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At least 145 records · Page 8

Optimal experimental design: Formulations and computations

Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

97 MATHEMATICS AND COMPUTING↗

A new cw-NMR Q-meter for dynamically polarized targets for particle physics

Polarized solid targets produced via Dynamic Nuclear Polarization rely on Continuous-Wave Nuclear Magnetism Resonance measurements to accurately determine the degree of polarization of bulk samples polarized to nearly 100%. Since the late 1970's phase sensitive detection methods have been utilized to observe the magnetization of a sample as a small change in inductance under RF excitation near the Larmor frequency of the nuclear species of interest, using a device known as a Q-meter. Liverpool Q-meters, produced in the UK in the 80's and 90's, have been the workhorse devices for these targets for decades, however their age and scarcity has meant new systems are needed. In conclusion, we describe a Q-meter system designed and built at Jefferson Lab in the Liverpool style to have comparable electronic performance with several improvements to update and adapt the devices for modern use.

Dynamic nuclear polarization↗

Refining Planetary Boundary Layer Height Retrievals From Micropulse‐Lidar at Multiple ARM Sites Around the World

Abstract Knowledge of the planetary boundary layer height (PBLH) is crucial for various applications in atmospheric and environmental sciences. Lidar measurements are frequently used to monitor the evolution of the PBLH, providing more frequent observations than traditional radiosonde‐based methods. However, lidar‐derived PBLH estimates have substantial uncertainties, contingent upon the retrieval algorithm used. In addressing this, we applied the Different Thermo‐Dynamic Stabilities (DTDS) algorithm to establish a PBLH data set at five separate Department of Energy's Atmospheric Radiation Measurement sites across the globe. Both the PBLH methodology and the products are subject to rigorous assessments in terms of their uncertainties and constraints, juxtaposing them with other products. The DTDS‐derived product consistently aligns with radiosonde PBLH estimates, with correlation coefficients exceeding 0.77 across all sites. This study delves into a detailed examination of the strengths and limitations of PBLH data sets with respect to both radiosonde‐derived and other lidar‐based estimates of the PBLH by exploring their respective errors and uncertainties. It is found that varying techniques and definitions can lead to diverse PBLH retrievals due to the inherent intricacy and variability of the boundary layer. Our DTDS‐derived PBLH data set outperforms existing products derived from ceilometer data, offering a more precise representation of the PBLH. This extensive data set paves the way for advanced studies and an improved understanding of boundary‐layer dynamics, with valuable applications in weather forecasting, climate modeling, and environmental studies.

54 ENVIRONMENTAL SCIENCES↗

Shifts in Evapotranspiration Components During Heatwaves Alter Surface Cooling

Heatwave events significantly alter ecosystem water and energy balance and are often accompanied by extreme surface temperatures. Understanding how surface temperatures during such events are regulated by soil evaporation (E) and vegetation transpiration (T) remains limited due to challenges in partitioning total evapotranspiration (ET). Here, high-frequency turbulence methods are used to partition observed ET at 32 National Ecological Observatory Network sites across the contiguous United States. Heatwaves were defined as at least three consecutive days with daily maximum air temperature exceeding the site-specific 90th percentile of the 2019–2021 record. Across 268 identified events, the T/ET ratio decreased by 32% ± 16% relative to the non-heatwave baseline of 0.65, with greater reductions at lower biomass sites. The T/ET ratio was typically suppressed below non-heatwave conditions during the early and middle stages of the heatwave (first two-thirds of event duration), but was on average higher than non-heatwave baseline levels during late stages (final third) due to extremely low soil evaporation. Of the studied heatwaves, 71% of these had surface temperatures above 38°C in their late stage; however, heatwaves sustaining higher evaporation fluxes (upper tertile of observed fluxes) during the late stage were associated with relative surface temperature anomalies that were on average 45% lower than those of heatwaves with lower evaporation fluxes (lower tertile). The commensurate surface cooling induced by higher transpiration was only 2% during heatwaves, suggesting that transpiration has a limited ability to mitigate extreme surface temperatures. This study allows for improved prediction of ecosystem feedbacks under extreme thermal stress.

