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DOE OSTI2015

Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input

Wind and solar power generators are commonly described by a system of stochastic ordinary differential equations (SODEs) where random input parameters represent uncertainty in wind and solar energy. The existing methods for SODEs are mostly limited to delta-correlated random parameters (white noise). Here we use the Probability Density Function (PDF) method for deriving a closed-form deterministic partial differential equation (PDE) for the joint probability density function of the SODEs describing a power generator with time-correlated power input. The resulting PDE is solved numerically. A good agreement with Monte Carlo Simulations shows accuracy of the PDF method.

PDF method, stochastic differential equations, pow↗

DOE OSTI2021

Solving inverse problems in stochastic models using deep neural networks and adversarial training

Inverse problems associated with stochastic models constitute a significant portion of scientific and engineering applications. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumption; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We propose a new method that estimates the unknown distribution by matching the statistical properties between observed and simulated random processes. We leverage the expressive power of neural networks to approximate the unknown distribution and use a discriminative neural network for computing the statistical discrepancies between the observed and simulated random processes. Here we demonstrated numerically that the proposed methods can estimate both the model parameters and learn complicated unknown distributions.

42 ENGINEERING↗

DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Post-Mastectomy Radiotherapy After Neoadjuvant Chemotherapy in Breast Cancer: A Pooled Retrospective Analysis of Three Prospective Randomized Trials

Background: The impact of locoregional radiotherapy (RT) after neoadjuvant chemotherapy (NACT) and mastectomy in breast cancer patients is currently unclear. Several publications have suggested that patients with a favorable response to NACT might not benefit from RT after mastectomy. Methods: A retrospective analysis of three prospective randomized NACT trials was performed. Information on the use of RT was available for 817 breast cancer patients with non-inflammatory breast cancer who underwent mastectomy after NACT within the GeparTrio, GeparQuattro, and GeparQuinto-trials. RT was administered to 676 of these patients (82.7%). Results: The 5-year cumulative incidence of locoregional recurrence (LRR) was 15.2% (95% confidence interval [CI] 9.0–22.8%) in patients treated without RT and 11.3% in patients treated with RT (95% CI 8.7–14.3%). In the multivariate analysis, RT was associated with a lower risk of LRR (hazard ratio 0.51, 95% CI 0.27–1.0; p = 0.05). This effect was shown especially in patients with cT3/4 tumors, as well as in patients who were cN+ before neoadjuvant therapy, including those who converted to ypN0 after neoadjuvant therapy. In the bivariate analysis, disease-free survival was significantly worse in patients who received RT, however this was not confirmed in the multivariate analysis. Conclusions: Our results suggest that RT reduces the LRR rates in breast cancer patients who receive a mastectomy after NACT without an improvement in DFS. Prospective randomized controlled trials such as the National Surgical Adjuvant Breast and Bowel Project B-51/RTOG 1304 trial will analyze whether RT has any benefit in patients who have a favorable response after NACT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗

DOE OSTI2019

A data-driven CO 2 leakage detection using seismic data and spatial–temporal densely connected convolutional neural networks

In carbon capture and sequestration (also known as carbon capture and storage, or CCS), developing effective monitoring methods is needed to detect and respond to CO 2 leakage. CO 2 leakage detection methods rely on geophysical observations and monitoring sensor network. However, traditional methods usually require the development of site-specific physical models and expert interpretation, and the effectiveness of these methods can be limited to different application locations, operational scenarios, and conditions. Here, we developed a novel data-driven leakage detection method based on densely connected convolutional neural networks. Our method is an end-to-end detection approach, that differs from conventional leakage monitoring methods by directly learning a mapping relationship between seismic data and the CO 2 leakage mass. To account for the spatial and temporal characteristics of seismic data, our novel networks architecture combines 1D and 2D convolutional neural networks. To overcome the computational expense of solving optimization problems, we apply a densely-connecting strategy in our network architecture that reduces the number of network parameters. Based on the features generated by our convolutional neural networks, we further incorporate a long short-term memory network to utilize time-sequential information, which further improves the detection accuracy. Lastly, we employ our detection method to synthetic seismic datasets generated based on flow simulations of a hypothetical CO 2 storage scenario with injection into a partially compartmentalized sandstone storage reservoir. To evaluate method performance, we conducted multiple experiments including a random leakage test, a sequential test, and a robustness test. Numerical results show that our CO 2 leakage detection method successfully detects the leakage and accurately predicts the leakage mass, suggesting that it has the potential for application in monitoring of real CO 2 storage sites.

