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DOE OSTI2025

On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation

The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. Here, this work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.

Hamiltonian mechanics↗

DOE OSTI2024

Experimental and numerical investigation of fracture conductivity between non-smooth rock surfaces with and without proppant

The enhancement of fracture conductivity is vital for the efficient recovery of subsurface resources, such as geothermal energy and petroleum hydrocarbons. Proppants, granular materials injected into hydraulic fractures to maintain their conductivity, have been studied primarily in the context of smooth fractures (i.e., fractures between smooth rock surfaces). However, non-smooth fractures (i.e., fractures between rough rock surfaces) are common in geoenergy reservoirs and thus require further investigations. In this study, we conducted laboratory measurements of fracture conductivity on shale slabs with non-smooth surfaces and carried out numerical simulation using the lattice Boltzmann (LB) method, which aimed to investigate the conductivity of non-smooth fractures with and without proppants placement. When ceramic proppant with an areal concentration of 2 lb/ft 2 was placed in the fracture, the conductivity was enhanced by roughly 3-8 times compared to fractures without proppant. In fractures with proppant, gas-measured conductivity was higher than that measured with water due to proppant embedment caused by water. The experiments demonstrate the advantages of using proppant in fractures, even if the rock surface roughness can provide certain fracture conductivity via the self-propping mechanism. For fractures without proppants, high rock surface roughness is not necessarily favorable for enhancing fracture conductivity because the self-propping mechanism requires shear slip along the fracture surface. If there is no shear slip, high rock surface roughness can cause a detrimental effect on the fracture conductivity due to the interlocking effect. Utilizing advanced experimental equipment and LB modeling, this research explores the interplays between proppant placement, fracture geometry, and stress conditions to develop a comprehensive understanding of the productivity in non-smooth fractures. Further, the outcomes of this investigation indicate the importance of creating fractures with surface roughness during hydraulic fracturing and will contribute to the development of more efficient stimulation techniques for subsurface energy extraction.

15 GEOTHERMAL ENERGY↗

DOE OSTI2025

A Smoothed Augmented Lagrangian Framework for Convex Optimization with Nonsmooth Constraints

Augmented Lagrangian (AL) methods have proven remarkably useful in solving optimization problems with complicated constraints. The last decade has seen the development of overall complexity guarantees for inexact AL variants. Yet, a crucial gap persists in addressing nonsmooth convex constraints. To this end, we present a smoothed augmented Lagrangian (AL) framework where nonsmooth terms are progressively smoothed with a smoothing parameter $\eta _k$ . The resulting AL subproblems are $\eta _k$ -smooth, allowing for leveraging accelerated schemes. By a careful selection of the inexactness level $\epsilon _k$ (for inexact subproblem resolution), the penalty parameter $\rho _k$ , and smoothing parameter $\eta _k$ at epoch k, we derive rate and complexity guarantees of $\tilde{\mathcal {O}}(1/{\varepsilon }^{3/2})$ and $\tilde{\mathcal {O}}(1/{\varepsilon })$ in convex and strongly convex regimes for computing an ${\varepsilon }$ -optimal solution, when $\rho _k$ increases at a geometric rate, a significant improvement over the best available guarantees for AL schemes for convex programs with nonsmooth constraints. Analogous guarantees are developed for settings with $\rho _k = \rho$ as well as $\eta _k = \eta$ . Preliminary numerics on a fused Lasso problem display promise.

augmented Lagrangian↗

DOE OSTI2025

Surface smoothing for laser powder-bed Ti-6Al-4V by a transient liquid phase

Surface roughness is the primary driver of fatigue for additively manufactured metals. To address surface roughness, this work introduces a new method to smooth features beyond line-of-sight without material removal. The method applies a coating that triggers local surface remelting by activating a eutectic reaction during heat treatment. The associated liquid phase then wets and isothermally solidifies into a smoother surface. For Ti-6Al-4V fabricated with laser powder bed fusion, samples with and without TLP smoothing (using a Cu coating) were characterized with a suite of techniques, including mechanical testing, electron backscatter diffraction, synchrotron X-ray tomography, and fractography. TLP smoothing reduced surface roughness by 80% and amplified compressive residual stress at the surface by about 50%. With statistically equivalent virtual microstructures, crystal plasticity scrutinized the roles of phases, porosity, and surface roughness. Although the tensile strain-to-failure was reduced to 1% strain, the TLP smoothing process increased high-cycle fatigue strength by about 20% compared to control samples, pointing to future opportunities to optimize the new process through various coating compositions and heat treatment schedules. Overall, this work establishes a new paradigm for treating surfaces of materials for smoothness and compressive residual stress.