54 ENVIRONMENTAL SCIENCES↗

Certifying almost all quantum states with few single-qubit measurements

Certifying that an n -qubit state synthesized in the laboratory is close to a given target state is a fundamental task in quantum information science. However, existing rigorous protocols applicable to general target states have potentially prohibitive resource requirements in the form of either deep quantum circuits or exponentially many single-qubit measurements. Here we prove that almost all n -qubit target states, including those with exponential circuit complexity, can be certified from only O ( n 2 ) single-qubit measurements. Given access to the target state’s amplitudes, our protocol requires only O ( n 3 ) classical computation. This result is established by a technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state and for learning and verifying neural networks, tensor networks and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties of a synthesized state that would otherwise require an exponential number of measurements on the state. We demonstrate these applications in numerical experiments with up to 120 qubits and observe an advantage over existing methods such as cross-entropy benchmarking.

information theory and computation↗

Numerical challenges for energy conservation in N -body simulations of collapsing self-interacting dark matter halos

Dark matter (DM) halos can be subject to gravothermal collapse if the DM is not collisionless, but engaged in strong self-interactions instead. When the scattering is able to efficiently transfer heat from the centre to the outskirts, the central region of the halo collapses and reaches densities much higher than those for collisionless DM. This phenomenon is potentially observable in studies of strong lensing. Current theoretical efforts are motivated by observations of surprisingly dense substructures. However, a comparison with observations requires accurate predictions. One method to obtain such predictions is to use N-body simulations. Collapsed halos are extreme systems that pose severe challenges when applying state-of-the-art codes to model self-interacting dark matter (SIDM). In this work, we investigate the root of such problems, with a focus on energy non-conservation. Moreover, we discuss possible strategies to avoid them. We ran N-body simulations, both with and without SIDM, of an isolated DM-only halo and we adjusted the numerical parameters to check the accuracy of the simulation. We find that not only the numerical scheme for SIDM can lead to energy non-conservation, but also the modelling of gravitational interaction and the time integration are problematic. The main issues we find are: (a) particles changing their time step in a non-time-reversible manner; (b) the asymmetry in the tree-based gravitational force evaluation; and (c) SIDM velocity kicks breaking the time symmetry. Tuning the parameters of the simulation to achieve a high level of accuracy allows us to conserve energy not only at early stages of the evolution, but also later on. However, the cost of the simulations becomes prohibitively large as a result. Some of the problems that make the simulations of the gravothermal collapse phase inaccurate can be overcome by choosing appropriate numerical schemes. However, other issues still pose a challenge. Our findings motivate further works on addressing the challenges in simulating strong DM self-interactions.

dark matter↗

Egg yolk as a model for gelation: From rheometry to flow physics

Egg yolks are an excellent model for studying sol-gel transitions, particularly the power law viscoelasticity that defines the critical point of gelation. However, prior studies lack comprehensive datasets and fail to visualize flow behavior linked to temperature and time-dependent linear and nonlinear rheology. Here, we present a detailed dataset characterizing egg yolk viscoelasticity across temperature, time, and forcing amplitude using oscillatory shear, step strain, step stress, and constant high strain rate. Novel protorheology visualizations link rheological properties with observable flow behavior. Our findings highlight the nuanced determination of the critical gel point, emphasizing observation timescale dependencies. We compare methods to identify critical temperatures for gelation, including power law viscoelasticity, moduli crossover, diverging zero-shear viscosity, and emerging equilibrium elastic modulus, while visualizing flow consequences near these transitions. Egg yolk is an accessible, realistic, and nontoxic material relevant to the physicist and the chef alike, making it ideal for understanding the rheology of critical gels. By integrating protorheology photos and videos with rigorous rheometric data, we deepen the understanding of critical gels, with broader impacts for studying other materials with sol-gel transitions.

