Real-time adaptive sparse-identification-based predictive control of nonlinear processes
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Abdullah, Fahim (ORCID:000000025094788X)↗
SEARCH · Engineering Papers
Results for “Nonlinear processes”
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Model predictive control of nonlinear processes using transfer learning-based recurrent neural networks
Not Available
Alhajeri, Mohammed S.↗
Model predictive control of nonlinear processes using neural ordinary differential equation models
Not Available
Luo, Junwei (ORCID:000900072609629X)↗
Nonlinear analog processing with anisotropic nonlinear films
Digital signal processing is the cornerstone of several modern-day technologies, yet in multiple applications it faces critical bottlenecks related to memory and speed constraints. Thanks to recent advances in metasurface design and fabrication, light-based analog computing has emerged as a viable option to partially replace or augment digital approaches. Several light-based analog computing functionalities have been demonstrated using patterned flat optical elements, with great opportunities for integration in compact nanophotonic systems. So far, however, the available operations have been restricted to the linear regime, limiting the impact of this technology to a compactification of Fourier optics systems. In this paper, we introduce nonlinear operations to the field of metasurface-based analog optical processing, demonstrating that nonlinear optical phenomena, combined with nonlocality in flat optics, can be leveraged to synthesize kernels beyond linear Fourier optics, paving the way to a broad range of new opportunities. As a practical demonstration, we report the experimental synthesis of a class of nonlinear operations that can be used to realize broadband, polarization-selective analog-domain edge detection.
analog image processing↗
Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth
The response of the cross-beam energy transfer instability (CBET) to laser bandwidth is investigated through a combination of theory and simulation. Existing linear theory is generalized to treat broadband lasers, demonstrating that CBET is most effectively suppressed when the bandwidth exceeds the ion-acoustic wave (IAW) frequency. It is shown that for such bandwidths, reverse (seed to pump) transfer becomes possible, which reduces the net energy transfer rapidly as bandwidth is increased. The CBET gain exponent in this regime scales with bandwidth (Δω) as Δω−3 for Gaussian or Lorentzian laser spectra with different scalings possible for other spectra. Comparison of our theory with linearized fluid and particle-in-cell simulations, performed with the laser-plasma simulation environment (LPSE) and vector particle in cell (VPIC) codes, respectively, finds that the model is accurate in the absence of nonlinear processes. However, linear analysis also finds that the IAW energy density scales as Δω−1, implying that nonlinear effects may be more difficult to control than the CBET scaling would suggest. Indeed, nonlinear effects are found to be present in VPIC simulations with high-intensity lasers, despite minimal apparent CBET. Nonlinear processes in the VPIC cases include particle trapping, the two-ion wave decay, and ion wave self-focusing. In some high intensity VPIC cases, these effects lead to net energy transfer from seed to pump and increases to backscatter stimulated Brillouin scattering reflectivities. Finally, for a given bandwidth, we show that improved control of nonlinear processes can be achieved via smoothing by spectral dispersion.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Similarity properties in capacitive radio frequency plasmas with nonlinear collision processes
Abstract Similarity laws (SL) are essential for correlating the characteristics of plasmas at different dimensional scales, which have been validated for radio frequency (rf) discharges at low pressure but under limited conditions. In this work, we evaluate the effects of nonlinear collisions (e.g. stepwise ionization) on the similarity properties in capacitive rf discharges in argon across a wide range of pressure regimes via fully kinetic particle-in-cell simulations. The SL scalings of fundamental discharge parameters, e.g. the electron power absorption and electron energy probability function, are examined with and without nonlinear collisions, respectively. Without the nonlinear collisions, the similarity scalings are found to be rigorously valid. When the nonlinear collisions are considered, the similarity properties in rf discharges still exist approximately, which indicates that the violations caused by the nonlinear collisions are still minor in the studied cases. The reasons for the effectiveness of SL scalings with nonlinear collision processes are also discussed. The results from this study confirmed the validity of similarity transformations with more complex reaction kinetics, which may promote the applicability of the SL scalings for the design and fabrications of plasma devices.
