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An initial investigation into neuron models aimed at efficient stochastic simulation of turbulent flows.
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This paper develops a unified model for staircase formation in both passive and active scalar systems, building upon prior numerical studies by offering new heuristic and physical insights. While prior studies primarily reported numerical results, they did not explore the underlying unifying physics that governs both types of scalar transport; this work addresses that gap by identifying shared mechanisms across both cases. Results of studies of passive and active scalar staircase formation in cellular flows are presented. Staircase formation in cellular flows occurs due to the interplay of fast mixing within cells and slow transport across the inter-cell boundary. The cell boundary emerges as a de facto transport barrier. Special attention is focused on the effects of cellular fluctuations and noise upon staircase structure. A forced, fluctuating vortex array model is used to drive the underlying flow structure. Cellular Peclet number and staircase profile curvature are identified as figures-of-merit to quantify the resiliency of layering. These are related to simple, multi-scatterer scalar random walk models. Results for Peclet number and curvature scaling with flow excitation are presented. We also study staircases of magnetic potential evolving in two-dimensional magnetohydrodynamics as examples of layering of active scalar concentration. Formation of magnetic potential staircases is indeed observed. Flux expulsion inhibits the intercellular transport of magnetic potential and strengthens staircase barriers. Magnetic staircases can be supported against resistive decay by magnetic potential noise forcing. Implications for staircase formation in magnetic confinement experiments are discussed.
Context.Within the framework of investigating the link between the central super massive black holes in the cores of galaxies and the galaxies themselves, we detected a variable X-ray source in the center of CGCG 077-102 NED02, which is a member of the CGCG 077-102 galaxy pair within the Abell 2063 cluster of galaxies. Aims.Our goal is to combine X-ray and optical data to demonstrate that this object harbors an active super massive black hole in its core, and to relate this to the dynamical status of the galaxy pair within the Abell 2063 cluster. Methods.We usedChandraandXMM-Newtonarchival data to derive the X-ray spectral shape and variability. We also obtained optical spectroscopy to detect the expected emission lines that are typically found in active galactic nuclei. Finally, we used public ZTF imaging data to investigate the optical variability. Results.There is no evidence of multiple X-ray sources or extended components within CGCG 077-102 NED02. Single X-ray spectral models fit the source well. We detect significant, nonrandom inter-observation 0.5–10 keV X-ray flux variabilities, for observations separated by ∼4 days for short-term variations and by up to ∼700 days for long-term variations. Optical spectroscopy points toward a passive galaxy for CGCG 077-102 NED01 and a Seyfert for CGCG 077-102 NED02. The classification of CGCG 077-102 NED02 is also consistent with its X-ray luminosity of over 10 42 erg s −1 . We do not detect short-term variability in the optical ZTF light curves. However, we find a significant long-term stochastic variability in theg-band that can be well described by the damped random walk model with a best-fit characteristic damping timescale ofτ DRW = 30 −12 +28 days. Finally, the CGCG 077-102 galaxy pair is deeply embedded within the Abell 2063 potential, with a long enough history within this massive structure to have been affected by the influence of this cluster for a long time. Conclusions.Our observations point toward a moderately massive black hole in the center of CGCG 077-102 NED02 of ∼10 6 M ⊙ . As compared to another similar pair in the literature, CGCG 077-102 NED02 is not heavily obscured, perhaps because of the surrounding intracluster medium ram-pressure stripping.
Power distribution systems are increasingly integrating heterogeneous sensors with varying data reporting rates and types, which pose challenges to achieving observability at the desired temporal resolution of distribution system state estimation (DSSE). Multisensor failures caused by extreme events exacerbate these issues, introducing substantial uncertainties into DSSE. This article proposes a novel solution to these challenges by ensuring high-resolution system observability despite heterogeneous data sources and multisensor failures. First, a deep learning architecture combining long short-term memory (LSTM) and graph convolutional network (GCN) is employed to synchronize meters with different reporting rates, aiming to achieve system observability. A random-walk-model-based approach is introduced to generate pseudo-measurements while properly characterizing their uncertainties under multisensor failures. Finally, a disaster-risk-informed observability metric (RiOM) is defined to quantify the uncertainty associated with state estimation results. The proposed framework offers deeper insights into the system observability on the fly compared with conventional analysis. The effectiveness of the framework is demonstrated on an IEEE standard test case and a large-scale real-world distribution feeder in mid-Minnesota in the U.S.
