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DOE OSTI2021

A consistent and conservative volume distribution algorithm and its applications to multiphase flows using Phase-Field models

In the present study, the multiphase volume distribution problem, where there can be an arbitrary number of phases, is addressed using a consistent and conservative volume distribution algorithm. The proposed algorithm satisfies the summation constraint, the conservation constraint, and the consistency of reduction. The first application of the volume distribution algorithm is to determine the Lagrange multipliers in multiphase Phase-Field models that enforce the mass conservation, and a multiphase conservative Allen-Cahn model that satisfies the consistency of reduction is developed. A corresponding consistent and conservative numerical scheme is developed for the model. The multiphase conservative Allen-Cahn model has a better ability than the multiphase Cahn-Hilliard model to preserve under-resolved structures. The second application is to develop a numerical procedure, called the boundedness mapping, to map the order parameters, obtained numerically from a multiphase model, into their physical interval, and at the same time to preserve the physical properties of the order parameters. Along with the consistent and conservative schemes for the multiphase Phase-Field models, the numerical solutions of the order parameters are reduction consistent, conservative, and bounded, which are theoretically analyzed and numerically validated. Then, the multiphase Phase-Field models are coupled with the momentum equation by satisfying the consistency of mass conservation and the consistency of mass and momentum transport, thanks to the consistent formulation. Finally, it is demonstrated that the proposed model and scheme converge to the sharp-interface solution and are capable of capturing the complicated multiphase dynamics even when there is a large density and/or viscosity ratio.

42 ENGINEERING↗
DOE OSTI2014

Intrafraction Prostate Translations and Rotations During Hypofractionated Robotic Radiation Surgery: Dosimetric Impact of Correction Strategies and Margins

Purpose: To investigate the dosimetric impact of intrafraction prostate motion and the effect of robot correction strategies for hypofractionated CyberKnife treatments with a simultaneously integrated boost. Methods and Materials: A total of 548 real-time prostate motion tracks from 17 patients were available for dosimetric simulations of CyberKnife treatments, in which various correction strategies were included. Fixed time intervals between imaging/correction (15, 60, 180, and 360 seconds) were simulated, as well as adaptive timing (ie, the time interval reduced from 60 to 15 seconds in case prostate motion exceeded 3 mm or 2° in consecutive images). The simulated extent of robot corrections was also varied: no corrections, translational corrections only, and translational corrections combined with rotational corrections up to 5°, 10°, and perfect rotational correction. The correction strategies were evaluated for treatment plans with a 0-mm or 3-mm margin around the clinical target volume (CTV). We recorded CTV coverage (V{sub 100%}) and dose-volume parameters of the peripheral zone (boost), rectum, bladder, and urethra. Results: Planned dose parameters were increasingly preserved with larger extents of robot corrections. A time interval between corrections of 60 to 180 seconds provided optimal preservation of CTV coverage. To achieve 98% CTV coverage in 98% of the treatments, translational and rotational corrections up to 10° were required for the 0-mm margin plans, whereas translational and rotational corrections up to 5° were required for the 3-mm margin plans. Rectum and bladder were spared considerably better in the 0-mm margin plans. Adaptive timing did not improve delivered dose. Conclusions: Intrafraction prostate motion substantially affected the delivered dose but was compensated for effectively by robot corrections using a time interval of 60 to 180 seconds. A 0-mm margin required larger extents of additional rotational corrections than a 3-mm margin but resulted in lower doses to rectum and bladder.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Economic Analyses in Squamous Cell Carcinoma of the Head and Neck: A Review of the Literature From a Clinical Perspective