Physics↗
Neural operator transformers capture bifurcating drift-wave turbulence in fusion plasma simulations
Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Simulating nonlinear optical processes on a superconducting quantum device
Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be modelled as wave–wave interactions. In this paper, we develop a quantization approach to convert nonlinear wave–wave interaction problems to Hamiltonian simulation problems. We demonstrate our approach using two qubits on a superconducting device. Unlike a photonic device, a superconducting device does not naturally have the desired interactions in its native Hamiltonian. Nevertheless, Hamiltonian simulations can still be performed by decomposing required unitary operations into native gates. To improve experimental results, we employ a range of error-mitigation techniques. Apart from readout error mitigation, we use randomized compilation to transform undiagnosed coherent errors into well-behaved stochastic Pauli channels. Moreover, to compensate for stochastic noise, we rescale exponentially decaying probability amplitudes using rates measured from cycle benchmarking. We carefully consider how different choices of product-formula algorithms affect the overall error and show how a trade-off can be made to best utilize limited quantum resources. This study provides an example of how plasma problems may be solved on near-term quantum computing platforms.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Understanding Dynamics and Thermodynamics of ENSO and Its Complexity Simulated by E3SM and Other Climate Models
Despite the seeming success of most state-of-the-art climate models in simulating the El Niño-Southern Oscillation (ENSO), there is strong evidence that models achieve realistic levels of ENSO activity do so often for wrong reasons. This is owing to an often occurred near cancelation of large errors in terms of contributions to ENSO growth rate from coupled dynamic and thermodynamic feedback processes. Climate models remain deficient in simulating the observed ENSO’s spatial and temporal complexity that involves interplays of coupled dynamic and thermodynamic feedbacks, interactions across multiple scales, nonlinear processes in the tropical atmosphere and ocean system, biases in mean sate and physical processes, and influences external to equatorial Pacific coupled ENSO dynamics. Our proposed research aims at advancing predictive and process-level understandings of ENSO simulated in E3SM and other climate models under current and future climate conditions with two main objectives: (i) better understanding the aforementioned broad range interactive processes and sources that control fundamental properties of ENSO in E3SM and CIMP6 outputs as well as in observational (reanalysis) data sets, using a hierarchical of coupled dynamical frameworks consisting of theoretical analysis, intermediate complexity modeling, and coupled dynamic diagnostics; (ii) to use this understanding to explore pathways towards improving E3SM’s capability of simulating ENSO and its complexity. More specifically, we will focus on four main thrusts of research: (1) ENSO’s dynamic and thermodynamic feedbacks; (2) the across-scale interactions of ENSO with annual cycle and MJO/WWB/TIW (Madden Julian Oscillation/Westerly Wind Burst/Tropical Instability Wave) activity; (3) key nonlinear processes of ENSO involving atmospheric convective thresholds, nonlinear ocean dynamic heating, and thermocline outcropping; and (4) the impacts of climate mean-state biases/changes and perturbed physical processes on simulated ENSO and its complexity.
54 ENVIRONMENTAL SCIENCES↗
Linear Quantum Coupler for Clean Bosonic Control
Quantum computing with superconducting circuits relies on high-fidelity driven nonlinear processes. An ideal quantum nonlinearity would selectively activate desired coherent processes at high strength, without activating parasitic mixing products or introducing additional decoherence. The wide bandwidth of the Josephson nonlinearity makes this difficult, with undesired drive-induced transitions and decoherence limiting qubit readout, gates, couplers, and amplifiers. Significant strides have recently been made into building better “quantum mixers,” with promise being shown by Kerr-free three-wave mixers that suppress driven frequency shifts, and balanced quantum mixers that explicitly forbid a significant fraction of parasitic processes. We propose a novel mixer that combines both these strengths, with engineered selection rules that make it essentially linear (not just Kerr-free) when idle, and activate clean parametric processes even when driven at high strength. Furthermore, its ideal Hamiltonian is simple to analyze analytically, and we show that this ideal behavior is first-order insensitive to dominant experimental imperfections. We expect this mixer to allow significant advances in high-𝑄 control, readout, and amplification.
