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DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Mineralized sclerites in the gorgonian coral Leptogorgia chilensis as a natural jamming system

The soft corals (Cnidaria, Octocorallia), a diverse group of colonial marine invertebrates, can reversibly tune their body stiffness in response to external stimuli. This capability is attributed to their dynamic skeletal systems, which consist of thousands of mineralized skeletal elements, called sclerites, embedded within a gel-like matrix that swells/deswells and unjams/jams the sclerites, thus modulating skeletal stiffness. While sclerite morphology is widely used for species identification, its role in the mechanical performance of a soft coral’s skeletal system is largely unknown. Here, we investigated structure-jamming relationships in sclerite-based skeletal architectures using the red gorgonian octocoral Leptogorgia chilensis as a model system. The sclerites of L. chilensis exhibit a shaft-like geometry with two axial branches and two sets of triradiate side branches, which are aligned with the crystallographic symmetry of the constituent magnesium-containing calcite. By combining multiscale three-dimensional (3D) structural characterization, parametric geometrical modeling, 3D printing, mechanical testing, and discrete element simulations, we demonstrate how sclerite geometry achieves a balanced jamming performance in terms of stiffness, weight, strength, and fracture resistance in comparison to alternative geometries parametrically modified from the native sclerites (e.g., changes in the length and number of side branches). Here, we also found that these performance metrics are achieved through the effective interlocking among side and axial branches, which is further enhanced by the fractal-like microscopic spikes on the branch tips. The findings in this natural jamming system offer insights for designing synthetic mechanotunable material architectures for a wide range of applications, from soft robotics to mechanical dampeners.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations

Here, we investigate a projection-based reduced order model of the steady incompressible Navier–Stokes equations for moderate Reynolds numbers. In particular, we construct an “embedded” reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

"embedded" basis↗

DOE OSTI2023

An Assessment of Additively Manufactured Bonded Permanent Magnets for a Distributed Wind Generator

In this paper, we examine and compare the performance of a generator design optimized using additively manufactured NdFeB-SmFeN in nylon-polymer-bonded permanent magnets (PMs) against a generator design with conventional NdFeB sintered PMs. To realize this, a commercially available 15-kW wind generator's rotor is re-optimized using both additively manufactured and sintered NdFeB magnets using simple geometric parameterization that allowed for two specific magnet shapes, namely, arc-shaped and crown-shaped designs. Results showed that for a similar generator performance, the designs with additively manufactured bonded PMs are more cost-competitive in terms of the estimated PM material cost and also have negligible eddy current magnet losses.

additive manufacturing↗

DOE OSTI2025

Spatially Patterned Architectures to Modulate CO 2 Reduction Cascade Catalysis Kinetics

Electrochemical CO 2 reduction using renewable sources of electrical energy holds promise for converting CO 2 into fuels and chemicals. The complex interactions among chemical/electrochemical reactions and mass transport make it difficult to analyze the effect of an individual process on electrode performance based only on experimental methods. Here, we developed a generalized steady-state simulation to describe an electrode surface in which sequential cascade catalysts are patterned in a periodic trench design. If appropriately constructed, this trench geometry is hypothesized to be able to yield a higher net current density for a CO 2 reduction (CO 2 R) cascade reaction. We have used realistic experimental reaction kinetics to investigate the role of trench geometry in mass transport, local microenvironments, and selectivity for a model CO 2 R cascade reaction. The model considers local concentration gradients of bicarbonate species at quasi-equilibrium and catalytic surface reactions based on concentration-dependent Butler–Volmer kinetics. Our results suggest that varying the spatial distribution of active sites plays a significant role in facilitating effective mass transport between active sites, modulating selectivity for the cascade reaction, and enhancing the yield of desirable cascade products. Moreover, we observe that this trench geometry significantly alters the cascade reaction rate by affecting the local pH, which can cause inadvertent depletion of available aqueous CO 2 to limit the CO 2 R cascade kinetics and modest suppression of the hydrogen evolution reaction (HER). The results highlight the trade-offs between mass transport, pH, and reaction kinetics that become apparent only when considering the coupled physics of all processes at the electrode surface. Here, this model can thus serve as a primary tool to build more selective and efficient patterned architectures for the CO 2 R cascade catalysis.