The purpose of this review was to describe cost-effectiveness and cost analysis studies across treatment modalities for squamous cell carcinoma of the head and neck (SCCHN), while placing their results in context of the current clinical practice. We performed a literature search in PubMed for English-language studies addressing economic analyses of treatment modalities for SCCHN published from January 2000 to March 2013. We also performed an additional search for related studies published by the National Institute for Health and Clinical Excellence in the United Kingdom. Identified articles were classified into 3 clinical approaches (organ preservation, radiation therapy modalities, and chemotherapy regimens) and into 2 types of economic studies (cost analysis and cost-effectiveness/cost-utility studies). All cost estimates were normalized to US dollars, year 2013 values. Our search yielded 23 articles: 13 related to organ preservation approaches, 5 to radiation therapy modalities, and 5 to chemotherapy regimens. In general, studies analyzed different questions and modalities, making it difficult to reach a conclusion. Even when restricted to comparisons of modalities within the same clinical approach, studies often yielded conflicting findings. The heterogeneity across economic studies of SCCHN should be carefully understood in light of the modeling assumptions and limitations of each study and placed in context with relevant settings of clinical practices and study perspectives. Furthermore, the scarcity of comparative effectiveness and quality-of-life data poses unique challenges for conducting economic analyses for a resource-intensive disease, such as SCCHN, that requires a multimodal care. Future research is needed to better understand how to compare the costs and cost-effectiveness of different modalities for SCCHN.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

High-Dose-Rate Brachytherapy Boost Effect on Local Tumor Control in Young Women With Breast Cancer

Purpose: To evaluate the local control rate and complications of a single fraction of high-dose-rate brachytherapy (HDR BT) boost in women aged 45 yeas and younger after breast-conserving therapy. Methods and Materials: Between 1999 and 2007, 167 patients between the ages of 26 and 45 years old (72 were 40 years old or younger), with stages T1 to T2 invasive breast cancer with disease-free margin status of at least 5 mm after breast-conserving surgery received 46 to 50 Gy whole-breast irradiation plus a 7-Gy HDR-BT boost (“fast boost”). An axillary dissection was performed in 72.5% of the patients and sentinel lymph node biopsy in 27.5%. A supraclavicular area was irradiated in 19% of the patients. Chemotherapy was used in 86% of the patients and hormone treatment in 77%. Clinical nodes were present in 18% and pathological nodes in 29%. The pathological stage was pT0: 5%, pTis: 3%, pT1: 69% and pT2: 23%. Intraductal component was present in 40% and 28% were G3. Results: At a median follow-up of 92 months, 9 patients relapsed on the margin of the implant, and 1 patient in another quadrant, resulting in a 10-year local relapse rate of 4.3% and a breast relapse rate of 4.9%, with breast preservation in 93.4%; no case of mastectomy due to poor cosmesis arose. Actuarial 5- and 10-year disease-free, cause-specific, and overall survival rates were 87.9% and 85.8%, and 92.1% and 88.4%, and 92.1% and 87.3%, respectively. In a univariate analysis, triple-negative cases and negative hormone receptors did worse, but in a multivariate analysis, only the last factor was significant for local and breast control. Asymptomatic fibrosis G2 was recorded in 3 cases, and there were no other late complications. Cosmetic results were good to excellent in 97% of cases. Conclusions: A single dose of 7 Gy using the fast-boost technique is well tolerated, with a low rate of late complications and improved local tumor control in women aged 45 and younger, compared to published data. This approach is recommended in breast-preserving treatment.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Theoretical Benefits of Dynamic Collimation in Pencil Beam Scanning Proton Therapy for Brain Tumors: Dosimetric and Radiobiological Metrics

Purpose: To quantify the dosimetric benefit of using a dynamic collimation system (DCS) for penumbra reduction during the treatment of brain tumors by pencil beam scanning proton therapy (PBS PT). Methods and Materials: Collimated and uncollimated brain treatment plans were created for 5 patients previously treated with PBS PT and retrospectively enrolled in an institutional review board–approved study. The in-house treatment planning system, RDX, was used to generate the plans because it is capable of modeling both collimated and uncollimated beamlets. The clinically delivered plans were reproduced with uncollimated plans in terms of target coverage and organ at risk (OAR) sparing to ensure a clinically relevant starting point, and collimated plans were generated to improve the OAR sparing while maintaining target coverage. Physical and biological comparison metrics, such as dose distribution conformity, mean and maximum doses, normal tissue complication probability, and risk of secondary brain cancer, were used to evaluate the plans. Results: The DCS systematically improved the dose distribution conformity while preserving the target coverage. The average reduction of the mean dose to the 10-mm ring surrounding the target and the healthy brain were 13.7% (95% confidence interval [CI] 11.6%-15.7%; P<.0001) and 25.1% (95% CI 16.8%-33.4%; P<.001), respectively. This yielded an average reduction of 24.8% (95% CI 0.8%-48.8%; P<.05) for the brain necrosis normal tissue complication probability using the Flickinger model, and 25.1% (95% CI 16.8%-33.4%; P<.001) for the risk of secondary brain cancer. A general improvement of the OAR sparing was also observed. Conclusion: The lateral penumbra reduction afforded by the DCS increases the normal tissue sparing capabilities of PBS PT for brain cancer treatment while preserving target coverage.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Boron Neutron Capture Therapy in the Treatment of Recurrent Laryngeal Cancer

