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DOE OSTI2022

Unsupervised discovery of nonlinear plasma physics using differentiable kinetic simulations

Plasma supports collective modes and particle–wave interactions that lead to complex behaviour in, for example, inertial fusion energy applications. While plasma can sometimes be modelled as a charged fluid, a kinetic description is often crucial for studying nonlinear effects in the higher-dimensional momentum–position phase space that describes the full complexity of the plasma dynamics. We create a differentiable solver for the three-dimensional partial-differential equation describing the plasma kinetics and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks that provide forcing function parameters to the differentiable solver given a set of initial conditions. We apply this to an inertial-fusion-relevant configuration and find that the optimization process exploits a novel physical effect.

plasma nonlinear phenomena↗

DOE OSTI2024

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Mathematics↗

DOE OSTI2026

An Anisotropic Yield and Damage Material Model to Improve the Contact Pressure Analysis in a Biomass Shredding System

Size reduction systems used in biomass processing break biomass into smaller pieces by utilizing the kinetic energy from the sharp rotating blades. Abrasive and/or erosive wear caused by biomass comminution results in blade wear of the sharp edged cutters, deteriorating the process efficiency. Here, this study aims to optimize the blade design and improve the system efficiency by attempting to understand the interactions between the blades and biomass particles. Since real-time monitoring of these interactions is impractical during operation, mechanical simulations offer a viable alternative for investigating the shredding process. Yet, the irregular geometry and complex mechanical properties of biomass—such as the anisotropic nature of woodchips and their nonlinear fracture behavior—pose significant challenges for accurately simulating contact pressure. In this work an anisotropic yield material model, along with a damage initiation and evolution function, is applied to the woodchip particle to study the contact pressure on shredder blade, offering a scientific basis for improved blade design and process efficiency. This approach can be extended to other biomass processing systems with similar anisotropic feedstocks, making it a valuable tool for advancing sustainable biomass utilization.

09 - BIOMASS FUELS↗

DOE OSTI2021

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

German, Péter (ORCID:0000000307285283)↗

DOE OSTI2023

Code for multi-shape Gaussian process (GP) fitting with uncertainty quantification (UQ)

This is code associated with the publication “Nonparametric Multi-shape Modeling with Uncertainty Quantification,” authored by Hengrui Luo (Lawrence Berkeley National Laboratory) and Justin Strait (Los Alamos National Laboratory). The code is used to fit multiple-output Gaussian process (GP) models of planar closed curves to collections of ordered point sets, allowing for flexible nonlinear prediction of the underlying curve under dense or sparse point set samplings and with or without noise, as well as tractable uncertainty quantification. To do this, we employ use of a periodic kernel to account for the nonlinear input space of closed curves, and combine with coregionalization models to account for dependence both (i) between curve coordinates, and (ii) between pairs of curves. Functions in the code are capable of fitting these models, as well as performing additional tasks with the fitted curves such as (a) shape registration and alignment, (b) shape averaging, and (c) fitting for curve sub-populations / clusters.

Strait, Justin↗

DOE OSTI2024

Excitation protocols for nonlinear phononics in bismuth and antimony

Here, we study the optical generation and control of coherent phonons in elemental bismuth (Bi) and antimony (Sb) using a classical equation of motion informed by first-principles calculations of the potential energy surface and the frequency-dependent macroscopic dielectric function along the zone-centered optical phonon coordinates. Using this approach, we demonstrate that phonons with the largest optomechanical couplings also have the strongest degree of anharmonicity among the zone-centered modes, a result of the broken-symmetry structural ground state of Bi and Sb. We show how this anharmonicity, explaining the light-induced phonon softening observed in experiments, prevents the application of standard phonon-amplification and annihilation protocols. We introduce a simple linearization protocol that extends the use of such protocols to the case of anharmonic phonons in broken-symmetry materials, and demonstrate its efficiency at high displacement amplitudes. Our formalism and results provide a path for improving optical control in nonlinear phononics.

36 MATERIALS SCIENCE↗

DOE OSTI2023

The brighter-fatter effect in the JWST MIRI Si:As IBC detectors: I. Observations, impact on science, and modeling

