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At least 523 records · Page 29

Decentralized digital twins of complex dynamical systems

Abstract In this article, we introduce a decentralized digital twin (DDT) modeling framework and its potential applications in computational science and engineering. The DDT methodology is based on the idea of federated learning, a subfield of machine learning that promotes knowledge exchange without disclosing actual data. Clients can learn an aggregated model cooperatively using this method while maintaining complete client-specific training data. We use a variety of dynamical systems, which are frequently used as prototypes for simulating complex transport processes in spatiotemporal systems, to show the viability of the DDT framework. Our findings suggest that constructing highly accurate decentralized digital twins in complex nonlinear spatiotemporal systems may be made possible by federated machine learning.

97 MATHEMATICS AND COMPUTING↗

Recipes for when physics fails: recovering robust learning of physics informed neural networks

Abstract Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.

97 MATHEMATICS AND COMPUTING↗

Anomalous ellipticity dependence of the generation of near-threshold harmonics in noble gases

We measured the ellipticity dependence of the harmonic yield of He, Ne, Ar, Kr, and Xe. It is found that the harmonic yield in general decreases monotonically with increasing laser ellipticity but anomalous dependence does occur for each atom for some harmonic orders. Additionally, we found that the degree of anomaly is weakest in helium but is stronger for the heavier atoms. The anomaly also depends on laser intensity. To explain these features, we developed a quantum trajectory Monte Carlo (QTMC) model based on the quantum path integral theory to study high-order harmonic generation (HHG). The model includes the effect of Coulomb potential from the target ion, thus it is capable of calculating near-threshold harmonics quantitatively. This model reveals that the presence of Coulomb potential would generate orbiting trajectories which are responsible for the anomalous ellipticity dependence near the threshold.

74 ATOMIC AND MOLECULAR PHYSICS↗

Silicon-Lattice-Matched Boron-Doped Gallium Phosphide: A Scalable Acousto-Optic Platform

The compact size, scalability, and strongly confined fields in integrated photonic devices enable new functionalities in photonic networking and information processing, both classical and quantum. Gallium phosphide (GaP) is a promising material for active integrated photonics due to its high refractive index, wide bandgap, strong nonlinear properties, and large acousto-optic figure of merit. Here, this study demonstrates that silicon-lattice-matched boron-doped GaP (BGaP), grown at the 12-inch wafer scale, provides similar functionalities as GaP. BGaP optical resonators exhibit intrinsic quality factors exceeding 25,000 and 200,000 at visible and telecom wavelengths, respectively. It further demonstrates the electromechanical generation of low-loss acoustic waves and an integrated acousto-optic (AO) modulator. High-resolution spatial and compositional mapping, combined with ab initio calculations, indicate two candidates for the excess optical loss in the visible band: the silicon-GaP interface and boron dimers. These results demonstrate the promise of the BGaP material platform for the development of scalable AO technologies at telecom and provide potential pathways toward higher performance at shorter wavelengths.

36 MATERIALS SCIENCE↗

Accelerating high-order mesh optimization using finite element partial assembly on GPUs

In this paper we present a new GPU-oriented mesh optimization method based on high order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU based HPC hardware. Furthermore, we describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

97 MATHEMATICS AND COMPUTING↗

Using Knowledge-Guided Machine Learning To Assess Patterns of Areal Change in Waterbodies across the Contiguous United States

Lake and reservoir surface areas are an important proxy for freshwater availability. Advancements in machine learning (ML) techniques and increased accessibility of remote sensing data products have enabled the analysis of waterbody surface area dynamics on broad spatial scales. However, interpreting the ML results remains a challenge. While ML provides important tools for identifying patterns, the resultant models do not include mechanisms. Thus, the “black-box” nature of ML techniques often lacks ecological meaning. Using ML, we characterized temporal patterns in lake and reservoir surface area change from 1984 to 2016 for 103,930 waterbodies in the contiguous United States. We then employed knowledge-guided machine learning (KGML) to classify all waterbodies into seven ecologically interpretable groups representing distinct patterns of surface area change over time. Many waterbodies were classified as having “no change” (43%), whereas the remaining 57% of waterbodies fell into other groups representing both linear and nonlinear patterns. This analysis demonstrates the potential of KGML not only for identifying ecologically relevant patterns of change across time but also for unraveling complex processes that underpin those changes.