58 GEOSCIENCES↗

DOE OSTI2021

Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems

Uncertainty quantification techniques such as the time-dependent generalized polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent the stochastic part of the solution space (aka random function space) in time. However, because the random function space is constructed using tensor products, TD-gPC-based methods are known to suffer from the curse of dimensionality. Here, we introduce a new numerical method called the flow-driven spectral chaos (FSC) which overcomes this curse of dimensionality at the random-function-space level. The proposed method is not only computationally more efficient than existing TD-gPC-based methods but is also far more accurate. The FSC method uses the concept of enriched stochastic flow maps to track the evolution of a finite-dimensional random function space efficiently in time. To transfer the probability information from one random function space to another, two approaches are developed and studied herein. In the first approach, the probability information is transferred in the mean-square sense, whereas in the second approach the transfer is done exactly using a new theorem that was developed for this purpose. The FSC method can quantify uncertainties with high fidelity, especially for the long-time response of stochastic dynamical systems governed by ODEs of arbitrary order. Six representative numerical examples, including a nonlinear problem (the Van-der-Pol oscillator), are presented to demonstrate the performance of the FSC method and corroborate the claims of its superior numerical properties. Finally, a parametric, high-dimensional stochastic problem is used to demonstrate that when the FSC method is used in conjunction with Monte Carlo integration, the curse of dimensionality can be overcome altogether.

(nonlinear) stochastic dynamical systems↗

DOE OSTI2015

Communication: Multiple atomistic force fields in a single enhanced sampling simulation

The main concerns of biomolecular dynamics simulations are the convergence of the conformational sampling and the dependence of the results on the force fields. While the first issue can be addressed by employing enhanced sampling techniques such as simulated tempering or replica exchange molecular dynamics, repeating these simulations with different force fields is very time consuming. Here, we propose an automatic method that includes different force fields into a single advanced sampling simulation. Conformational sampling using three all-atom force fields is enhanced by simulated tempering and by formulating the weight parameters of the simulated tempering method in terms of the energy fluctuations, the system is able to perform random walk in both temperature and force field spaces. The method is first demonstrated on a 1D system and then validated by the folding of the 10-residue chignolin peptide in explicit water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Second-Order Uncertainty Analysis for Radiation Shielding Problems Using MCNP

Standard uncertainty propagation is based on a first-order Taylor expansion. This approximation is usually justified by assuming that 'uncertainties are very small numbers compared with the values of their corresponding quantities'. Furthermore, the second derivatives needed for a second-order analysis are not usually available, and a second-order analysis requires more knowledge regarding the distribution of the random variables. For radiation shielding problems, the MCNP6 Monte Carlo code computes first and second derivatives of a response with respect to nuclide density or reaction cross section. This paper explores the application of these derivatives to second-order uncertainty analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2011

Schematic microscopic approach to the description of M1 transitions between mixed-symmetry and fully symmetric collective states in {gamma}-soft nuclei based on RPA-IBM boson mapping

A schematic microscopic method is developed to calculate the M1 transition probabilities between the mixed-symmetry and the fully symmetric states in {gamma}-soft nuclei. The method is based on the random-phase approximation-interacting boson model (RPA-IBM) boson mapping of the most collective isoscalar boson. All other boson modes with higher excitation energies, including the mixed-symmetry boson, are described in the framework of RPA. As an example the M1 transition probabilities are calculated for the {sup 124-134}Xe isotopes and compared with the experimental data. The results agree well with the data for the ratio B(M1;1{sub ms}{sup +}{yields}2{sub 2}{sup +})/B(M1;1{sub ms}{sup +}{yields}0{sub 1}{sup +}). However, the calculated ratio B(M1;2{sub ms}{sup +}{yields}2{sub 1}{sup +})/B(M1;1{sub ms}{sup +}{yields}0{sub 1}{sup +}) shows a significantly weaker dependence on the mass number than the experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2010

Posterior predictive modeling using multi-scale stochastic inverse parameter estimates.

Multi-scale binary permeability field estimation from static and dynamic data is completed using Markov Chain Monte Carlo (MCMC) sampling. The binary permeability field is defined as high permeability inclusions within a lower permeability matrix. Static data are obtained as measurements of permeability with support consistent to the coarse scale discretization. Dynamic data are advective travel times along streamlines calculated through a fine-scale field and averaged for each observation point at the coarse scale. Parameters estimated at the coarse scale (30 x 20 grid) are the spatially varying proportion of the high permeability phase and the inclusion length and aspect ratio of the high permeability inclusions. From the non-parametric, posterior distributions estimated for these parameters, a recently developed sub-grid algorithm is employed to create an ensemble of realizations representing the fine-scale (3000 x 2000), binary permeability field. Each fine-scale ensemble member is instantiated by convolution of an uncorrelated multiGaussian random field with a Gaussian kernel defined by the estimated inclusion length and aspect ratio. Since the multiGaussian random field is itself a realization of a stochastic process, the procedure for generating fine-scale binary permeability field realizations is also stochastic. Two different methods are hypothesized to perform posterior predictive tests. Different mechanisms for combining multi Gaussian random fields with kernels defined from the MCMC sampling are examined. Posterior predictive accuracy of the estimated parameters is assessed against a simulated ground truth for predictions at both the coarse scale (effective permeabilities) and at the fine scale (advective travel time distributions). The two techniques for conducting posterior predictive tests are compared by their ability to recover the static and dynamic data. The skill of the inference and the method for generating fine-scale binary permeability fields are evaluated through flow calculations on the resulting fields using fine-scale realizations and comparing them against results obtained with the ground truth fine-scale and coarse-scale permeability fields.