Quantum circuits↗
Cross-beam energy transfer in direct-drive ICF. I. Nonlinear and kinetic effects
Results are presented from a series of simulations examining the susceptibility of the cross-beam energy transfer (CBET) instability to nonlinear processes in the context of direct-drive inertial confinement fusion experiments on the OMEGA laser facility. These form the basis for the second paper of this series [A. G. Seaton, L. Yin, R. Follett, B. J. Albright, and A. Le, “Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth,” Phys. Plasmas 29, 042707 (2022)], where we examine the efficacy of increases in laser bandwidth at suppressing CBET. We choose laser and plasma conditions for the simulations that are favorable to CBET and promote nonlinearity. Through a comparison of outputs from the particle-in-cell code vector particle in cell (VPIC) and the linearized fluid code laser-plasma simulation environment (LPSE), a series of nonlinear effects have been identified in the kinetic simulations that include particle trapping, the two-ion wave decay, and ion-acoustic wave self-focusing. These effects produce time-dependent energy transfer, in contrast to the linearized fluid simulations in which a steady state is reached after an initial transient. Ion trapping is shown to allow for increased energy transfer relative to fluid simulations, with the remaining nonlinear processes acting to reduce the energy transfer. Nonlinear dynamics is contrasted for low- and high-intensity beams as well as between speckled and planar beams. For the parameters under consideration, beam profile has a significant effect on nonlinear dynamics, though the greatest sensitivity is to beam intensity.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Flat nonlinear optics with intersubband polaritonic metasurfaces
Nonlinear intersubband polaritonic metasurfaces produce some of the strongest second- and third-order nonlinear optical responses reported for condensed matter systems at infrared frequencies. These metasurfaces are fabricated as two-dimensional arrays of nanoresonators from multi-quantum-well semiconductor heterostructures, designed to produce strong nonlinear responses associated with intersubband transitions. By optimally coupling the optical modes of the nanoresonators to vertically polarized intersubband transitions in semiconductor heterostructures, one can boost the nonlinear response associated with intersubband transitions, make intersubband transitions interact with free-space radiation at normal incidence, and hence produce optically thin flat nonlinear optical elements compatible with free-space optical setups. As a result of the strong nonlinear response in these systems, significant nonlinear conversion efficiencies (>0.1 %) can be attained in deeply subwavelength optical films using modest pumping intensities of only 10–100 kW/cm 2 . Subwavelength metasurface thickness relaxes phase-matching constraints limiting the operation of bulk nonlinear crystals. Furthermore, the amplitude and phase of the nonlinear optical response in intersubband polaritonic metasurfaces can be tailored for a specific pump wavelength and a nonlinear process of interest through the co-optimization of quantum engineering of electron states in semiconductor heterostructures and photonic engineering of the metasurface nanoresonators design. Additionally, an applied voltage can dynamically control the amplitude and phase of the nonlinear optical response at a nanoresonator level. Here, we review the current state of the art in this rapidly expanding field, focusing on nonlinear processes supporting second-harmonic generation, saturable absorption, and optical power limiting.
flat optics↗
Nonlinear Optical Processes in Centrosymmetric Systems by Cavity-Induced Symmetry Breaking
Not provided.
Materials Science↗
Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes
In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.