54 ENVIRONMENTAL SCIENCES↗

Molecular dynamics on quantum annealers

Abstract In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer.

74 ATOMIC AND MOLECULAR PHYSICS↗

LOKI

LOKI is a simulation code that models weakly-coupled plasma evolution using Eulerian kinetic models in four phase space dimensions. The code is useful to understand basic plasma nonlinear plasma physics phenomena - in particular, wave-particle and wave-wave resonances that occur in laser plasma interactions. LOKI can simulate fundamental physical process in low-density plasmas on a scale of hundreds of light wavelengths. It does so by solving the relativistic Vlasov and Valsov-Fokker-Planck differential transport equations describing the collision less and low-collisionality evolution of charged particles in electromagnetic fields in two configuration space and two velocity space dimensions. Two principle electromagnetic models are provided: electrostatic (Poisson's Equation) and electromagnetic (Maxwell's equations).

DIMITS, ANDRIS↗

Using Knowledge-Guided Machine Learning To Assess Patterns of Areal Change in Waterbodies across the Contiguous United States

Lake and reservoir surface areas are an important proxy for freshwater availability. Advancements in machine learning (ML) techniques and increased accessibility of remote sensing data products have enabled the analysis of waterbody surface area dynamics on broad spatial scales. However, interpreting the ML results remains a challenge. While ML provides important tools for identifying patterns, the resultant models do not include mechanisms. Thus, the “black-box” nature of ML techniques often lacks ecological meaning. Using ML, we characterized temporal patterns in lake and reservoir surface area change from 1984 to 2016 for 103,930 waterbodies in the contiguous United States. We then employed knowledge-guided machine learning (KGML) to classify all waterbodies into seven ecologically interpretable groups representing distinct patterns of surface area change over time. Many waterbodies were classified as having “no change” (43%), whereas the remaining 57% of waterbodies fell into other groups representing both linear and nonlinear patterns. This analysis demonstrates the potential of KGML not only for identifying ecologically relevant patterns of change across time but also for unraveling complex processes that underpin those changes.

58 GEOSCIENCES↗

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗

Size-Dependent Photon Avalanching in Tm 3+ Doped LiYF 4 Nano, Micro, and Bulk Crystals

Photon avalanche (PA) is a highly nonlinear mode of upconversion that is characterized by 100–1000-fold increase in luminescence intensity upon minute increments of pumping power. The practical realization of numerous possible nano-bio-technology applications utilizing the PA phenomenon will require information on its susceptibility to the material volume and surface. In this report these parameters are investigated via experimental and theoretical PA. The two-color, highly nonlinear PA emission at 475 and 800 nm is clearly observed in bulk single crystal, individual microcrystals, and ensembles of colloidal core and core–shell nanoparticles of LiYF 4 host doped with either 3 or 8% of thulium ions. The properties of PA emission, such as PA nonlinearity, PA gain, PA intensity, and luminescence kinetics in these materials show dependence on crystal volume and surface quenching. Theoretical simulations provide understanding of key physical processes that influence PA performance. Moreover, photon avalanche single beam super-resolution imaging is realized for the first time in 3% Tm 3+ doped LiYF 4 core–shell nanoparticles. The obtained insights and predictions form a solid background for further development and applications of new optimized PA materials.