Purpose: To investigate the safety and efficacy of boron neutron capture therapy (BNCT) as a larynx-preserving treatment option for patients with recurrent laryngeal cancer. Methods and Materials: Six patients with locally recurrent squamous cell laryngeal carcinoma and 3 patients with persistent laryngeal cancer after prior treatment were treated with BNCT at the FiR1 facility (Espoo, Finland) in 2006 to 2012. The patients had received prior radiation therapy with or without concomitant chemotherapy to a cumulative median dose of 66 Gy. The median tumor diameter was 2.9 cm (range, 1.4-10.9 cm) before BNCT. Boron neutron capture therapy was offered on a compassionate basis to patients who either refused laryngectomy (n=7) or had an inoperable tumor (n=2). Boronophenylalanine-fructose (400 mg/kg) was used as the boron carrier and was infused over 2 hours intravenously before neutron irradiation. Results: Six patients received BNCT once and 3 twice. The estimated average gross tumor volume dose ranged from 22 to 38 Gy (W) (mean; 29 Gy [W]). Six of the 8 evaluable patients responded to BNCT; 2 achieved complete and 4 partial response. One patient died early and was not evaluable for response. Most common side effects were stomatitis, fatigue, and oral pain. No life-threatening or grade 4 toxicity was observed. The median time to progression within the target volume was 6.6 months, and the median overall survival time 13.3 months after BNCT. One patient with complete response is alive and disease-free with a functioning larynx 60 months after BNCT. Conclusions: Boron neutron capture therapy given after prior external beam radiation therapy is well tolerated. Most patients responded to BNCT, but long-term survival with larynx preservation was infrequent owing to cancer progression. Selected patients with recurrent laryngeal cancer may benefit from BNCT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Identification of subsurface structures using electromagnetic data and shape priors

We consider the inverse problem of identifying large-scale subsurface structures using the controlled source electromagnetic method. To identify structures in the subsurface where the contrast in electric conductivity can be small, regularization is needed to bias the solution towards preserving structural information. We propose to combine two approaches for regularization of the inverse problem. In the first approach we utilize a model-based, reduced, composite representation of the electric conductivity that is highly flexible, even for a moderate number of degrees of freedom. With a low number of parameters, the inverse problem is efficiently solved using a standard, second-order gradient-based optimization algorithm. Further regularization is obtained using structural prior information, available, e.g., from interpreted seismic data. The reduced conductivity representation is suitable for incorporation of structural prior information. Such prior information cannot, however, be accurately modeled with a gaussian distribution. To alleviate this, we incorporate the structural information using shape priors. The shape prior technique requires the choice of kernel function, which is application dependent. We argue for using the conditionally positive definite kernel which is shown to have computational advantages over the commonly applied gaussian kernel for our problem. Numerical experiments on various test cases show that the methodology is able to identify fairly complex subsurface electric conductivity distributions while preserving structural prior information during the inversion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Hybrid approaches for multiple-species stochastic reaction–diffusion models

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Variational integrators for reduced magnetohydrodynamics

Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws is described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Multi-level spectral deferred corrections scheme for the shallow water equations on the rotating sphere