CO2 reduction↗

DOE OSTI2021

Planar Transformer With Asymmetric Integrated Leakage Inductance Using Horizontal Air Gap

This article presents a novel planar-based transformer winding and core structure with controllable leakage inductance generation for integrated magnetics applications. As a result of limitations in integrated magnetics from the literature, a new approach is proposed utilizing semi-interleaved windings and controllable leakage via a leakage flux core leg featuring a horizontal air gap. Here, the proposed transformer design is analyzed via detailed reluctance modeling to determine closed-form equations for the magnetizing and asymmetrically distributed leakage inductances. Next, a genetic-algorithm-based multiobjective design optimization problem is developed, seeking to minimize the core and winding losses of the proposed transformer subject to a set of parametric and geometric constraints in a dc-ac dual-active-bridge topology for microinverter applications. The optimization was extended to include other integrated magnetic structures from the literature, where it is determined that the proposed transformer is superior from the perspectives of efficiency, footprint area, and parasitic capacitance. Based on the results of the optimization analysis, two designs with theoretical transformer California Energy Commission (CEC) efficiency drops (i.e., CEC efficiency reduction specifically due to the transformer loss mechanisms) of 1.19% and 0.83% were fabricated and evaluated for electrical and thermal performance in the proposed 40 V, 400 W microinverter.

42 ENGINEERING↗

DOE OSTI2026

Geometric optics model of Thomson scattering enhanced by parametric coupling

We formulate a theory of Thomson scattering (TS) from inhomogeneous plasmas using a ray-tracing approach. The scattered radiation is described within the eikonal approximation, including convective gain arising from scattering instabilities driven by the TS probe laser. In the limit of a weak probe and vanishing gain, the theory recovers the standard TS cross section and scattered power due to volumetric particle noise. The ray-tracing formalism is implemented in a TS fitting framework, enabling accurate analysis of inhomogeneous plasmas whose background profiles can be provided by large-scale hydrodynamic simulations or experimental diagnostics. Here, several examples of synthetic TS spectra are presented, and further extensions of the theory are discussed.

Carleton, D. E. [University of Alberta, Edmonton, ↗

DOE OSTI2025

Reduced Order Modeling conditioned on monitored features for response and error bounds estimation in engineered systems

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to provide numerical error bounds associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.

Conditional VAEs↗

DOE OSTI2022

Macrovoid resolved simulations of transport through HPRO relevant membrane geometries

Modeling the transport properties such as diffusivity and permeability of high pressure reverse osmosis (HPRO) membranes is critical for the selection and manufacture of membranes suitable for operation under high pressure. These properties can be significantly affected by the changes in heterogeneous pore structures due to compaction. Here, the modeling platform presented in this work resolves the two scale porosity in HPRO relevant membranes. A synthetic membrane geometry is constructed based on available experimental visualizations of pore structures. The simulations directly capture the flow channeling that results from a combination of material properties and geometric features of the macrovoids. A parametric study is presented to account for the transition of flow characteristics from a material governed regime to a macrovoid governed regime. Permeability of the membrane is evaluated using the simulation data and compared with an existing model that scales with the square of tortuosity over a range of material properties. The model is found to perform well under a narrow range of tortuosity while deviating from the calculated permeabilities at extreme conditions. The effective permeability of the membrane is found to vary by at least two orders of magnitude between the two flow regimes. It is also observed that tortuosity is a bounded property with its upper limit determined by the macrovoid geometry. Consequently, the tortuosity based correlations fail near a flow regime that is mainly governed by the macrovoids. The modeled permeability can be more than an order of magnitude smaller than the simulation result. A new model based on flux-weighted porosity of a membrane is introduced and its correlation with tortuosity is studied. The model agrees with the simulated data as, in addition to tortuosity, it also accounts for the flux partition within and outside the flow channels. Such correlations enable extending the existing understanding of flow characteristics to enhance predictability of porous media models.