36 MATERIALS SCIENCE↗

Detecting isolated resonance curves using fixed frequency voltage control tests

Isolated resonance curves, or isolas, are resonance branches of the harmonically forced system that exist separately from the main nonlinear forced response curve, leading to excessive vibrations. Traditional stepped or swept sine simulations and tests rely on continuation along the frequency parameter, typically resulting in a jump phenomenon along the primary resonance branch, prior to the disconnected isola. The main objective of this research is to propose an approach to identify isolated resonance curves by performing continuation along the input amplitude that initializes the response from a low-amplitude solution in the linear regime. Furthermore, this is achieved with the open-loop fixed frequency voltage control method that continues along the shaker voltage parameter and measures the so-called S-curves, which are theoretically a continuous solution branch that connect to the isola. The methodology is demonstrated on a fixture-wing-pylon assembly with a vibro-impact nonlinearity localized in a pylon subcomponent attachment. Multi-harmonic balance simulations are deployed to compute both the nonlinear forced response curves and S-curves to demonstrate the isola detection strategy on a reduced-order finite element model of the nonlinear system. Swept sine and fixed frequency voltage control tests are then conducted on the physical structure to demonstrate the isola detection experimentally, revealing the existence of the large amplitude vibrations that are undetected in the forces levels and frequencies measured with traditional frequency sweeping.

Characterization and Analytical Technique↗

Coupled effect of Cr and Al on interactions between a prismatic interstitial dislocation loop and an edge dislocation line in Fe-Cr-Al alloy

Segregation of alloying elements to a prismatic dislocation loop under irradiation is an important phenomenon in understanding the role of loops in radiation effects in alloys. In this work, various segregation sequences of Cr and Al atoms to a $\langle$100$\rangle$ and a 1/2 $\langle$111$\rangle$ prismatic dislocation loop in a Fe-Cr-Al alloy are explored using molecular dynamics method and ab initio energy calculation. Here, the results reveal that Cr can readily segregate to the loops while Al atoms cannot by themselves, but the segregated Cr atoms are able to promote Al segregation at the loops, defined as a coupled segregation of Cr and Al. After interacting with Cr and Al, a previously mobile 1/2 $\langle$111$\rangle$ loop becomes sessile. Al segregation through the coupled segregation process can further affect the pinning behavior of a dislocation loop to an edge dislocation motion. By varying the Al fraction in the segregated solutes, a nonlinear dependence of the pinning effect on dislocation motion is determined. At lower fractions, the pinning strength increases with the increasing Al fraction until Al fraction reaches a critical value of about 19%, above which the pinning strength decreases with further increase of Al fraction. All these results suggest that, in addition to the effect of Al on the surface resistance to oxidation, Al effect on the dislocation loop behavior is important to optimize the composition of Fe-Cr-Al alloys for their applications in accident tolerant fuel concepts.

36 MATERIALS SCIENCE↗

Deep Learning Segmentation of Complex Features in Atomic-Resolution Phase-Contrast Transmission Electron Microscopy Images

Phase-contrast transmission electron microscopy (TEM) is a powerful tool for imaging the local atomic structure of materials. TEM has been used heavily in studies of defect structures of two-dimensional materials such as monolayer graphene due to its high dose efficiency. However, phase-contrast imaging can produce complex nonlinear contrast, even for weakly scattering samples. It is, therefore, difficult to develop fully automated analysis routines for phase-contrast TEM studies using conventional image processing tools. For automated analysis of large sample regions of graphene, one of the key problems is segmentation between the structure of interest and unwanted structures such as surface contaminant layers. In this study, we compare the performance of a conventional Bragg filtering method with a deep learning routine based on the U-Net architecture. We show that the deep learning method is more general, simpler to apply in practice, and produces more accurate and robust results than the conventional algorithm. We provide easily adaptable source code for all results in this paper and discuss potential applications for deep learning in fully automated TEM image analysis.

