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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Nowcasting Earthquakes With Stochastic Simulations: Information Entropy of Earthquake Catalogs

Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes can be computed using Receiver Operating Characteristic methods. Furthermore, analysis of the Shannon information content of the earthquake catalogs has been used to show that there is information contained in the catalogs, and that it can vary in time. So an important question remains, where does the information originate? In this paper, we examine this question using stochastic simulations of earthquake catalogs. Our catalog simulations are computed using an Earthquake Rescaled Aftershock Seismicity (“ERAS”) stochastic model. This model is similar in many ways to other stochastic seismicity simulations, but has the advantage that the model has only 2 free parameters to be set, one for the aftershock (Omori-Utsu) time decay, and one for the aftershock spatial migration away from the epicenter. Generating a simulation catalog and fitting the two parameters to the observed catalog such as California takes only a few minutes of wall clock time. While clustering can arise from random, Poisson statistics, we show that significant information in the simulation catalogs arises from the “non-Poisson” power-law aftershock clustering, implying that the practice of de-clustering observed catalogs may remove information that would otherwise be useful in forecasting and nowcasting. We also show that the nowcasting method provides similar results with the ERAS model as it does with observed seismicity.

58 GEOSCIENCES↗
DOE OSTI2025

Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties With Deep Learning Multi‐Member and Stochastic Parameterizations

Abstract Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: (a) a single Deep Neural Network (DNN) with Monte Carlo Dropout; (b) a multi‐member parameterization; and (c) a Variational Encoder Decoder with latent space perturbation. We show that the multi‐member parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods (b) and (c) are advantageous compared to a dropout‐based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best‐performing multi‐member parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the superparameterization for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth‐like simulations but enables model stability over 5 months with our multi‐member parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the multi‐member parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of multi‐member machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

Behrens, Gunnar [Deutsches Zentrum für Luft‐ und R↗
DOE OSTI2023

Machine learning unifies flexibility and efficiency of spinodal structure generation for stochastic biomaterial design

Abstract Porous biomaterials design for bone repair is still largely limited to regular structures (e.g. rod-based lattices), due to their easy parameterization and high controllability. The capability of designing stochastic structure can redefine the boundary of our explorable structure–property space for synthesizing next-generation biomaterials. We hereby propose a convolutional neural network (CNN) approach for efficient generation and design of spinodal structure—an intriguing structure with stochastic yet interconnected, smooth, and constant pore channel conducive to bio-transport. Our CNN-based approach simultaneously possesses the tremendous flexibility of physics-based model in generating various spinodal structures (e.g. periodic, anisotropic, gradient, and arbitrarily large ones) and comparable computational efficiency to mathematical approximation model. We thus successfully design spinodal bone structures with target anisotropic elasticity via high-throughput screening, and directly generate large spinodal orthopedic implants with desired gradient porosity. This work significantly advances stochastic biomaterials development by offering an optimal solution to spinodal structure generation and design.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Stochastic gradient descent for optimization for nuclear systems

The use of gradient descent methods for optimizing k-eigenvalue nuclear systems has been shown to be useful in the past, but the use of k-eigenvalue gradients have proved computationally challenging due to their stochastic nature. ADAM is a gradient descent method that accounts for gradients with a stochastic nature. This analysis uses challenge problems constructed to verify if ADAM is a suitable tool to optimize k-eigenvalue nuclear systems. ADAM is able to successfully optimize nuclear systems using the gradients of k-eigenvalue problems despite their stochastic nature and uncertainty. Furthermore, it is clearly demonstrated that low-compute time, high-variance estimates of the gradient lead to better performance in the optimization challenge problems tested here.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Lignin valorization process control under feedstock uncertainty through a dynamic stochastic programming approach