42 ENGINEERING↗

DOE OSTI2023

CFD Data on a Vertical Axis Wave Turbine

In this study January to July, 2023, different variations of the original geometry of a vertical-axis wave turbine (VAWT) were generated and evaluated for hydrodynamic power efficiency using computational fluid dynamics (CFD). The key geometrical parameters considered in this parametric study included the chord length of the rotor blades and the horizontal semi-axis length. The immersion depth of the rotor was also examined as a key deployment parameter for the wave turbine. The CFD simulation results revealed that a medium chord length of the blade (i.e., the same as that of the baseline design) and a shorter horizontal semi-axis for the guide curve of the blade than that of the baseline design resulted in higher hydrodynamic power to extract. With the most efficient turbine rotor geometry identified in this study, a deployment depth that could assure full submergence of the rotor in waves but as close to the free surface as possible led to a higher hydrodynamic power. These findings revealed a pathway for the improvement of the wave turbine energy efficiency.

16 TIDAL AND WAVE POWER↗

DOE OSTI2020

Shaping High Efficiency, High Temperature Cavity Tubular Solar Central Receivers

High temperature solar receivers are developed in the context of the Gen3 solar thermal power plants, in order to power high efficiency heat-to-electricity cycles. Since particle technology collects and stores high temperature solar heat, CNRS (French National Center for Scientific Research) develops an original technology using fluidized particles as HTF (heat transfer fluid). The targeted particle temperature is around 750 °C, and the walls of the receiver tubes, reach high working temperatures, which impose the design of a cavity receiver to limit the radiative losses. Therefore, the objective of this work is to explore the cavity shape effect on the absorber performances. Geometrical parameters are defined to parametrize the design. The size and shape of the cavity, the aperture-to-absorber distance and its tilt angle. A thermal model of a 50 MW hemi-cylindrical tubular receiver, closed by refractory panels, is developed, which accounts for radiation and convection losses. Parameter ranges that reach a thermal efficiency of at least 85% are explored. This sensitivity analysis allows the definition of cavity shape and dimensions to reach the targeted efficiency. For an aperture-to-absorber distance of 9 m, the 85% efficiency is obtained for aperture areas equal or less than 20 m2 and 25 m2 for high, and low convection losses, respectively.

Gueguen, Ronny (ORCID:0000000252368638)↗

DOE OSTI2025

Scalable phononic metamaterials: Tunable bandgap design and multi-scale experimental validation

Phononic metamaterials offer unprecedented control over wave propagation, making them essential for applications such as vibration isolation, waveguiding, and acoustic filtering. However, achieving scalable and precisely tunable bandgap properties across different length scales remains challenging. This study presents a user-friendly design framework for phononic metamaterials, enabling ultra-wide bandgap tunability (B/ω c ratios up to 172 %) across multiple frequency ranges and scales. Using finite element simulations of a Yablonovite-inspired unit cell, we establish a comprehensive parametric design space that illustrates how geometric parameters, such as sphere size and beam diameter, controls bandgap width and frequency. The scalability and robustness of the framework are validated through experimental testing on additively manufactured structures at both macro (10 mm) and micro (80 µm) scales, fabricated using Stereolithography and Two-Photon Polymerization. Transmission loss measurements, conducted with piezoelectric transducers and laser vibrometry, closely match simulations in the kHz and MHz frequency ranges, confirming the reliability and consistency of the bandgap behavior across scales. This work bridges theory and experiments at multiple scales, offering a practical methodology for the rapid design of phononic metamaterials and expanding their potential for diverse applications across a broad range of frequencies.

