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Technical Note: Iterative megavoltage CT (MVCT) reconstruction using block-matching 3D-transform (BM3D) regularization
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An inexact regularized Newton framework with a worst-case iteration complexity of $ {\mathscr O}(\varepsilon^{-3/2}) $ for nonconvex optimization
Abstract An algorithm for solving smooth nonconvex optimization problems is proposed that, in the worst-case, takes ${\mathscr O}(\varepsilon ^{-3/2})$ iterations to drive the norm of the gradient of the objective function below a prescribed positive real number $\varepsilon $ and can take ${\mathscr O}(\varepsilon ^{-3})$ iterations to drive the leftmost eigenvalue of the Hessian of the objective above $-\varepsilon $. The proposed algorithm is a general framework that covers a wide range of techniques including quadratically and cubically regularized Newton methods, such as the Adaptive Regularization using Cubics (arc) method and the recently proposed Trust-Region Algorithm with Contractions and Expansions (trace). The generality of our method is achieved through the introduction of generic conditions that each trial step is required to satisfy, which in particular allows for inexact regularized Newton steps to be used. These conditions center around a new subproblem that can be approximately solved to obtain trial steps that satisfy the conditions. A new instance of the framework, distinct from arc and trace, is described that may be viewed as a hybrid between quadratically and cubically regularized Newton methods. Numerical results demonstrate that our hybrid algorithm outperforms a cubically regularized Newton method.
Enhanced nearfield acoustic holography for larger distances of reconstructions using fixed parameter Tikhonov regularization
This paper evaluates the performance of various regularization parameter choice methods applied to different approaches of nearfield acoustic holography when a very nearfield measurement is not possible. For a fixed grid resolution, the larger the hologram distance, the larger the error in the naive nearfield acoustic holography reconstructions. These errors can be smoothed out by using an appropriate order of regularization. In conclusion, this study shows that by using a fixed/manual choice of regularization parameter, instead of automated parameter choice methods, reasonably accurate reconstructions can be obtained even when the hologram distance is 16 times larger than the grid resolution.
Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers
We derive and assess two new classes of regularizers that cope with offending denominators in the single-reference second-order Møller-Plesset perturbation theory (MP2). In particular, we discuss the use of two types of orbital energy dependent regularizers, κ and σ, in conjunction with orbital-optimized MP2 (OOMP2). The resulting fifth-order-scaling methods, κ-OOMP2 and σ-OOMP2, have been examined for bond-breaking, thermochemistry, nonbonded interactions, and biradical problems. Both methods with strong enough regularization restore restricted to unrestricted instability (i.e., Coulson-Fischer points) that unregularized OOMP2 lacks when breaking bonds in H 2 , C 2 H 6 , C 2 H 4 , and C 2 H 2 . The training of the κ and σ regularization parameters was performed with the W4-11 set. We further developed scaled correlation energy variants, κ-S-OOMP2 and σ-S-OOMP2, by training on the TAE140 subset of the W4-11 set. Those new OOMP2 methods were tested on the RSE43 set and the TA13 set where unmodified OOMP2 itself performs very well. The modifications we made were found insignificant in these data sets. Furthermore, we tested the new OOMP2 methods on singlet biradicaloids using Yamaguchi's approximate spin-projection. Unlike the unregularized OOMP2, which fails to converge these systems due to the singularity, we show that regularized OOMP2 methods successfully capture strong biradicaloid characters. While further assessment on larger data sets is desirable, κ-OOMP2 with κ = 1.45 E h-1 appears to combine favorable recovery of Coulson-Fischer points with good numerical performance.
A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows
Abstract Partial differential equations (PDEs) are often dependent on input quantities that are uncertain. To quantify this uncertainty PDEs must be solved over a large ensemble of parameters. Even for a single realization this can be a computationally intensive process. In the case of flows governed by the Navier–Stokes equations, an efficient method has been devised for computing an ensemble of solutions. To further reduce the computational cost of this method, an ensemble-proper orthogonal decomposition (POD) method was recently proposed. The main contribution of this work is the introduction of POD spatial filtering for ensemble-POD methods. The POD spatial filter makes possible the construction of the Leray ensemble-POD model, which is a regularized-reduced order model for the numerical simulation of convection-dominated flows of moderate Reynolds number. The Leray ensemble-POD model employs the POD spatial filter to smooth (regularize) the convection term in the Navier–Stokes equations, and diminishes the numerical inaccuracies produced by the ensemble-POD method in the numerical simulation of convection-dominated flows. Specifically, for the numerical simulation of a convection-dominated two-dimensional flow between two offset cylinders, we show that the Leray ensemble-POD method better reflects the dynamics of the benchmark results than the ensemble-POD scheme. The second contribution of this work is a new numerical discretization of the variable viscosity ensemble algorithm in which the average viscosity is replaced with the maximum viscosity. It is shown that this new numerical discretization is significantly more stable than those in current use. Furthermore, error estimates for the novel Leray ensemble-POD algorithm with this new numerical discretization are also proven.