58 GEOSCIENCES↗

DOE OSTI2023

A fast Monte Carlo cell-by-cell simulation for radiobiological effects in targeted radionuclide therapy using pre-calculated single-particle track standard DNA damage data

Introduction: We developed a new method that drastically speeds up radiobiological Monte Carlo radiation-track-structure (MC-RTS) calculations on a cell-by-cell basis. Methods: The technique is based on random sampling and superposition of single-particle track (SPT) standard DNA damage (SDD) files from a “pre-calculated” data library, constructed using the RTS code TOPAS-nBio, with “time stamps” manually added to incorporate dose-rate effects. This time-stamped SDD file can then be input into MEDRAS, a mechanistic kinetic model that calculates various radiation-induced biological endpoints, such as DNA double-strand breaks (DSBs), misrepairs and chromosomal aberrations, and cell death. As a benchmark validation of the approach, we calculated the predicted energy-dependent DSB yield and the ratio of direct-to-total DNA damage, both of which agreed with published in vitro experimental data. We subsequently applied the method to perform a superfast cell-by-cell simulation of an experimental in vitro system consisting of neuroendocrine tumor cells uniformly incubated with 177 Lu. Results and discussion: The results for residual DSBs, both at 24 and 48 h post-irradiation, are in line with the published literature values. Our work serves as a proof-of-concept demonstration of the feasibility of a cost-effective “in silico clonogenic cell survival assay” for the computational design and development of radiopharmaceuticals and novel radiotherapy treatments more generally.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2018

Fe Vacancy Order and Domain Distribution in A{sub x}Fe{sub 2−y}Se{sub 2}

The Fe vacancy and its ordering pattern is a unique property of the A{sub x}Fe{sub 2−y}Se{sub 2} (A = K, Rb, Cs) superconductors. Below the structural transition temperature T{sub S} ∼ 550 K, the system phase separates into the I4/mmm phase with no Fe vacancy and the I4/m phase with the √5×√5×1 vacancy order. In this work, an Ising-like Hamiltonian defined on the Fe-sublattice is constructed and employed in a Metropolis Monte Carlo simulation to study the Fe vacancy order and the domain distribution under different thermal treatments. A third phase with randomly distributed Fe vacancies and space group I4/mmm is observed in the simulation. The response of the volume fraction of this simulated phase under thermal treatment shows a direct connection to the change of the superconducting shielding fraction under annealing and quenching processes, indicating a close relation between the vacancy disordered I4/mmm phase and the superconducting phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2013

Theory of the Miscibility of Fullerenes in Random Copolymer Melts

We combine polymer integral equation theory and computational chemistry methods to study the interfacial structure, effective interactions, miscibility and spatial dispersion mechanism of fullerenes dissolved in specific random AB copolymer melts characterized by strong non-covalent electron donor-acceptor interactions with the nanofiller. A statistical mechanical basis is developed for designing random copolymers to optimize fullerene dispersion at intermediate copolymer compositions. Pair correlation calculations reveal a strong sensitivity of interfacial packing near the fullerene to copolymer composition and adsorption energy mismatch. The potential of mean force between fullerenes displays rich trends, often non-monotonic with copolymer composition, reflecting a non-additive competition between direct filler attractions and polymer-mediated bridging and steric stabilization. The spinodal phase diagrams are in qualitative agreement with recent solubility limit experimental observations on three systems, and testable predictions are made for other random copolymers. The distinctive non-monotonic variation of miscibility with copolymer composition is found to be primarily a consequence of composition-dependent, spatially short-range attractions between the A and B monomers with the fullerene. A remarkably rich, polymer-specific temperature dependence of the spinodal diagram is predicted which reflects the thermal sensitivity of spatial correlations which can result in fullerene miscibility either increasing or decreasing with cooling. The calculations are contrasted with a simpler effective homopolymer model and the random structure Flory-Huggins model. The former appears to be qualitatively reasonable but can incur large quantitative errors since it misses preferential packing of monomers near nanoparticles, while the latter appears to fail qualitatively due to its neglect of all spatial correlations.