47 OTHER INSTRUMENTATION↗

Data-Efficient Methods for Determining Flory–Huggins χ Parameters in Multicomponent Polymer Formulations

Polymer formulations are essential in diverse applications including personal care products, coatings, paints, adhesives, and plastic materials. Designing these formulations requires navigating large, complex design spaces, where phase and self-assembly behavior critically impact performance. The Flory–Huggins χ parameter, which quantifies segmental miscibility, is widely used to parametrize the excess free energy of mixing in formulation models. In this work, we introduce two data-efficient, top-down methods for estimating χ parameters using the Random Phase Approximation (RPA): (i) Boundary Nonlinear Regression (Boundary-NLR), which fits theoretical spinodal boundaries to experimental phase boundaries, and (ii) Surrogate Model Inverse Parameter Estimation (SMIPE), which uses a Gaussian Process Classifier to fit sparse phase maps via a surrogate model. Both methods allow rapid parametrization of polymer field-theoretic models without the need for additional experiments. We evaluate these approaches on data sets involving polymer–solvent–nonsolvent ternary mixtures and block copolymer–solvent systems, demonstrating their robustness to experimental noise and their relevance for real-world formulation design.

copolymers↗

A Two-Stage Decomposition Approach for AC Optimal Power Flow

The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. Furthermore, this paper proposes a scalable decomposition approach in which the power network is decomposed into a master network and a number of subnetworks, where each network has its own AC-OPF subproblem. This formulates a two-stage optimization problem and requires only a small amount of communication between the master and subnetworks. The key contribution is a smoothing technique that renders the response of a subnetwork differentiable with respect to the input from the master problem, utilizing properties of the barrier problem formulation that naturally arises when subproblems are solved by a primal-dual interior-point algorithm. Consequently, existing efficient nonlinear programming solvers can be used for both the master problem and the subproblems. The advantage of this framework is that speedup can be obtained by processing the subnetworks in parallel, and it has convergence guarantees under reasonable assumptions. The formulation is readily extended to instances with stochastic subnetwork loads. Numerical results show favorable performance and illustrate the scalability of the algorithm which is able to solve instances with more than 11 million buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Advances in SRF cavity architectures for quantum computing

Superconducting radio frequency (SRF) cavities offer an excellent platform for storing and processing quantum information due to their exceptionally long lifetimes and large accessible Hilbert spaces. A common strategy to manipulate the quantum states is to use a nonlinear element like a transmon. Nevertheless, constructing a 3D SRF architecture with sustained cavity lifetimes presents several challenges. In this talk, we present our successful integration of transmons with single-cell Nb SRF cavities, enabling the preparation of several non-classical states. Preliminary results reveal the potential of this platform to build a qudit-based quantum computer, departing from traditional qubit-based architectures. We discuss strategies to enhance coherence times, develop high-fidelity gate schemes, and expand the system for constructing a multi-qudit quantum processor. Furthermore, we explore how this architecture can bolster dark matter detection efficiency through multi-photon quantum state preparation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals

Highlights: • Linear and photogalvanic anomalous Hall responses are systematically derived. • Extrinsic mechanisms of AHE include Gaussian, diffractive, hybrid skew scattering. • Diagrammatic calculations are matched to semiclassical picture of AHE. • The Pancharatnam phase of multifold fermions determines the skew scattering amplitude. • Photon-induced interband scattering are accompanied by coordinate shifts. We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an AC electrical driving field is kept up to quadratic order, and both cases of small and large frequencies corresponding to intra- and interband transitions are considered. In particular, this formulation is suitable for the study of nonlinear Hall effect and photogalvanic phenomena. The role of impurity scattering is carefully addressed. Specifically, in addition to previously studied side-jump and skew-scattering processes, quantum interference diffractive contributions are now explicitly incorporated within the developed framework. This theory is applied to multifold fermions in topological semimetals, for which the generic formula for the skew scattering rate from the Pancharatnam phase is obtained along with the corresponding anomalous Hall conductivity.

36 MATERIALS SCIENCE↗