Additive manufacturing↗

DOE OSTI2025

Optimizing the Smoothness and Thickness Uniformity of Thin-Film Parylene-N Vapor-Deposited Coatings for Inertial Confinement Fusion Experiments

Polymer coatings with submicrometer smoothness and constant thickness are a required component in a variety of inertial confinement fusion experiments. Smoothness is important for minimizing Rayleigh-Taylor-driven hydrodynamic instabilities, and uniform thickness is important for uniform shock propagation and shell convergence, both of which are critical phenomena that affect the experiment. The preferred polymer coating method is to vapor deposit the parylene-N polymer because it provides nominally smooth conformal coatings. As the coating thickness exceeds 5 µm, however, dome-shaped nodular growth defects develop and the thickness will vary by up to 17% over a distance of 3 cm. This study presents a deterministic method for achieving uniform film thicknesses with ±2% variability over 3 cm and a predictive method to control the thickness to within 5% of the desired value. A coating smoothness of ∼50 nm rms, measured over 40 000 µm 2 , was achieved by adding additional surfaces near the substrates. This additional area improved the thickness uniformity, an effect that is attributed to the low sticking coefficient of the parylene monomer.

chemical vapor deposition (CVD)↗

DOE OSTI2024

Non-smooth Bayesian optimization in tuning scientific applications

Tuning algorithmic parameters to optimize the performance of large, complicated computational codes is an important problem involving finding the optima and identifying regimes defined by non-smooth boundaries in black-box functions. Within the Bayesian optimization framework, the Gaussian process surrogate model produces smooth mean functions, but functions in the tuning problem are often non-smooth, which is exacerbated by the fact that we usually have limited sequential samples from the black-box function. Here, motivated by these issues encountered in tuning, we propose a novel Gaussian process model called a clustered Gaussian process (cGP), where the components are dynamically updated by clustering. In our studies, the performance of cGP can be better than stationary GPs in nearly 90% of the experiments and better than non-stationary GPs in nearly 70% of the repeated experiments while requiring less computational cost. cGP provides a novel approach for dynamic GP, computes more efficiently than recursive partitioning, and discovers non-smoothness regimes. We provide extensive experiments including high-performance computing (HPC) and industrial simulation functions to show the effectiveness of our methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

In Situ MOVPE Smoothing of Acoustically Spalled GaAs for Substrate Reuse

High material costs, especially for substrates, have limited the widespread adoption of III-V photovoltaics. A potential to reduce this cost is to reuse the III-V substrate via acoustic spalling, however this technique can leave a rough surface, hindering subsequent device performance. This research investigates the potential of using metalorganic vapor-phase epitaxy growth as a buffer layer to smooth the surface of acoustically spalled germanium and gallium arsenide (GaAs) substrates for improved III-V photovoltaic cell yield and performance, while retaining the maximum number of reuses of a substrate. Three potential smoothing layers were explored: lightly doped C:GaAs, highly doped Se:GaInP, and lightly doped Se:GaInP. C:GaAs showed the most promise as a smoothing layer, while Se:GaInP tended to conform to the underlying morphology, potentially increasing roughness in some areas. Utilizing 5 ..mu..m of C:GaAs as a planarizing buffer increased the average efficiency (without an antireflection coating) from an as-spalled baseline from 2.1% to 4.9% and performing a 5-min 30 degrees C 8:1:1 H2SO4:H2O2:H2O etch prior to a 5 ..mu..m of C:GaAs as a planarizing buffer further increased efficiency to 11.1%.