Marsh, Maxwell C. [Department of Mechanical Scienc↗

Hamiltonian simulation in Zeno subspaces

Here, we investigate the quantum Zeno effect as a framework for designing and analyzing quantum algorithms for Hamiltonian simulation. We show that frequent projective measurements of an ancilla qubit register can be used to simulate quantum dynamics on a target qubit register with a circuit complexity similar to randomized approaches. The classical sampling overhead in the latter approaches is traded for ancilla qubit overhead in Zeno-based approaches. A second-order Zeno sequence is developed to improve scaling and implementations through unitary kicks are discussed. We derive rigorous error bounds that allow for identifying the associated circuit complexities for the first- and second-order Zeno sequences. We show that the circuits over the combined register can be identified as a subroutine commonly used in post-Trotter Hamiltonian simulation methods. We build on this observation to reveal connections between different Hamiltonian simulation algorithms.

Hamiltonian simulation↗

Optimizing entanglement and Bell inequality violation in top antitop events

A top quark and an antitop quark produced together at colliders have correlated spins. These spins constitute a quantum state that can exhibit entanglement and violate Bell’s inequality. In realistic collider experiments, most analyses allow the axes, as well the Lorentz frame, to vary event by event, thus introducing a dependence on the choice of event-dependent basis leading us to adopt “fictitious states,” rather than genuine quantum states. The basis dependence of fictitious states allows for an optimization procedure, which makes the usage of fictitious states advantageous in measuring entanglement and Bell inequality violation. In this work, we show analytically that the basis that diagonalizes the spin-spin correlations is optimal for maximizing spin correlations, entanglement, and Bell inequality violation. We show that the optimal basis is approximately the same as the fixed beam basis (or the rotated beam basis) near the t t ¯ production threshold, while it approaches the helicity basis far above threshold. Using this basis, we present the sensitivity for entanglement and Bell inequality violation in t t ¯ events at the Large Hadron Collider (LHC) and a future e + e − collider. Since observing Bell inequality violation appears to be quite challenging experimentally, and requires a large dataset in collider experiments, choosing the optimal basis is crucially important to observe Bell inequality violation. Our method and general approach are equally applicable to other systems beyond t t ¯ , including interactions beyond the Standard Model. Published by the American Physical Society 2025

Cheng, Kun (ORCID:0000000249592997)↗

Magnetic excitations from the hexagonal spin clusters in the 𝑆 = $\frac{1}{2}$ distorted honeycomb lattice antiferromagnet Cu 2 ⁢(pymca)⁢ 3 ⁢(ClO 4 )

Cu 2 ⁢(pymca) ⁢3 (ClO 4 ) (pymca: pyrimidine-2-carboxylate) consists of a slightly distorted honeycomb lattice of Cu 2+ spins, which shows no long-range magnetic order down to 0.6 K. A magnetization study revealed 1/3 and 2/3 plateau phases [A. Okutani et al., J. Phys. Soc. Jpn. 88, 013703 (2019)], which is not expected for regular honeycomb antiferromagnets. Inelastic neutron scattering experiments were performed using a powder sample to investigate the exchange interactions of this material. The spin excitations from the singlet ground state to the first three triplet states, predicted from the antiferromagnetic hexagonal spin cluster interacting with 3.9 meV, were observed. Using the exact diagonalization methods, the intercluster coupling was estimated from the excitation peak width to be about 20% of the intracluster interaction, which is consistent with the previously reported value. Finally, our exchange path model explains the anisotropic exchange interactions in the distorted honeycomb plane.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Predicting initial trans-membrane pressure across cycles in the ultrafiltration process using random forest