36 MATERIALS SCIENCE↗

DOE OSTI2021

DES Y1 results: Splitting growth and geometry to test $\Lambda$CDM

We analyze Dark Energy Survey (DES) data to constrain a cosmological model where a subset of parameters—focusing on Ωm—are split into versions associated with structure growth (e.g., Ωmgrow) and expansion history (e.g., Ωmgeo). Once the parameters have been specified for the ΛCDM cosmological model, which includes general relativity as a theory of gravity, it uniquely predicts the evolution of both geometry (distances) and the growth of structure over cosmic time. Any inconsistency between measurements of geometry and growth could therefore indicate a breakdown of that model. Our growth-geometry split approach therefore serves both as a (largely) model-independent test for beyond-ΛCDM physics, and as a means to characterize how DES observables provide cosmological information. We analyze the same multiprobe DES data as [Phys. Rev. Lett. 122, 171301 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.171301] : DES Year 1 (Y1) galaxy clustering and weak lensing, which are sensitive to both growth and geometry, as well as Y1 BAO and Y3 supernovae, which probe geometry. We additionally include external geometric information from BOSS DR12 BAO and a compressed Planck 2015 likelihood, and external growth information from BOSS DR12 RSD. We find no significant disagreement with Ωmgrow=Ωmgeo. When DES and external data are analyzed separately, degeneracies with neutrino mass and intrinsic alignments limit our ability to measure Ωmgrow, but combining DES with external data allows us to constrain both growth and geometric quantities. We also consider a parametrization where we split both Ωm and w, but find that even our most constraining data combination is unable to separately constrain Ωmgrow and wgrow. Relative to ΛCDM, splitting growth and geometry weakens bounds on σ8 but does not alter constraints on h.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Prediction of dislocation - grain boundary interactions in FCC aluminum bicrystals using a modified continuum criterion and machine learning methods

Mechanical properties of metals such as strength and toughness are strongly correlated to complex interactions between various defects in the crystalline structure. While elementary interactions between these defects have been investigated using recent micro- and nano-characterization techniques, understanding of the detailed interaction mechanisms has hardly been obtained. To understand defect-driven plasticity at various time and length scales, it is necessary to formulate a general guideline to predict both the interaction type (transmission or reflection) and the dislocation's subsequent slip system after the interaction. Many criteria based on the geometric alignment of the defects have been developed to predict this phenomenon, but these have yet to be found to be accurate when applied to general data sets of grain boundaries (GBs). With this motivation, we conduct a systematic study using molecular dynamics (MD) models of bicrystals to analyze defect interaction process between a prismatic dislocation loop and eleven different grain boundaries of the following character: three tilt, three twist, and five mixed. Based on the MD observations, two new prediction methods are developed: the first is a new data-driven parametric score function based on the classical geometric criteria, and the second is by applying Gaussian process machine learning methods to find the probability distribution of a hidden function. In conclusion, the proposed data-driven prediction methods could pave a new way to predict the unit interaction of dislocations with various GBs, which could show much higher accuracy compared to pre-existing geometric criteria.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Toward Robust and Routine Determination of Mw for Small Earthquakes: Application to the 2020 Mw 5.7 Magna, Utah, Seismic Sequence

To better characterize seismic hazard, particularly, for induced seismicity, there is an increasing interest in methods to estimate moment magnitude (M w ) for small earthquakes. M w is generally preferred over other magnitude types, but, it is difficult to estimate M w for earthquakes with local magnitude (M L ) <3-3.5, using conventional moment tensor (MT) inversion. The 2020 M ww 5.7 Magna, Utah, seismic sequence provides an opportunity to illustrate and evaluate the value of spectral methods for this purpose. Starting with a high-quality seismic catalog of 2103 earthquakes (M L <5.6), we estimate M w using two independent spectral methods—one based on direct waves, yielding M w,direct , and the other based on coda waves, yielding M w,coda . For the direct-wave method, we present a non-parametric (NP) inversion scheme that solves for apparent geometrical spreading, G(R), and site effects (S), similar to other NP procedures that have been used to calibrate regional M L scales. The NP inversion is constrained using M ws derived from MTs for nine events in the Magna sequence. We recover statistically robust and physically reasonable G(R) and S and compute M w,direct for 635 Magna earthquakes down to M L 0.7. For the coda-wave method, we consider two separate calibration schemes involving previous MT solutions and compute M w,coda for 311 earthquakes down to M L 1.0. For 280 of the events that were processed with both methods—M w,direct and M w,coda —are strongly correlated (r = 0.98), with a mean difference of only 0.05. We compare M w,direct and M w,coda with M L and find reasonably good agreement for M L <3.6 with the theoretically predicted relationship of M w =(2/3)M L +C, in which C is a regional constant. Our results imply that seismic network operators can use spectral-based M w estimates to replace M L estimates for events with M L ≥1.0, and possibly smaller. The main requirement is the existence of a small number of MT solutions for calibration purposes.