The randomness introduced by reactants is an issue when processing renewable bioresources. In this paper, we apply tools from dynamic stochastic programming theory to the biochemical process. Instead of introducing extra preprocessing units, we consider the inherent randomness of the process and optimize in expectation the performance of the system. In a general setting, this is a multistage stochastic optimization problem and we investigate its approximate solution via two approaches, namely stochastic dual dynamic programming (SDDP) and the finite state, finite action Markov decision process (MDP) framework. These two methods are implemented to a case study of lignin valorization that is crucial to a cost-effective biorefinery process using biomass as the feedstock.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Proactive Operations and Investment Planning via Stochastic Optimization to Enhance Power Systems’ Extreme Weather Resilience

We present scalable stochastic optimization approaches for improving power systems’ resilience to extreme weather events. We consider both proactive redispatch and transmission line hardening as alternatives for mitigating expected load shed due to extreme weather, resulting in large-scale stochastic linear programs (LPs) and mixed-integer linear programs (MILPs). We solve these stochastic optimization problems with progressive hedging (PH), a parallel, scenario-based decomposition algorithm. Our computational experiments indicate that our proposed method for enhancing power system resilience can provide high-quality solutions efficiently. With up to 128 scenarios on a 2,000-bus network, the operations (redispatch) and investment (hardening) resilience problems can be solved in approximately 6 min and 2 h of wall-clock time, respectively. Additionally, we solve the investment problems with up to 512 scenarios, demonstrating that the approach scales very well with the number of scenarios. Moreover, the method produces high quality solutions that result in statistically significant reductions in expected load shed. Our proposed approach can be augmented to incorporate a variety of other operational and investment resilience strategies, or a combination of such strategies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Time and frequency resolved transient-absorption and stimulated-Raman signals of stochastic light

Covariance spectroscopy signals based on the transmission of broadband stochastic probe light undergoing a nonlinear optical process with matter are studied. The resulting signal depends on intensity correlation functions of the probe pulse. Application is made to transient absorption and stimulated Raman signals, where an ultraviolet pump and a delayed stochastically modulated infrared or optical Raman probe are used for monitoring vibrational excitations. We show that the stochastic properties of light can be exploited to circumvent the limitations on the joint temporal and spectral resolution of the signal. We study a model system with a time-dependent frequency and show that the dynamical information can be fully extracted from the covariance signal. Finally, this information is heavily suppressed upon averaging of noisy signals and practically inaccessible in conventional stimulated Raman measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Stochastic density functional theory: Real- and energy-space fragmentation for noise reduction

Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground-state properties of extended materials. The computational complexity of describing the Kohn-Sham orbitals is replaced by introducing a set of random (stochastic) orbitals leading to linear and often sub-linear scaling of certain ground-state observables at the account of introducing a statistical error. Schemes to reduce the noise are essential, for example, for determining the structure using the forces obtained from sDFT. Recently, we have introduced two embedding schemes to mitigate the statistical fluctuations in the electron density and resultant forces on the nuclei. Both techniques were based on fragmenting the system either in real space or slicing the occupied space into energy windows, allowing for a significant reduction in the statistical fluctuations. For chemical accuracy, further reduction of the noise is required, which could be achieved by increasing the number of stochastic orbitals. However, the convergence is relatively slow as the statistical error scales as 1 / N χ according to the central limit theorem, where N χ is the number of random orbitals. In this paper, we combined the embedding schemes mentioned above and introduced a new approach that builds on overlapped fragments and energy windows. The new approach significantly lowers the noise for ground-state properties, such as the electron density, total energy, and forces on the nuclei, as demonstrated for a G-center in bulk silicon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Benchmarking the semi-stochastic CC( P;Q ) approach for singlet–triplet gaps in biradicals

Here, we recently proposed a semi-stochastic approach to converging high-level coupled-cluster (CC) energetics, such as those obtained in the CC calculations with singles, doubles, and triples (CCSDT), in which the deterministic CC(P;Q) framework is merged with the stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)]. In this work, we investigate the ability of the semi-stochastic CC(P;Q) methodology to recover the CCSDT energies of the lowest singlet and triplet states and the corresponding singlet–triplet gaps of biradical systems using methylene, (HFH) − , cyclobutadiene, cyclopentadienyl cation, and trimethylenemethane as examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Noise reduction of stochastic density functional theory for metals

Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic systems at low electron temperatures is difficult due to their highly delocalized density matrix. Second, modeling metallic warm-dense materials at very high electron temperatures is challenging because it requires the computation of a large number of partially occupied orbitals. This study demonstrates that both challenges can be effectively addressed using the latest advances in linear-scaling stochastic DFT methodologies. Despite the inherent introduction of noise into all computed properties by stochastic DFT, this research evaluates the efficacy of various noise reduction techniques under different thermal conditions. Our observations indicate that the effectiveness of noise reduction strategies varies significantly with the electron temperature. Furthermore, we provide evidence that the computational cost of stochastic DFT methods scales linearly with system size for metal systems, regardless of the electron temperature regime.

Chemistry↗
DOE OSTI2026

Mixed stochastic-deterministic density functional theoretic decomposition of Kubo–Greenwood conductivities in the projector augmented wave formalism

Pairing the accuracy of the Kohn–Sham density-functional framework with the efficiency of a stochastic algorithmic approach, mixed stochastic-deterministic density functional theory (mDFT) achieves a favorable computational scaling with system sizes and electronic temperatures. We employ the recently developed mDFT formalism to investigate the dynamic charge-transport properties of systems in the warm dense matter regime. The optical conductivity spectra are computed for single- and multi- component mixtures of carbon, hydrogen, and beryllium using two complementary approaches: Kubo–Greenwood in the mDFT picture and real-time time-dependent mDFT. We further devise a decomposition of the Onsager coefficients leading up to the Kubo–Greenwood spectra to exhibit contributions from the deterministic, stochastic, and mixed electronic state transitions at different incident photon energies.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Instability and turbulent relaxation in a stochastic magnetic field

An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic differential equation, which is solved by the method of averaging. The dynamics are rendered multi-scale, due to the size disparity between the test mode and magnetic perturbations. Maintaining quasi-neutrality at all orders requires that small-scale convective cell turbulence be driven by disparate scale interaction. Here, the cells in turn produce turbulent mixing of vorticity and pressure, which is calculated by fluctuation-dissipation type analyses, and are relevant to pump-out phenomena. The development of correlation between the ambient magnetic perturbations and the cells is demonstrated, showing that turbulence will 'lock on' to ambient stochasticity. Magnetic perturbations are shown to produce a magnetic braking effect on vorticity generation at large scale. Detailed testable predictions are presented. The relations of these findings to the results of available simulations and recent experiments are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Stochastic gravitational wave background from PBH-ABH mergers *

Abstract The measurement of gravitational waves produced by binary black-hole mergers at the Advanced LIGO has encouraged extensive studies on the stochastic gravitational wave background. Recent studies have focused on gravitational wave sources made of the same species, such as mergers from binary primordial black holes or those from binary astrophysical black holes. In this paper, we study a new possibility – the stochastic gravitational wave background produced by mergers of one primordial black hole and one astrophysical black hole. Such systems are necessarily present if primordial black holes exist. We study the isotropic gravitational wave background produced through the history of the universe. We find it is very challenging to detect such a signal. We also demonstrate that it is improper to treat the gravitational waves produced by such binaries in the Milky Way as a directional stochastic background due to a very low binary formation rate.