14 SOLAR ENERGY↗

DOE OSTI2025

Achieving Electrode Smoothing by Controlling the Nucleation Phase of Metal Deposition Through Polymer‐Substrate Binding

Polymer additives [like polyethylene oxide (PEO)] are widely used for smooth electrode deposition in aqueous zinc and many other battery systems. However, the precise mechanism by which they regulate morphology and suppress dendrite formation remains unclear. In this study, the knowledge gap is addressed by using in situ electrochemical atomic force microscopy to directly observe the interfacial evolution during Zn electrodeposition and polymer adsorption on Cu substrates in the presence of varying concentrations of ZnSO 4 and PEO. Contrary to previous literature assumptions, which emphasize the binding to the growing Zn crystal surfaces or Zn 2+ ions, the results demonstrate that PEO smooths Zn films by promoting nucleation of (002)-oriented Zn platelets through interactions with the Cu substrate. Density functional theory simulations support this finding by showing that PEO adsorption on Cu modifies the interfacial energy of Zn/Cu/electrolyte interfaces, favoring the stabilization of Zn (002) on the Cu substrate, as well as confines Zn electrodeposition to a narrow near-surface region. In conclusion, these findings elucidate a novel design principle for electrode smoothing, emphasizing the importance of substrate selection paired with polymer additives that exhibit an attractive interaction with the substrate but minimal interaction with growing crystals, offering a mechanistic perspective for improved battery performance.

Electrodeposition↗

DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗

DOE OSTI2025

Low-mode nonuniformity in direct-drive ICF implosions due to laser smoothing techniques employed on OMEGA

For successful laser-direct-drive inertial confinement fusion implosions, the laser irradiation must be highly uniform over the target surface. On OMEGA, multiple laser beams are used to illuminate targets quasi-uniformly. High-mode-number nonuniformities due to laser speckle on each individual beam are reduced by splitting each beam into two orthogonal polarizations (i.e., polarization smoothing, or PS) and a range of wavelengths (i.e., smoothing by spectral dispersion) that are dispersed at the target plane. However, cross-beam energy transfer (CBET) is sensitive to both the polarizations and wavelengths of the interacting beams, so the interplay between CBET and the laser-smoothing schemes results in unique intensity variation across each beam profile, which is a systematic source of low-mode drive nonuniformity on OMEGA. Here, we model these effects and find that the predicted ℓ = 1 mode in the laser-absorption distribution is consistent with the systematic core-flow direction that has been determined from the OMEGA implosion database. We also observe good agreement with the measured core-flow directions for two specific sets of implosions (one with PS, the other without PS) when we also account for the measured beam mispointing and the beam power imbalance.

Crossed beam scattering↗

DOE OSTI2024

Smoothing and flattening the universe through slow contraction versus inflation

In a systematic study, we use an equivalent pair of improved numerical relativity codes based on a tetrad-formulation of the classical Einstein-scalar field equations to examine whether slow contraction or inflation (or both) can resolve the homogeneity, isotropy and flatness problems. Our finding, based on a set of gauge/frame invariant diagnostics and the models considered, is that slow contraction robustly and rapidly smooths and flattens spacetime beginning from initial conditions that are outside the perturbative regime of the flat Friedmann-Robertson-Walker metric, whereas inflation fails these tests. We present new numerical evidence supporting the conjecture that the combination of ultralocal evolution and an effective equation-of-state with pressure much greater than energy density is the key to having robust and rapid smoothing. The opposite of ultralocality occurs in expanding spacetimes, which is the leading obstruction to smoothing following a big bang.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Demonstration of controlled spatial incoherence for beam smoothing

A concept for beam smoothing of high-energy laser systems is demonstrated. Multiple coherent beams are multiplexed so that their incoherent mix decreases the far-field nonuniformity after random spatial phase modulation introduced by a phase plate. Modeling shows that the incoherent mix effectively leads to the expected scaling in terms of the number of uncorrelated beams, and that spatial multiplexing can be combined with smoothing by spectral dispersion. The results of an experimental demonstration of this concept with up to six beams, leading to more than 40 modes with polarization multiplexing and angular dispersion, are consistent with expectations. The potential practical advantages of this smoothing scheme and future developments are discussed.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗

DOE OSTI2025

Overset-Grid Method with Smooth Orbital Partitioning for Molecular Scattering Calculations

To solve molecular photoionization and electron scattering problems, we use an overset-grid representation of electronic continuum functions, which has an extended central spherical grid that overlaps small spherical grids (subgrids) centered on each atom of a polyatomic molecule. Here, in this work, we present an improved algorithm that smoothly partitions the total wave function between the central grid and the atomic subgrids. The smooth partitioning allows one to use approximately one-fourth the number of partial waves on the central grid compared to our previous implementation with switching functions. The resulting numerical method for treating electron scattering and photoionization of polyatomic molecules combines the accuracy and flexibility of pure numerical grid representations with the rapid convergence of hybrid combinations of atom-centered basis-set expansions and grid methods. The overset-grid representation is implemented using the complex Kohn variational principle for scattering and photoionization amplitudes. The faster convergence with respect to the number of central grid partial waves is demonstrated and accuracy is verified by comparisons with the previous implementation and with far more computationally demanding single-center numerical expansions in electron-molecule scattering and photoionization calculations on the neon dimer (Ne 2 ) system, carbon tetrafluoride (CF 4 ) molecule, and the pyridine (C 5 H 5 N) molecule in the static-exchange approximation.