58 GEOSCIENCES↗

DOE OSTI2024

Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding Numbers

Point containment queries for regions bound by watertight geometric surfaces, i.e., closed and without self-intersections, can be evaluated straightforwardly with a number of well-studied algorithms. When this assumption on domain geometry is not met, such methods are either unusable, or prone to misclassifications that can lead to cascading errors in downstream applications. More robust point classification schemes based on generalized winding numbers have been proposed, as they are indifferent to these imperfections. However, existing algorithms are limited to point clouds and collections of linear elements. We extend this methodology to encompass more general curved shapes with an algorithm that evaluates the winding number scalar field over unstructured collections of rational parametric curves. In particular, we evaluate the winding number for each curve independently, making the derived containment query robust to how the curves are arranged. We ensure geometric fidelity in our queries by treating each curve as equivalent to an adaptively constructed polyline that provably has the same generalized winding number at the point of interest. Our algorithm is numerically stable for points that are arbitrarily close to the model, and explicitly treats points that are coincident with curves. We demonstrate the improvements in computational performance granted by this method over conventional techniques as well as the robustness induced by its application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Geometric prior of multi-resolution yielding manifolds and the local closest point projection for nearly non-smooth plasticity

Elastoplasticity models often introduce a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. Here this paper introduces a new alternative where the yield envelope is represented by a manifold of which the topology and the geometry are learned from a set of data points in a parametric space (e.g. principal stress space, π-plane). Here, deep geometric learning enables us to reconstruct a highly complex yield envelope by breaking it down into multiple coordinate charts. The global atlas that consists of these coordinate charts in return allows us to represent the yield surface via multiple overlapping patches, each with a specific local parametrization. This setup provides several advantages over the classical implicit function representation approach. For instance, the availability of coordinate charts enables us to introduce an alternative stress integration algorithm where the trial stress may project directly on a local patch and hence circumvent the issues related to non-smoothness and the lack of convexity of yield surfaces. Meanwhile, the local parametric approach also enables us to predict hardening/softening locally in the parametric space, even without complete knowledge of the yield surface. Comparisons between the classical yield function approach on the non-smooth plasticity and anisotropic cam-clay plasticity model are provided to demonstrate the capacity of the models for highly precise yield surface and the feasibility of the implementation of the learned model in the local stress integration algorithm.

42 ENGINEERING↗

DOE OSTI2022

Summary of Geometric Parameters and Their Effects on Performance of U-10Mo Fuel Plates

A monolithic plate-type fuel system has been under development to convert high-performance test reactors from highly enriched uranium to low-enrichment uranium fuels and is now moving into the qualification phase, a predecessor to the timely conversion of the target reactors. To qualify this fuel system, the plates must meet safety standards and perform well in a reactor. The plates must maintain mechanical integrity, exhibit geometric stability, and have stable and predictable in-reactor behavior. The requirement to maintain mechanical integrity under normal operating conditions is primarily demonstrated by successful testing. However, each high-performance reactor employs a distinct design, resulting in distinct plate geometries, with unique features, attributes, irregularities, and tolerances. Due to the abundance of such distinct geometric varieties, a single “generic” plate geometry capturing all extremes is not achievable. It is also impractical to test each of these proposed designs in a reactor. This limitation necessitates cautious evaluations since the thermomechanical response of a plate with a certain geometry may not be representative for a plate with a significantly different geometry. To address concerns related to in-reactor plate performance, large set of sensitivity studies were performed. These parametric studies aimed to better understand irradiation performance, while evaluating the sensitivity of results to various modeling inputs, including geometric, operational, and material parameters. This work studied selected geometric parameters based on provided fuel specifications and performed a series of parametric simulations. The resulting temperature, displacement, and stress strains were comparatively evaluated to determine the effects of various geometric parameters. This draft provides a “high-level summary” of our parametric sensitivity studies and summarizes the key findings.

42 ENGINEERING↗