With growing freshwater scarcity, direct potable reuse (DPR) systems that reclaim wastewater for drinking are becoming increasingly important for sustainable water supply. Reliable operation requires minimizing downtime in ultrafiltration (UF) units, where membrane fouling leads to elevated trans-membrane pressure (TMP). This study develops data-driven regression models based on random forest (RF) and autoregressive (AR) approaches to forecast the initial TMP at the start of each UF filtration cycle in a pilot-scale DPR system. The RF model consistently outperforms baseline methods, including historical mean, last observation carried forward, and AR models, across multiple forecast horizons, achieving the lowest root mean square error. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent input variables across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is assessed for both direct and recursive RF modelling approaches. The proposed RF framework establishes a robust foundation for predictive monitoring and real-time optimization of UF operations, supporting sustainable and reliable water reuse.

direct potable reuse↗

Identification of Kelvin-Helmholtz generated vortices in magnetised fluids

The Kelvin-Helmholtz Instability (KHI), arising from velocity shear across the magnetopause, plays a significant role in the viscous-like transfer of mass, momentum, and energy from the shocked solar wind into the magnetosphere. While the KHI leads to growth of surface waves and vortices, suitable detection methods for these applicable to magnetohydrodynamics (MHD) are currently lacking. A novel method is derived based on the well-established λ-family of hydrodynamic vortex identification techniques, which define a vortex as a local minimum in an adapted pressure field. The J × B Lorentz force is incorporated into this method by using an effective total pressure in MHD, including both magnetic pressure and a pressure-like part of the magnetic tension derived from a Helmholtz decomposition. The λ MHD method is shown to comprise of four physical effects: vortical momentum, density gradients, fluid compressibility, and the rotational part of the magnetic tension. A local three-dimensional MHD simulation representative of near-flank magnetopause conditions (plasma β’s 0.5 – 5 and convective Mach numbers M f ∼ 0.4) under northward interplanetary magnetic field (IMF) is used to validate λ MHD . Analysis shows it correlates well with hydrodynamic vortex definitions, though the level of correlation decreases with vortex evolution. Overall, vortical momentum dominates λ MHD at all times. During the linear growth phase, density gradients act to oppose vortex formation. By the highly nonlinear stage, the formation of small-scale structures leads to a rising importance of the magnetic tension. Compressibility was found to be insignificant throughout. Finally, a demonstration of this method adapted to tetrahedral spacecraft observations is performed.

79 ASTRONOMY AND ASTROPHYSICS↗

Role of chemical production and depositional losses on formaldehyde in the Community Regional Atmospheric Chemistry Multiphase Mechanism (CRACMM)

Abstract. Formaldehyde (HCHO) is an important air pollutant with direct cancer risk and ozone-forming potential. HCHO sources are complex because HCHO is both directly emitted and produced from oxidation of most gas-phase reactive organic carbon. We update the secondary production of HCHO in the Community Regional Atmospheric Chemistry Multiphase Mechanism (CRACMM) in the Community Multiscale Air Quality (CMAQ) model. Production of HCHO from isoprene and monoterpenes is increased, correcting an underestimate in the current version. Simulated June–August surface HCHO during peak photochemical production (11:00–15:00 LT, local time) increased by 0.6 ppb (32 %) over the southeastern USA and by 0.2 ppb (13 %) over the contiguous USA. The increased HCHO compares more favorably with satellite-based observations from the TROPOspheric Monitoring Instrument (TROPOMI) and from aircraft-based observations. Evaluation against hourly surface observations indicates a missing nighttime sink that can be improved by increased nighttime deposition, which reduces June–August nocturnal (20:00–04:00 LT) surface HCHO by 1.1 ppb (36 %) over the southeastern USA and 0.5 ppb (29 %) over the contiguous USA. The ability of CRACMM to capture peak levels of HCHO at midday is improved, particularly at sites in the northeastern USA, while peak levels at sites in the southeastern USA are improved, although still lower than observed. Using established risk assessment methods, lifetime exposure of the population in the contiguous USA (∼ 320 million) to ambient HCHO levels predicted here may result in 6200 lifetime cancer cases, with 40 % from controllable anthropogenic emissions of nitrogen oxides and reactive organic compounds. Chemistry updates will be available in CRACMM version 2 (CRACMM2) in CMAQv5.5.