Molecules↗

DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

From Sim to Real: A Pipeline for Training and Deploying Traffic Smoothing Cruise Controllers

Designing and validating controllers for connected and automated vehicles to enhance traffic flow presents significant challenges, from the complexity of replicating real-world stop-and-go traffic dynamics in simulation, to the intricacies involved in transitioning from simulation to actual deployment. In this work, we present a full pipeline from data collection to controller deployment. Specifically, we collect 772 km of driving data from the I-24 in Tennessee, and use it to build a one-lane simulator, placing simulated vehicles behind real-world trajectories. Using policy-gradient methods with an asymmetric critic, we improve fuel efficiency by over 10% when simulating congested scenarios. Our comprehensive approach includes reinforcement learning for controller training, software verification, hardware validation and setup, and navigating various sim-to-real challenges. Furthermore, we analyze the controller's behavior and wave-smoothing properties, and deploy it on four Toyota Rav4’s in a real-world validation experiment on the I-24. Lastly, we release the driving dataset, the simulator and the trained controller, to enable future benchmarking and controller design.

42 ENGINEERING↗

DOE OSTI2025

Smooth splitting and zeros from on-shell recursion

We describe a new approach to understanding the origins of recently discovered “hidden zeros” and “smooth splitting” of tree-level amplitudes in Tr ϕ 3 , Non-Linear Sigma Model (NLSM), Yang-Mill-Scalar (YMS) and the special Galileon. Introducing a new type of linear shift in kinematic space we demonstrate that the mysterious splitting formulae follow from a simple contour integration argument in the style of on-shell recursion. The argument makes use of only standard notions of tree-level factorization on propagators, but assumes improved UV behavior in the form of the absence of a residue at infinity. In the case of Tr ϕ 3 and NLSM this is proven by identifying our shift as a special case of a more general construction called a g-vector shift; in the case of YMS it remains an unproven conjecture. This recursive perspective leads to numerous new results: we derive generalizations of the splitting formulae on more relaxed near-zero kinematics, including interesting new kinematic limits in which the amplitude splits into a triple-product; we also demonstrate that the uncolored special Galileon model has improved UV scaling and hence also splits. We also investigate the possible realization of hidden zeros in four dimensions. The conditions under which the dimensionality constraints are compatible with zero kinematics is investigated in detail for Tr ϕ 3 and YMS; for the latter we find they can be realized only with certain restrictions on external helicity states. The realizable 4d zeros are proven by a similar recursive argument based on BCFW and is found to generalize to a new class of intrinsically 4d “helicity zeros” present in all sectors of YM and also gravity.

effective field theories↗

DOE OSTI2025

Au assisted smooth ultrathin epitaxial ZnO film grown by pulsed laser deposition on sapphire(0001)

High quality ZnO has applications in photonics and electronics. Literature has shown that continuous, but rough ZnO film can be grown on sapphire substrate by pulsed laser deposition (PLD). In this work, ZnO and Au were co-deposited by PLD on sapphire(0001) substrates from a single ZnO target overlaid with an Au strip that serves as a catalyst. The reflection high-energy electron diffraction (RHEED) patterns show paired double stripes from sample of ZnO-Au where the difference of in-plane lattice parameters between ZnO and Au is 11.4 %. The two-dimensional (2D) reciprocal space maps constructed from azimuthal RHEED (ARHEED) patterns reveal parallel epitaxial relationship between ZnO and Au in the continuous ZnO-Au film on sapphire substrate. Transmission electron microscopy (TEM) cross section images and energy dispersive spectroscopy maps show a minute amount of Au nanocrystals distributed in the entire ultrathin ZnO film. Atomic force microscopy shows the root-mean-square roughness of the surface of ultrathin ZnO film with Au is in the sub-nm range. The ARHEED and TEM results show that a couple of atomic percentages of Au co-deposited with ZnO catalyzes the growth of smooth ultrathin epitaxial ZnO film.

36 MATERIALS SCIENCE↗