97 MATHEMATICS AND COMPUTING↗
ETG turbulence in a tokamak pedestal
This paper explores the fundamental characteristics of electron-temperature-gradient (ETG)-driven turbulence in the tokamak pedestal. The extreme gradients in the pedestal produce linear instabilities and nonlinear turbulence that are distinct from the corresponding ETG phenomenology in the core plasma. The linear system exhibits multiple (greater than ten) unstable eigenmodes at each perpendicular wave vector, representing different toroidal and slab branches of the ETG instability. Proper orthogonal decomposition of the nonlinear fluctuations reveals no clear one-to-one correspondence between the linear and nonlinear modes for most wave vectors. Moreover, nonlinear frequencies deviate strongly from those of the linear instabilities, with spectra peaking at positive frequencies, which is opposite the sign of the ETG instability. The picture that emerges is one in which the linear properties are preserved only in a narrow range of k-space. Outside this range, nonlinear processes produce strong deviations from both the linear frequencies and eigenmode structures. This is interpreted in the context of critical balance, which enforces alignment between the parallel scales and fluctuation frequencies. We also investigate the nonlinear saturation processes. We observe a direct energy cascade from the injection scale to smaller scales in both perpendicular directions. However, in the bi-normal direction, there is also nonlocal inverse energy transfer to larger scales. Neither streamers nor zonal flows dominate the saturation.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Time-dependent saturation and physics-based nonlinear model of cross-beam energy transfer
The nonlinear physics of cross-beam energy transfer (CBET) for multi-speckled laser beams is examined using large-scale particle-in-cell simulations for a range of laser and plasma conditions relevant to indirect-drive inertial confinement fusion (ICF) experiments. The time-dependent growth and saturation of CBET involve complex, nonlinear ion and electron dynamics, including ion trapping-induced enhancement and detuning, ion acoustic wave (IAW) nonlinearity, oblique forward stimulated Raman scattering (FSRS), and backward stimulated Brillouin scattering (BSBS) in a CBET-amplified seed beam. Ion-trapping-induced detuning of CBET is captured in the kinetic linear response by a new δf-Gaussian-mixture algorithm, enabling an accurate characterization of trapping-induced non-Maxwellian distributions. Ion trapping induces nonlinear processes, such as changes to the IAW dispersion and nonlinearities (e.g., bowing and self-focusing), which, together with pump depletion, FSRS, and BSBS, determine the time-dependent nature and level of CBET gain as the system approaches a steady state. Using VPIC simulations at intensities at and above the onset threshold for ion trapping and the insight from the time-dependent saturation analyses, we construct a nonlinear CBET model from local laser and plasma conditions that predicts the CBET gain and the energy deposition into the plasma. This model is intended to provide a more accurate, physics-based description of CBET saturation over a wide range of conditions encountered in ICF hohlraums compared with linear CBET gain models with ad hoc saturation clamps often used in laser ray-based methods in multi-physics codes.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Anomalous two-photon Compton scattering
Abstract X-ray free-electron lasers can generate radiation pulses with extreme peak intensities at short wavelengths. This enables the investigation of laser–matter interactions in a regime of high fields, yet at a non-relativistic ponderomotive potential, where ordinary rules of light–matter interaction may no longer apply and nonlinear processes are starting to become observable. Despite small cross-sections, first nonlinear effects in the hard x-ray regime have recently been observed in solid targets, including x-ray-optical sum-frequency generation (XSFG), x-ray second harmonic generation (XSHG) and two-photon Compton scattering (2PCS). Nonlinear interactions of bound electrons in the x-ray range are fundamentally different from those dominating at optical frequencies. Whereas in the optical regime nonlinearities are predominantly caused by anharmonicities of the atomic potential in the chemical bonds, x-ray nonlinearities far above atomic resonances are expected to be due to nonlinear oscillations of quasi-free electrons, including inner-shell atomic electrons. While the quasi-free-electron model agrees reasonably well with the experimental data for XSFG and XSHG, 2PCS measurements have led to unexpected results: the energy of the nonlinearly scattered photons from non-relativistic electrons shows a substantial unexpected red shift in addition to the Compton shift that is well beyond that predicted by a nonlinear quantum electrodynamics model for free electrons. A potential explanation for the spectral broadening is based on a previously unexplored scattering process that involves the whole atom rather than just quasi-free electrons. A first simulation that includes the atomic binding potential was successful in describing a broadening of the spectrum of the nonlinearly scattered photons to longer wavelengths for soft x-rays. However, the same model does not show any broadening at hard x-ray wavelengths, which is in agreement with other simulation approaches. To this point no calculation has been able to reproduce the experimentally observed broadening. Here we present further experimental data of 2PCS for an extended parameter range using additional diagnostics. In particular, we present measurements of the electron momentum distribution during the interaction that strongly suggest that the spectral broadening is not caused by an increased plasma temperature. We extend our measurement of the magnitude of the red shift in beryllium to > 1.9 k e V in addition to the Compton shift expected for free electrons and expand the measurement of the angular distribution to include forward scattering angles. We also present first measurements of 2PCS from diamond.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