Efficient time integration schemes are necessary to capture the complex processes involved in atmospheric flows over long periods of time. We propose a high-order, implicit–explicit numerical scheme that combines Multi-Level Spectral Deferred Corrections (MLSDC) and the Spherical Harmonics (SH) transform to solve the wave-propagation problems arising from the shallow-water equations on the rotating sphere. The iterative temporal integration is based on a sequence of corrections distributed on coupled space–time levels to perform a significant portion of the calculations on a coarse representation of the problem and hence to reduce the time-to-solution while preserving accuracy. In our scheme, referred to as MLSDC-SH, the spatial discretization plays a key role in the efficiency of MLSDC, since the SH basis allows for consistent transfer functions between space–time levels that preserve important physical properties of the solution. We study the performance of the MLSDC-SH scheme with shallow-water test cases commonly used in numerical atmospheric modeling. We use this suite of test cases, which gradually adds more complexity to the nonlinear system of governing partial differential equations, to perform a detailed analysis of the accuracy of MLSDC-SH upon refinement in time. We illustrate the stability properties of MLSDC-SH and show that the proposed scheme achieves up to eighth-order convergence in time. Finally, we study the conditions in which MLSDC-SH achieves its theoretical speedup, and we show that it can significantly reduce the computational cost compared to single-level Spectral Deferred Corrections (SDC).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm compresses the particle population per spatial cell by constructing a velocity distribution function using GM. Particles are reconstructed at restart time by local resampling of the Gaussians. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction by exactly matching the density profile at restart time. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. Here, we demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Stabilized bases for high-order, interpolation semi-Lagrangian, element-based tracer transport

In a computational fluid model of the atmosphere, the advective transport of trace species, or tracers, can be computationally expensive. For efficiency, models often use semi-Lagrangian advection methods. High-order interpolation semi-Lagrangian (ISL) methods, in particular, can be extremely efficient, if the problem of property preservation specific to them can be addressed. Atmosphere models often use geometrically and logically nonuniform grids for efficiency and, as a result, element-based discretizations. Such grids and discretizations make stability a particular problem for ISL methods. Generally, high-order, element-based ISL methods that use the natural polynomial interpolant associated with a nodal finite-element discretization are unstable. Here, we derive new bases having order of accuracy up to nine, with positive nodal weights, that stabilize the element-based ISL method. We use these bases to construct the linear advection operator in the property-preserving Interpolation Semi-Lagrangian Element-based Transport (Islet) method. Then we discuss key software implementation details. Finally, we show performance results for the Energy Exascale Earth System Model's atmosphere dynamical core, comparing the original and new transport methods. These simulations used up to 27,600 Graphical Processing Units (GPU) on the Oak Ridge Leadership Computing Facility's Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗
DOE OSTI2022

Electronic structure and magnetism of pristine, defected, and strained $\mathrm{Ti_2N}$ $\mathrm{MX}$ene

Here, from first principles electronic structure calculations, we unravel the evolution of structural, electronic, and magnetic properties of pristine, defected, and strained titanium nitride MXene with different functional groups (-F, -O, -H, and -OH). The formation and cohesive energies reveal their chemical stability. The dynamical stability of Ti 2 N mono-layer is also confirmed by phonon calculations. The MAX phase and defect free functionalized MXenes are metallic except for oxygen terminated (Ti 2 NO 2 ) one which is 100% spin polarized half-metallic ferromagnet. The spin–orbit coupling significantly influences the bare MXene (Ti 2 N) to exhibit Dirac topology and band inversion near the high symmetry directions. The strain effect sways the Fermi level thereby shifting it towards lower energy state under compression and towards higher energy state under tensile strain in Ti 2 NH 2 . The Ti 2 NO 2 exhibits exotic electronic structure not only in pristine but also in strained and defected structures. Its half-metallic nature changes to semi-metallic under 1% compression and it is completely destroyed under 2% compression. In single vacancy defect, its band structure remarkably transforms from half-metallic to semi-conducting with large band gap in 12.5% Ti, weakly semi-conducting in 5.5% Ti, and semi-metallic in 12.5% O. The 25% N defect changes its half-metallic characteristic to metallic. Further, the 12.5% Co substitution preserves its half-metallic character, whereas Mn substitution allows it to convert half-metallic characteristic into weak semi-metallic characteristic preserving ferromagnetism. However, Cr substitution converts half-metallic ferromagnetic state to half-metallic anti-ferromagnetic state. The understanding made here on collective structural stability, and electronic band structure, and magnetic phenomena in novel 2D Ti 2 N derived MXenes open up their possibility in designing them for synthesis.

36 MATERIALS SCIENCE↗