Diffusivity of species and defects on grain boundaries is usually several orders of magnitude larger than that inside grains. Such strongly inhomogeneous diffusivity requires prohibitively high computational demands for modeling microstructural evolution. Here, this paper presents a highly-efficient numerical solver, combining the Finite Difference method and Random Walk model, designed for accurately modeling strongly inhomogeneous diffusion within polycrystalline structures. The proposed solver, termed Finite Difference informed Random Walk (FDiRW), integrates a customized Finite Difference (cFD) scheme tailored for fast diffusion along thin grain boundaries represented by a single-layer of nodes. Numerical experiments demonstrate that the FDiRW solver achieves an impressive efficiency gain of 1560x compared to traditional Finite Difference methods while maintaining accuracy, making it feasible for personal computer machines to handle diffusional systems with strongly inhomogeneous diffusivity across static polycrystalline microstructures. The model has been successfully applied to simulate radiation defect evolution, showcasing its scalability to engineering scales in both length and time dimensions.
We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals—particularly natural images—and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, in this study, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.
In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.
We present the first systematic search for electric vector position angle (EVPA) swings in the millimeter-wave (mm-wave) emission of blazars, using five years of observations from the South Pole Telescope SPT-3G camera at 95 and 150 GHz, and investigate their connection to gamma-ray flares. Of the 168 bright sources in the ~1500 square degrees SPT-3G Main Field, eight have sufficient polarization signal-to-noise for reliable EVPA measurement, four of which have continuous Fermi LAT gamma-ray detections. We detect EVPA swings in all four gamma-ray-active blazars and in none of the remaining four, consistent with the established connection between EVPA swings and high-energy emission seen at optical wavelengths. The observed swing amplitudes and rotation rates are smaller than those found in optical studies, consistent with mm-wave EVPA variability being slower than at shorter wavelengths. Random walk simulations of the polarization angle using a multi-cell model fail to reproduce both the number, amplitude, and duration of the observed swings, suggesting that this mechanism is insufficient to explain the observed swing population. Analysis of EVPA variability on one-week timescales is consistent with the anti-correlation between polarization degree and EVPA rotation rate previously observed at optical wavelengths. Of the 14 detected swings, eight are within 30 days of a gamma-ray flare. While many individual swing-flare associations are found to have a very low probability of happening by chance, the full ensembles of 95 and 150 GHz swing time lags with respect to gamma-ray flares are found to be consistent with random coincidence.
ABSTRACT The stochastic photometric variability of quasars is known to follow a random-walk phenomenology on emission time-scales of months to years. Some high-cadence rest-frame optical monitoring in the past has hinted at a suppression of variability amplitudes on shorter time-scales of a few days or weeks, opening the question of what drives the suppression and how it might scale with quasar properties. Here, we study a few thousand of the highest luminosity quasars in the sky, mostly in the luminosity range of $L_{\rm bol}$$=[46.4, 47.3]$ and redshift range of $z=[0.7, 2.4]$. We use a data set from the NASA/Asteroid Terrestrial-impact Last Alert System facility with nightly cadence, weather permitting, which has been used before to quantify strong regularity in longer term rest-frame-UV variability. As we focus on a careful treatment of short time-scales across the sample, we find that a linear function is sufficient to describe the UV variability structure function. Although the result can not rule out the existence of breaks in some groups completely, a simpler model is usually favoured under this circumstance. In conclusion, the data are consistent with a single-slope random walk across rest-frame time-scales of $\Delta t=[10, 250]$ d.
Dark matter-dominated cores have long been claimed for the well-studied local group dwarf galaxies. More recently, extended stellar halos have been uncovered around several of these dwarfs through deeper imaging and spectroscopy. Such core-halo structures (inner flat core and a characteristic r −3 asymptotic outer halo profile) are not a feature of conventional cold dark matter (CDM). In contrast, smooth and prominent dark matter cores are predicted for wave/fuzzy dark matter (ψDM). The question arises as to what extent the visible stellar profiles should reflect this dark matter core structure. Here we compare cosmological hydrodynamical simulations of CDM, “WDM” (model used as a proxy for ψDM) & ψDM, aiming to predict the stellar profiles for these three DM scenarios. We show that cores surrounded by extended halos are distinguishable for ψDM, where the stellar density is enhanced in the core due to the presence of the relatively dense soliton. Our analysis demonstrates that, in our simulations, a distinctive core-halo structure does not appear in the case of CDM in the DM, gas, or stars. Whereas we do find a core-halo transition for DM, gas, and stars for ψDM, and the scale of this transition is in line with the predicted core radius set by the soliton scale anticipated for the adopted boson mass of 2.5×10 −22 eV. The presence of a core-halo structure in the stellar profile for Galaxy 1 for ψDM is visible for the most massive and the first galaxy to form in the simulation. Clearly, further simulations are needed to establish how strict this possible relationship is between the DM and stellar core-halo profile as a potential observational discriminator. Furthermore, we observe the anticipated asymmetry for ψDM due to the soliton's motion (jumping and random walk), a distinctive characteristic not found in the symmetric distributions of stars in the warm and CDM models.