Dadmun, Mark D↗

DOE OSTI2011

ORIGIN OF ULTRA-HIGH-ENERGY GALACTIC COSMIC RAYS: THE ISOTROPY PROBLEM

We study the propagation of ultra-high-energy cosmic rays (UHECRs) in the Galaxy, concentrating on the energy range below the ankle in the spectrum at 4 EeV. A Monte Carlo method, based on analytical solutions to the time-dependent diffusion problem, is used to account for intermittency by placing sources at random locations. Assuming a source population that scales with baryon mass density or star formation (e.g., long GRB), we derive constraints arising from intermittency and the observational limits on the composition and anisotropy. It is shown that the composition and anisotropy at 10{sup 18} eV are difficult to reproduce and require that either (1) the particle mean free path is much smaller than a gyroradius, implying the escape time is very long, (2) the composition is heavier than suggested by recent Auger data, (3) the ultra-high-energy sub-ankle component is mostly extragalactic, or (4) we are living in a rare lull in the UHECR production, and the current UHECR intensity is far below the Galactic time average. We therefore recommend a strong observational focus on determining the UHECR composition around 10{sup 18} eV.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Interaction between ions in hot dense plasma via screened Cornell potential

Hot dense plasma with non-ideal ions and weakly coupled electrons is studied analytically in the framework of the random phase approximation. It is shown that at some plasma parameters ions interact by a screened Cornell potential. The reduction in the transport coefficients due to the localization of the electron around the ion is predicted. This prediction is confirmed by the molecular dynamics simulation of the one-component ion plasma interacting via the obtained screened Cornell type potential.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

AN APPLICATION OF THE WIENER HERMITE EXPANSION TO THE NONLINEAR EVOLUTION OF DARK MATTER

We apply the Wiener Hermite (WH) expansion to the nonlinear evolution of the large-scale structure and obtain an approximate expression for the matter power spectrum in the full order of the expansion. This method allows us to expand any random function in terms of an orthonormal basis in the space of random functions in such a way that the first order of the expansion expresses the Gaussian distribution, and others are the deviations from Gaussianity. It is proved that the WH expansion is mathematically equivalent to the {Gamma}-expansion approach in the renormalized perturbation theory (RPT). While exponential behavior in the high-k limit has been proved for the mass density and velocity fluctuations of dark matter in the RPT, we prove the behavior again in the context of the WH expansion using the result of the standard perturbation theory (SPT). We propose a new approximate expression for the matter power spectrum which interpolates the low-k expression corresponding to the 1-loop level in SPT and the high-k expression obtained by taking a high-k limit of the WH expansion. The validity of our prescription is specifically verified by comparing with the 2-loop solutions of the SPT. The proposed power spectrum agrees with the result of the N-body simulation with accuracy better than 1% or 2% in a range of baryon acoustic oscillation scales, where the wave number is about k = 0.2-0.4 h Mpc{sup -1} at z = 0.5-3.0. This accuracy is comparable to or slightly less than the ones in the closure theory, the fractional difference of which from the N-body result is within 1%. One merit of our method is that the computational time is very short because only single and double integrals are involved in our solution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2012

Radiotherapy Breast Boost With Reduced Whole-Breast Dose Is Associated With Improved Cosmesis: The Results of a Comprehensive Assessment From the St. George and Wollongong Randomized Breast Boost Trial

Purpose: To evaluate comprehensively the effect of a radiotherapy boost on breast cosmetic outcomes after 5 years in patients treated with breast-conserving surgery. Methods: The St. George and Wollongong trial (NCT00138814) randomized 688 patients with histologically proven Tis-2, N 0-1, M0 carcinoma to the control arm of 50 Gy in 25 fractions (342 patients) and the boost arm of 45 Gy in 25 fractions to the whole breast followed by a 16 Gy in 8 fraction electron boost (346 patients). Five-year cosmetic outcomes were assessed by a panel subjectively in 385 patients and objectively using pBRA (relative breast retraction assessment). A subset of patients also had absolute BRA measurements. Clinician assessment and patient self-assessment of overall cosmetic and specific items as well as computer BCCT.core analysis were also performed. Results: The boost arm had improved cosmetic overall outcomes as scored by the panel and BCCT.core software with 79% (p = 0.016) and 81% (p = 0.004) excellent/good cosmesis respectively compared with 68% in no-boost arm. The boost arm also had lower pBRA and BRA values with a mean difference of 0.60 and 1.82 mm, respectively, but was not statistically significant. There was a very high proportion of overall excellent/good cosmetic outcome in 95% and 93% in the boost and no-boost arms using patient self-assessment. However, no difference in overall and specific items scored by clinician assessment and patient self-assessment was found. Conclusion: The results show the negative cosmetic effect of a 16-Gy boost is offset by a lower whole-breast dose of 45 Gy.

62 RADIOLOGY AND NUCLEAR MEDICINE↗