Phase-Field enable control of the (numerical) interface thickness. However, the interplay between the grid resolution (including potential adaptive mesh refinement) and the interface thickness is unclear. In this work, the resolution requirements for numerical simulations of a two-dimensional cylindrical water droplet impacting a rigid wall at Mach four are computationally investigated. Numerical simulations are performed using a second-order accurate scheme with adaptive mesh refinement and a Phase-Field interface model. The choice of numerical interface thickness and resolution parameters affects the maximum pressure and location of the maximum pressure along the wall. The overall maximum pressure does not converge even at high resolutions. The number of levels and thickness (number of cells across the interface) play a role in obtaining a well behaved solution.

Burrell, E.↗

DOE OSTI2025

Time correlations from steady-state expectation values

Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.

Górecki, Wojciech [INFN, Pavia]↗

DOE OSTI2025

Time correlations from steady-state expectation values

Górecki, Wojciech [INFN, Pavia]↗

DOE OSTI2020

Pulse Radiolysis Study of Radiation Effect on Molten Salt

The molten salt reactor concept, where nuclear fuel is dissolved in a molten salt that also serves as the heat transfer fluid, is a leading candidate for next generation nuclear reactors. This necessitates a thorough understanding of radiation effects on molten salt media to support the design, development, and deployment of such reactors. Early, pioneering pulse radiolysis molten salt experiments observed key primary radiolysis products such as the solvated electron (esolv?) and dichloride radical anion (Cl2??), but left many fundamental mechanistic and reactivity questions unanswered. Here we report on the reaction kinetics of esolv? and Cl2?? in molten LiCl-KCl eutectic salt doped with Zn2+ ion, using electron pulse radiolysis to observe the transient behavior from nanosecond to microsecond time scales. Experiments were performed at the BNL Laser-Electron Accelerator Facility using a recently-developed high-temperature sample holder. Prompt formation of esolv? and Cl2?? are observed; esolv? decays within hundreds of nanoseconds while Cl2?? decays more slowly by second-order kinetics, more likely by cross-recombination rather than disproportionation. This work was supported as part of the Molten Salts in Extreme Environments Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science.

38 - RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCL↗

DOE OSTI2026

CoLoRe-2LPT: Lyman-$α$ mock catalogues for the validation of DESI cosmological analyses

The Lyman-$α$ (Ly$α$) forest has become a crucial probe for studying the large-scale structure of the universe at high redshift ($z > 2$), providing powerful constraints on Baryon Acoustic Oscillations (BAO) and the full-shape (FS) clustering of matter. As a key ingredient for upcoming BAO and FS analyses, we present a new generation of fast cosmological Ly$α$ mocks based on second-order Lagrangian perturbation theory (2LPT). These new mocks significantly improve upon previous log-normal approaches, both at accurately capturing small scale clustering and at recovering the non-linear broadening of the BAO peak. They are able to reproduce Ly$α$ statistics within $10\%$ of the latest DESI measurement; including the Ly$α$ bias and the redshift-space distortion $β$ parameter, mean transmitted flux, and 1D power spectrum. The corresponding quasar (QSO) clustering is also improved with respect to previous approaches, calibrated against high-resolution Abacus simulations, recovering the observational QSO linear bias to less than $5\%$ and improving redshift-space distortions via 2LPT velocities and the addition of Fingers-of-God effects. Furthermore, these mocks incorporate high column density systems and metal lines, allowing us to explore the effects and systematics induced by these astrophysical contaminants. This new set of mocks has been key for enhancing the modeling and validation of the DESI DR2 Ly$α$ full shape cosmological analysis. This work provides a physically motivated and computationally efficient tool for simulating current and next-generation Ly$α$ surveys and validating FS and BAO analysis.

Bernal, M.F. Ruiz-Herrera [Madrid, CIEMAT] (ORCID:↗

DOE OSTI2026

Higher-order space-charge stability in anisotropic beams: Vlasov-Poisson derivation, refined dispersion relations, and stability charts

The Hofmann stability chart is used to screen working points in space-charge-dominated linacs. We identify two errors in its published higher-order dispersion relations: missing $(1\mp2\hatη^2/α)$ factors in the third-order $S^4$ coupling residues, and a sign error in the stated isotropic reduction of the fourth-order relation. Both corrections follow from Hofmann's Vlasov-Poisson equations without fitted parameters. They reproduce coherent tune-shift coefficients in the author's later monograph that the printed forms miss by 24% and 127%. Mode-resolved figures from a published application agree with the corrected relations and reject the printed forms, indicating an inconsistency between the 1998 equations and the calculations underlying those tested figures. We quantify the effect on the non-oscillatory stability chart. Inside the adopted $S^2\le10$ comparison domain, printed and corrected forms disagree on 0.73-2.11% of cells, with no preferred direction. Among excluded cells, disagreement reaches 22%, and the printed relation over-predicts instability at every sampled anisotropy. This concentration may help explain why the errors persisted, although it does not establish their historical cause. For PIP-II, the corrected chart flags four of thirty-two evaluable periods, including one on a third-order odd branch missed by a second-order screen. This count covers non-oscillatory modes only and remains conditional on an unresolved factor-five disagreement between two codes on transverse emittance growth.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗

DOE OSTI2025

Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.

97 MATHEMATICS AND COMPUTING↗