Context.The Mid-Infrared Instrument (MIRI) on board theJames WebbSpace Telescope (JWST) uses three Si:As impurity band conduction (IBC) detector arrays. The output voltage level of each MIRI detector pixel is digitally recorded by sampling up the ramp. For uniform or low-contrast illumination, the pixel ramps become nonlinear in a predictable way, but in areas of high contrast, the nonlinearity curve becomes much more complex. The origin of the effect is poorly understood and currently not calibrated out of the data. Aims.We provide observational evidence of the brighter-fatter effect (BFE) in MIRI conventional and high-contrast coronagraphic imaging, low-resolution spectroscopy, and medium-resolution spectroscopy data, and we investigate the physical mechanism that gives rise to the effect on the MIRI detector pixel raw voltage integration ramps. Methods.We used public data from the JWST/MIRI commissioning and Cycle 1 phase. We also developed a numerical electrostatic model of the MIRI detectors using a modified version of the publicPoisson_CCDcode. Results.We find that the physical mechanism behind the BFE manifesting in MIRI data is fundamentally different to that of charge-coupled devices and photodiode arrays such as the Hawaii-XRG near-infrared detectors used by the NIRISS, NIRCam, and NIRSpec instruments on board JWST. Observationally, the BFE makes the JWST MIRI data yield 10–25% larger point sources and spectral line profiles as a function of the relative level of de-biasing of neighboring detector pixels. This broadening impacts the MIRI absolute flux calibration, time-series observations of faint companions, and point spread function modeling and subtraction. We also find that the intra-pixel 2D profile of the shrinking Si:As IBC detector depletion region directly impacts the accuracy of the pixel ramp nonlinearity calibration model.

Astronomy & Astrophysics↗

DOE OSTI2020

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

The Green's Function Model Intercomparison Project (GFMIP) Protocol

The atmospheric Green's function method is a technique for modeling the response of the atmosphere to changes in the spatial field of surface temperature. While early studies applied this method to changes in atmospheric circulation, it has also become an important tool to understand changes in radiative feedbacks due to evolving patterns of warming, a phenomenon called the “pattern effect.” To better study this method, this paper presents a protocol for creating atmospheric Green's functions to serve as the basis for a model intercomparison project, GFMIP. The protocol has been developed using a series of sensitivity tests performed with the HadAM3 atmosphere-only general circulation model, along with existing and new simulations from other models. Our preliminary results have uncovered nonlinearities in the response of the atmosphere to surface temperature changes, including an asymmetrical response to warming versus cooling patch perturbations, and a change in the dependence of the response on the magnitude and size of the patches. These nonlinearities suggest that the pattern effect may depend on the heterogeneity of warming as well as its location. These experiments have also revealed tradeoffs in experimental design between patch size, perturbation strength, and the length of control and patch simulations. The protocol chosen on the basis of these experiments balances scientific utility with the simulation time and setup required by the Green's function approach. Running these simulations will further our understanding of many aspects of atmospheric response, from the pattern effect and radiative feedbacks to changes in circulation, cloudiness, and precipitation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Integrated control of individual plasma scalars with simultaneous neoclassical tearing-mode suppression

A novel integrated-control architecture has been tested in nonlinear, one-dimensional simulations using the control-oriented transport simulator (COTSIM©) and in DIII-D experiments. Integrated architectures that can perform continuous-mission control while also handling off-normal events will be vital in future reactor-grade tokamaks. Continuous-mission controllers for individual magnetic and kinetic scalars (thermal stored-energy (W), volume-average toroidal rotation (Ω Φ ), and safety factor profile (q) at different spatial locations) have been integrated in this work with event-triggered neoclassical tearing-mode (NTM) suppression controllers by combining them into an architecture augmented by a supervisory and exception handling (S&EH) system and an actuator management (AM) system. Here, the AM system, which enables the integration of competing controllers, solves in real time a nonlinear optimization problem that takes into account the high-level control priorities dictated by the S&EH system. The resulting architecture offers a high level of integration and some of the functionalities that will be required to fulfill the advanced-control requirements anticipated for ITER. Initial simulations using COTSIM suggest that the plasma performance and its MHD stability may be improved under integrated feedback control. In addition, the integrated-control architecture has been implemented in the DIII-D plasma control system and tested experimentally for the first time ever in DIII-D in a high-q min scenario, which is a candidate for steady-state operation in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Remote quantification of Cm(III) and HNO 3 by fluorescence spectroscopy and chemometrics

A unique approach to remotely quantify Cm(III) (0–100 µg mL −1 ) in HNO 3 (1–12 M) using steady-state laser fluorescence spectroscopy and multivariate regression models was developed. Photoluminescence is amenable to remote measurements using fiber-optic cables and is sensitive to numerous lanthanide and actinide species. In-line measurements can provide feedback to support complex processing in harsh environments (e.g., hot cells) to help guide and optimize radiochemical separations. In this work, Cm(III) spectra were acquired remotely in a glove box as a function of HNO 3 concentration to better understand spectral characteristics and evaluate the utility of multivariate regression models in this system. Furthermore, the Cm(III) fluorescence peak shape, width, position, and intensity changed significantly as a function of HNO 3 concentration, likely because of the displacement of emission quenching inner-sphere water molecules and complexation with nitrate ions. Despite significant covariance and nonlinearity in the data, a D-optimal design strategy successfully minimized training set sample size and was used to build effective partial least squares regression models for Cm(III) and HNO 3 concentrations without a priori knowledge of solution conditions. Chemometrics for modeling complex fluorescence spectra are promising and may find widespread applicability for online analysis in numerous chemical systems found in the nuclear field.