Unexpected series of regular frequency spacing of δ Scuti stars in the non-asymptotic regime - I. The methodology
In this study, a sequence search method was developed to search the regular frequency spacing in δ Scuti stars through visual inspection and an algorithmic search. We searched for sequences of quasi-equally spaced frequencies, containing at least four members per sequence, in 90 δ Scuti stars observed by CoRoT. We found an unexpectedly large number of independent series of regular frequency spacing in 77 δ Scuti stars (from one to eight sequences) in the non-asymptotic regime. We introduce the sequence search method presenting the sequences and echelle diagram of CoRoT 102675756 and the structure of the algorithmic search. Four sequences (echelle ridges) were found in the 5–21 d –1 region where the pairs of the sequences are shifted (between 0.5 and 0.59 d –1 ) by twice the value of the estimated rotational splitting frequency (0.269 d –1 ). The general conclusions for the whole sample are also presented in this paper. The statistics of the spacings derived by the sequence search method, by FT (Fourier transform of the frequencies), and the statistics of the shifts are also compared. In many stars more than one almost equally valid spacing appeared. The model frequencies of FG Vir and their rotationally split components were used to formulate the possible explanation that one spacing is the large separation while the other is the sum of the large separation and the rotational frequency. In CoRoT 102675756, the two spacings (2.249 and 1.977 d –1 ) are in better agreement with the sum of a possible 1.710 d –1 large separation and two or one times, respectively, the value of the rotational frequency.
Potential Flow Generator With L 2 Optimal Transport Regularity for Generative Models
Not provided.
High-pressure phase transformation of carbonate malachite Cu2(CO3)(OH)2 driven by [CuO6] regularization and [CO3] rotation
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Few- and many-nucleon systems with semilocal coordinate-space regularized chiral two- and three-body forces
We illustrate calculations of nucleon-deuteron scattering as well as ground and low-lying excited states of light nuclei in the mass range A = 3 – 16 up through next-to-next-to-leading order in chiral effective field theory using semilocal coordinate-space regularized two- and three-nucleon forces. It is demonstrated that both of the low-energy constants entering the three-nucleon force at this order can be determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. From all considered nucleon-deuteron scattering observables, the strongest constraint on these low-energy constants emerges from the precisely measured cross section minimum at E N = 70 MeV. The inclusion of the three-nucleon force is found to improve the agreement with the data for most of the considered observables.
A demonstration of force estimation and regularization methods for multi-shaker testing.
Abstract not provided.
Estimating regional effects of climate change and altered land use on biosphere carbon fluxes using distributed time delay neural networks with Bayesian regularized learning
Not Available
In situ observation of faceted growth and morphological instability of a complex-regular eutectic in
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Full particle orbit effects in regular and stochastic magnetic fields
Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.
Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography
Here we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization. We emphasize that the key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation regularization which results in a nonlinear degenerate operator. Inspired by residual neural networks, to learn the optimal strength of regularization and the exponent of fractional Laplacian, we develop a dedicated bilevel optimization neural network with a variable depth for a general regularized inverse problem. We illustrate how to incorporate various regularizer choices into our proposed network. As an example, we consider tomographic reconstruction as a model problem and show an improvement in reconstruction quality, especially for limited data, via fractional Laplacian regularization. We successfully learn the regularization strength and the fractional exponent via our proposed bilevel optimization neural network. We observe that the fractional Laplacian regularization outperforms total variation regularization. This is specially encouraging, and important, in the case of limited and noisy data.
Regularization via f -Divergence: An Application to Multi-Oxide Spectroscopic Analysis
In this paper, we explore the application of convolutional neural networks (CNNs) for predicting the chemical composition of complex geologic samples in a simulated Martian atmospheric environment. Specifically, we aim to characterize oxide weight percentages (wt.%) of rock samples analyzed by remote Laser-Induced Breakdown Spectroscopy (LIBS), framing the problem as a multi-target regression task . Neural networks trained on LIBS spectra are prone to overfitting due to high spectral complexity, limited labeled data, and measurement noise. While regularization is critical for improving generalization, common methods (e.g., ℓ 2 regularization) impose constraints not directly tied to data distribution properties. We propose a novel regularization method based on a specific ƒ-divergence induced by a graph-based estimator, designed to constrain the distributional discrepancy between predictions and targets. This regularizer serves a dual purpose: (a) mitigating overfitting by enforcing a constraint on the distributional difference between predictions and noisy targets, and (b) acting as an auxiliary loss that penalizes large divergences. To enable backpropagation, we develop a differentiable approximation of this particular ƒ-divergence, making the method feasible for neural networks. Experiments on ChemCam and SuperCam LIBS calibration spectra show that mathematical equation-divergence regularization outperforms or matches standard regularization methods (ℓ 1 , ℓ 2 , dropout) and the classical baseline, partial least squares (PLS). Combining ƒ-divergence regularization with standard regularization yields further performance gains, indicating that distributional regularization is useful in this context giving a promising direction for robust model training in planetary science applications. Source code is publicly available at Klein and Li (2025), https://doi.org/10.11578/dc.20250530.7.