Skipper, T. Nash↗

Predicting Initial Trans-Membrane Pressure for Optimized Operations in UF Unit Using Random Forest

With the growing scarcity of freshwater, innovative process design mechanisms like Reverse Osmosis (RO) are increasingly gaining attention among water treatment utilities to address the rising demand. Ensuring reliable water production necessitates efficient resource utilization, minimizing downtime in (ultra-filtration) UF systems. Recent advancements in machine learning (ML) have enabled the development of accurate data-driven models for Model Predictive Control (MPC), often requiring minimal prior knowledge of underlying physical processes. In this study, we present predictive regression models based on Random Forest (RF) and Auto-Regressive (AR) approaches to forecast the initial Trans-Membrane Pressure (TMP) for each filtration cycle in data generated by Direct Potable Reuse (DPR) systems. The proposed RF-based model demonstrates superior performance compared to baseline methods, including historical mean, Last Observation Carried Forward (LOCF), and naïve AR models, across various forecasting horizons in terms of root mean square error (RMSE) metric. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent covariates across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is studied for both direct and recursive RF modelling approaches across increasing forecast horizons. Accurate prediction of initial TMP is critical for optimizing RO operations, as it enables the development of robust modelling frameworks by accurately estimating membrane fouling trends, thereby enhancing process efficiency and long-term reliability. The demonstrated efficacy of the RF-based approach highlights its potential as a tool for real-time decision-making in water treatment systems, paving the way for advanced process optimization and sustainable water resource management.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗

Predicting Initial Trans-Membrane Pressure for Optimized Operations in UF Unit Using Random Forest

With the growing scarcity of freshwater, innovative process design mechanisms like Ultra-filtration(UF) units are increasingly gaining attention among water treatment utilities to address the rising demand. Ensuring reliable water production necessitates efficient resource utilization, minimizing downtime in UF systems. Recent advancements in machine learning (ML) have enabled the development of accurate data-driven models for Model Predictive Control (MPC), often requiring minimal prior knowledge of underlying physical processes. In this study, we present predictive regression models based on Random Forest (RF) and Auto-Regressive (AR) approaches to forecast the initial Trans-Membrane Pressure (TMP) for each filtration cycle in data generated by Direct Potable Reuse (DPR) systems. The proposed RF-based model demonstrates superior performance compared to baseline methods, including historical mean, Last Observation Carried Forward (LOCF), and naïve AR models, across various forecasting horizons in terms of root mean square (RMSE) metric. Accurate prediction of initial TMP is critical for optimizing CCRO operations, as it enables the development of robust modelling frameworks that enhance process efficiency and reliability. The demonstrated efficacy of the RF-based approach highlights its potential as a tool for real-time decision-making in water treatment systems, paving the way for advanced process optimization and sustainable water resource management.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗

Galaxy cluster matter profiles - I. Self-similarity, mass calibration, and observable-mass relation validation employing cluster mass posteriors