In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.
Dense bacterial suspensions exhibit turbulent-like flows at low Reynolds numbers, driven by the activity of the microswimmers. In this study, we develop a model system to examine these dynamics using motile colloids that mimic bacterial locomotion. The colloids are powered by the Quincke instability, which causes them to spontaneously roll in a random-walk pattern when exposed to a square-wave electric field. We experimentally investigate the flow dynamics in dense suspensions of these Quincke random walkers under quasi two-dimensional conditions, where the particle size is comparable to the gap between the electrodes. The results suggest a scaling regime in the energy spectrum ∼k −4 at high wavenumbers, observed consistently across activity levels and particle concentrations. We observe that velocity time correlations decay within a single period of the square-wave field, yet an anti-correlation appears between successive field applications, indicative of a dynamic structural memory of the ensemble.
Flat-histogram Monte Carlo simulations are well-established, robust methods to perform random walks in a physical observable or parameter space, making them suitable for finding ground states or studying phase transitions in complex systems in statistical physics. However, their efficiency can be limited by the time to attain the desired flat distribution, which is generally unknown prior to the simulations. In particular, they might suffer from slowing down towards the end of a simulation due to the diffusive nature of random walks. In this work we apply irreversibility to the multicanonical Monte Carlo method via the lifting approach to alleviate this behavior. We achieve a 2–4 times speedup in ground-state search for a two-dimensional (2D) Ising model, and up to an order of magnitude of speedup for finding the ground-state energy in an Edwards–Anderson spin glass, compared to traditional multicanonical sampling. In conclusion, the round-trip times between ground states show a narrower distribution and are significantly shorter compared to the reversible counterpart, suggesting that a lower convergence time with a smaller time variance is feasible.
Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.
Iron carbide (Fe x C y ) nanoparticles (NPs) are promising candidates for replacing platinum group metals in industrial applications, such as high-temperature Fischer–Tropsch synthesis. However, due to their amorphous nature, characterization of the active sites has been challenging experimentally and computationally. Here, using a combined density functional theory (DFT), neural network interatomic potential-assisted global optimization, and ensemble learning study, we evaluate dynamic surface changes associated with syngas (H and CO) interactions. For this purpose, we have developed a general procedure that we use to model an experimentally relevant 270-atom Fe 182 C 88 NP using the neural network-assisted stochastic surface walk global optimization algorithm (SSW-NN). Once generated, the Fe 182 C 88 NP active sites and particle morphology are thoroughly characterized before the effects of syngas adsorbate interactions are explored by using DFT and molecular dynamics simulations. Lastly, we explore correlations between geometric and electronic features of the active sites and the adsorption of H (H ads ), using a regularized random forest machine learning algorithm. In doing so, we identified the Fe–C coordination number and p orbital occupancy as the most important descriptors affecting H ads . Furthermore, using a combined ML and quantum chemistry approach, our work demonstrates a general and efficient procedure for generating and probing complex surface phenomena on binary nanoparticles.
With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.
Discovering pragmatic and efficient approaches to construct ε-approximations of quantum operators such as real (imaginary) time-evolution propagators in terms of the basic quantum operations (gates) is challenging. Prior ε-approximations are invaluable, in that they enable the compilation of classical and quantum algorithm modeling of, e.g., dynamical and thermodynamic quantum properties. In parallel, symmetries are powerful tools concisely describing the fundamental laws of nature; the symmetric underpinnings of physical laws have consistently provided profound insights and substantially increased predictive power. In this work, we consider the interplay between the ε-approximate processes and the exact symmetries in a semicoherent context—where measurements occur at each logical clock cycle. Here we draw inspiration from Pascual Jordan's groundbreaking formulation of nonassociative, but commutative, symmetric algebraic form. Our symmetrized formalism is then applied in various domains such as quantum random walks, real-time evolutions, variational algorithm ansatzes, and efficient entanglement verification. Our work paves the way for a deeper understanding and greater appreciation of how symmetries can be used to control quantum dynamics in settings where coherence is a limited resource.