Actinide↗

DOE OSTI2025

Quantum sensing of paramagnetic analytes by nanodiamonds in levitated microdroplets and aqueous solutions

Nanodiamonds (ND) hosting negatively charged nitrogen-vacancy (NV-) color centers have received attention for applications in magnetic field, electric field, chemical, and bio-sensing. The versatility of these probes is their excellent room-temperature optical and spin properties, along with their small size, functionalized surfaces and resistance to bleaching, making them ideal as nanoscopic sensors in picoliter volumes (e.g. single cells, but also microcompartments and aerosols). For quantitative ND-NV- sensing of paramagnetic analytes in such contexts, however, there remains an incomplete understanding of how factors related to the aqueous phase environment control detection efficiency. To address this, optically detected magnetic resonance (ODMR) is measured in bulk macroscale solutions and single levitated microdroplets as a function of Gd+3 concentration (340 nM to 1.5 mM), nanodiamond size, pH, competitor ions, and ligands. The ODMR response to [Gd+3] is found to be nonlinear, and pH, ND and sample volume dependent; indicating the detection of Gd+3 requires efficient adsorption of the analyte to the diamond surface. Langmuir adsorption isotherms embedded in a quantitative photophysical model links the ODMR response to adsorption thermodynamics of Gd+3. The equilibrium constant for Gd+3 adsorption to a carboxylated ND surface is determined to be (1 ± 0.5) x 105 M-1 corresponding to a free energy of adsorption of (-28 ± 1) kJ mol-1. These results provide general insight into how complex aqueous and microscale environments impact nanodiamond based quantum sensing modalities, and portend their application as quantitative chemical sensors in microenvironments.

Brown, Emily K↗

DOE OSTI2024

Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots

Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. These hypergraphs offer a natural platform for organizing, communicating, and processing computational knowledge. While most scientific problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known (Type 2), many require the data-driven discovery of the structure (connectivity) of the hypergraph itself (Type 3). We introduce an interpretable Gaussian Process (GP) framework for such (Type 3) problems that does not require randomization of the data, access to or control over its sampling, or sparsity of the unknown functions in a known or learned basis. Its polynomial complexity, which contrasts sharply with the super-exponential complexity of causal inference methods, is enabled by the nonlinear ANOVA capabilities of GPs used as a sensing mechanism.

Science & Technology - Other Topics↗

DOE OSTI2026

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Ultrafast snapshots of terahertz electric potentials across ring-shaped quantum barriers

Probing the time evolution of the terahertz electric field within subwavelength dimensions plays a crucial role in observing the nanoscale lightwave interactions with fundamental excitations in condensed-matter systems and in artificial structures, such as metamaterials. Here, we propose a novel probing method for measuring terahertz electric potentials across nanogaps using a combination of optical and terahertz pulse excitations. To achieve this, we employ ring-shaped nanogaps that enclose a metallic island, allowing us to capture tunneling charges when subjected to terahertz electromagnetic pulse illumination. By controlling and manipulating the terahertz tunneling charges through a focused optical gate pulse, we can obtain the terahertz potential strength as a function of spatial coordinates and time delays between pulses. To accurately quantify the time evolution of terahertz electric potential across quantum barriers, we carefully calibrate the recorded nonlinear tunneling current. Its on-resonance and off-resonance behaviors are also discussed, providing valuable insights into the antenna’s characteristics and performance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Impact of longitudinal phase-matching variations on three-wave nonlinear interactions

A general study of three-wave nonlinear mixing in the presence of longitudinal variations in phase-matching conditions is presented. The efficiency of second-harmonic generation and optical parametric amplification is quantified using a normalized set of equations and a polynomial description of the wave-vector mismatch as a function of the longitudinal coordinate. These modeling results are used to estimate the impact of spatial variations in wave-vector mismatch experimentally obtained for five partially deuterated potassium dihydrogen phosphate crystals. The longitudinal inhomogeneities in the properties of crystals of similar quality are not expected to have a significant impact on their use for second-harmonic generation and optical parametric amplification, but the efficiency of nonlinear processes in crystals with larger variations could decrease.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Optimization of nonlinear turbulence in stellarators

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC . Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