We present a study of the weak lensing inferred matter profiles ΔΣ(R) of 698 South Pole Telescope (SPT) thermal Sunyaev-Zel’dovich effect (tSZE) selected and MCMF optically confirmed galaxy clusters in the redshift range 0.25 < z < 0.94 that have associated weak gravitational lensing shear profiles from the Dark Energy Survey (DES). Rescaling these profiles to account for the mass dependent size and the redshift dependent density produces average rescaled matter profiles ΔΣ(R/R200c)/(ρcritR200c) with a lower dispersion than the unscaled ΔΣ(R) versions, indicating a significant degree of self-similarity. Galaxy clusters from hydrodynamical simulations also exhibit matter profiles that suggest a high degree of self-similarity, with RMS variation among the average rescaled matter profiles with redshift and mass falling by a factor of approximately six and 23, respectively, compared to the unscaled average matter profiles. We employed this regularity in a new Bayesian method for weak lensing mass calibration that employs the so-called cluster mass posterior P(M200|ζ̂, λ̂, z), which describes the individual cluster masses given their tSZE (ζ̂) and optical (λ̂, z) observables. This method enables simultaneous constraints on richness λ-mass and tSZE detection significance ζ-mass relations using average rescaled cluster matter profiles. We validated the method using realistic mock datasets and present observable-mass relation constraints for the SPT×DES sample, where we constrained the amplitude, mass trend, redshift trend, and intrinsic scatter. Our observable-mass relation results are in agreement with the mass calibration derived from the recent cosmological analysis of the SPT×DES data based on a cluster-by-cluster lensing calibration. Our new mass calibration technique offers a higher efficiency when compared to the single cluster calibration technique. We present new validation tests of the observable-mass relation that indicate the underlying power-law form and scatter are adequate to describe the real cluster sample but that also suggest a redshift variation in the intrinsic scatter of the λ-mass relation may offer a better description. In addition, the average rescaled matter profiles offer high signal-to-noise ratio (S/N) constraints on the shape of real cluster matter profiles, which are in good agreement with available hydrodynamical ΛCDM simulations. This high S/N profile contains information about baryon feedback, the collisional nature of dark matter, and potential deviations from general relativity.Key words: gravitational lensing: weak / galaxies: clusters: general / large-scale structure of Universe

79 ASTRONOMY AND ASTROPHYSICS↗

The Ductility of 49Fe-49Co-2V Soft Magnetic Alloy Bar: Surface Effects and Test Methods

The tensile ductility of 49Fe-49Co-2V (Hiperco® 50A) bar was investigated in both as-received and heat-treated conditions. The as-received/machined specimens exhibit very low ductility compared to samples where heat treatment was the final step prior to testing. Microstructural characterization showed that internal residual strain from bar processing and, most importantly, surface machining damage, cause lower elongation in the as-received material. Because fracture of this intermetallic alloy initiates at the surface, it is particularly susceptible to surface machining damage, i.e., the near-surface region has already exhausted most of its ability to accumulate tensile strain. During heat treatment, the internal residual strain and near-surface machining damage are eliminated and ductility is improved, despite a higher degree of crystallographic ordering in the heat-treated condition (which typically lowers ductility). Furthermore, if machining is again performed after heat treatment, the material again exhibits brittle behavior, even with only light touch-up machining passes. Here, in this work, methods of tensile strain measurement were investigated, namely conventional knife-edge extensometry and noncontact digital image correlation (DIC) on heat-treated material. For clip-on knife-edge extensometry, the range of failure strain was 2.5-5.5% for heat-treated Hiperco. For noncontact methods, ductility up to 7% was observed. The results highlight the tendency for the alloy to fail at surface imperfections, even those produced by application of the extensometer itself. Noncontact laser extensometry is recommended for determining the intrinsic ductility of the alloy. A method of laser surface modification was developed which increased ductility by ~ 100% compared to unmodified samples. The high cooling rates achieved during laser surface processing can bypass the ordering reaction and produce a ductile disordered structure at the surface that exhibits ductile fracture characteristics.

EBSD↗

SDYN-GANs: Adversarial learning methods for multistep generative models for general order stochastic dynamics

We introduce adversarial learning methods for data-driven generative modeling of dynamics of nth-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable m-step stochastic numerical integrators. From observations of trajectory samples, we introduce methods for learning long-time predictors and stable representations of the dynamics. Our approaches use discriminators based on Maximum Mean Discrepancy (MMD), training protocols using both conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. Our adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.

• Artificial intelligence (AI) / machine learning ↗