Physics↗
DOE OSTI2021

Blinking statistics and molecular counting in direct stochastic reconstruction microscopy (dSTORM)

Abstract Motivation Many recent advancements in single-molecule localization microscopy exploit the stochastic photoswitching of fluorophores to reveal complex cellular structures beyond the classical diffraction limit. However, this same stochasticity makes counting the number of molecules to high precision extremely challenging, preventing key insight into the cellular structures and processes under observation. Results Modelling the photoswitching behaviour of a fluorophore as an unobserved continuous time Markov process transitioning between a single fluorescent and multiple dark states, and fully mitigating for missed blinks and false positives, we present a method for computing the exact probability distribution for the number of observed localizations from a single photoswitching fluorophore. This is then extended to provide the probability distribution for the number of localizations in a direct stochastic optical reconstruction microscopy experiment involving an arbitrary number of molecules. We demonstrate that when training data are available to estimate photoswitching rates, the unknown number of molecules can be accurately recovered from the posterior mode of the number of molecules given the number of localizations. Finally, we demonstrate the method on experimental data by quantifying the number of adapter protein linker for activation of T cells on the cell surface of the T-cell immunological synapse. Availability and implementation Software and data available at https://github.com/lp1611/mol_count_dstorm. Supplementary information Supplementary data are available at Bioinformatics online.

Patel, Lekha↗
DOE OSTI2023

Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels

Abstract We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behaviour. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.

Karwa, Vishesh↗
DOE OSTI2025

Logical error rates for the surface code under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions

With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical errors in plausible hardware implementations of quantum error-correcting codes. Detailed error modeling of computational instructions on particular FTQC architectures will enable the better prediction of error propagation in FT-encoded quantum circuits while revealing where greater attention is needed in hardware design. In this work, we consider logical error rates for the surface code implemented on a hypothetical grid-based trapped-ion quantum charge-coupled device architecture. Specifically, we construct logical channels for the idling surface code and examine its diamond error under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions. We include the coherent dephasing noise that is known to accumulate during physical qubit idling and transport in these systems, determining idling and transport durations using the time-resolved output of an open-source trapped-ion surface code compiler. To estimate expectation values of logical Pauli observables following hardware circuits containing non-Clifford sources of noise, we utilize a Monte Carlo technique to sample from an underlying quasiprobability distribution of Clifford circuits that we independently simulate in a phase-sensitive fashion. We verify error suppression up to code distance 𝑑 = 11 at coherent dephasing rates near and below those of current-generation trapped-ion quantum computers and find that logical error rates align with those of analogous fully stochastic simulations in this regime. Exploring higher dephasing rates at 𝑑 = 3−5, we find evidence for growing coherent rotations about all three logical Pauli axes, increased diagonal logical error process matrix elements relative to those of stochastic simulations, and a reduced dephasing rate threshold. Overall, our work paves a way toward realistic hardware emulation of small fault-tolerant quantum processes, e.g., members of an FTQC instruction set.

Quantum benchmarking↗
DOE OSTI2025

Stochastic noise can be helpful for variational quantum algorithms

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms. Published by the American Physical Society 2025

Liu, Junyu↗
DOE OSTI2024

Searching for cosmological stochastic backgrounds by notching out resolvable compact binary foregrounds with next-generation gravitational-wave detectors

Stochastic gravitational-wave backgrounds can be of either cosmological or astrophysical origin. The detection of an astrophysical stochastic gravitational-wave background with ground-based interferometers is expected in the near future. Perhaps even more excitingly, the detection of stochastic backgrounds of cosmological origin by future ground-based interferometers could reveal invaluable information about the early Universe. From this perspective, the astrophysical background is a foreground that can prevent the extraction of this information from the data. In this paper, we revisit a time-frequency domain notching procedure previously proposed to remove the astrophysical foreground in the context of next-generation ground-based detectors, but we consider the more realistic scenario where we remove individually detectable signals by taking into account the uncertainty in the estimation of their parameters. We find that time-frequency domain masks can still efficiently remove the astrophysical foreground and suppress it to about 5% of its original level. Further removal of the foreground formed by unresolvable events (in particular, unresolvable binary neutron stars), which is about 10 times larger than the residual foreground from realistic notching, would require detector sensitivity improvements. Therefore, the main limitation in the search for a cosmological background is the unresolvable foreground itself, and not the residual of the notching procedure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