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NASA NTRS1986

Combined optimization of image-gathering optics and image-processing algorithm for edge detection

This paper investigates the relationships between the image-gathering and image-processing systems for minimum mean-squared error estimation of scene characteristics. A stochastic optimization problem is formulated in which the objective is to determine a spatial characteristic of the scene rather than a feature of the already blurred, sampled, and noisy image data. The Wiener filter for the sampled image case is obtained as a special case, where the desired characteristics is scene restoration. Optimal edge detection is investigated. It is shown that the optimal edge detector compensates for the blurring introduced by the image-gathering optics, and, notably, that it is not circularly symmetric. The lack of circular symmetry is largely due to the geometric effects of the sampling lattice used in image acquisition.

Halyo, N.↗

NASA NTRS2013

Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing

A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.

Ono, Masahiro↗

NASA NTRS2016

Model-Based Fatigue Prognosis of Fiber-Reinforced Laminates Exhibiting Concurrent Damage Mechanisms

Prognostics of large composite structures is a topic of increasing interest in the field of structural health monitoring for aerospace, civil, and mechanical systems. Along with recent advancements in real-time structural health data acquisition and processing for damage detection and characterization, model-based stochastic methods for life prediction are showing promising results in the literature. Among various model-based approaches, particle-filtering algorithms are particularly capable in coping with uncertainties associated with the process. These include uncertainties about information on the damage extent and the inherent uncertainties of the damage propagation process. Some efforts have shown successful applications of particle filtering-based frameworks for predicting the matrix crack evolution and structural stiffness degradation caused by repetitive fatigue loads. Effects of other damage modes such as delamination, however, are not incorporated in these works. It is well established that delamination and matrix cracks not only co-exist in most laminate structures during the fatigue degradation process but also affect each other's progression. Furthermore, delamination significantly alters the stress-state in the laminates and accelerates the material degradation leading to catastrophic failure. Therefore, the work presented herein proposes a particle filtering-based framework for predicting a structure's remaining useful life with consideration of multiple co-existing damage-mechanisms. The framework uses an energy-based model from the composite modeling literature. The multiple damage-mode model has been shown to suitably estimate the energy release rate of cross-ply laminates as affected by matrix cracks and delamination modes. The model is also able to estimate the reduction in stiffness of the damaged laminate. This information is then used in the algorithms for life prediction capabilities. First, a brief summary of the energy-based damage model is provided. Then, the paper describes how the model is embedded within the prognostic framework and how the prognostics performance is assessed using observations from run-to-failure experiments

Prognostics↗

DOE OSTI2026

Preparing Fermions via Classical Sampling and Linear Combinations of Unitaries

We present an extension of the Evolving density matrices on Qubits (E$ρ$OQ) framework that enables efficient fault-tolerant preparation of fermionic quantum states. The original method circumvents state preparation by stochastic sampling, but faces a sign problem in fermionic systems leading to a large number of circuits necessary. We resolve this by combining classical stochastic sampling with a linear combination of unitaries method that avoids the exponential circuit scaling that plagued naïve implementations. The resulting algorithm requires $\mathcal{O}(M^2)$$R_Z$ rotations for circuit preparation, where $M$ is the number of retained basis states. We validate the method for ground and excited states in the Thirring model, including by computing two-point correlation functions relevant to scattering. In this model for fixed accuracy $\varepsilon$, $M$ is found to scale empirically as $M \propto \frac{1}{mg}\log(1/g)\log(1/m)$.

Gustafson, Erik J. [RIACS, Mtn. View] (ORCID:00000↗

DOE OSTI2022

Probabilistic Neural Computing with Stochastic Devices

Abstract The brain has effectively proven a powerful inspiration for the development of computing architectures in which processing is tightly integrated with memory, communication is event‐driven, and analog computation can be performed at scale. These neuromorphic systems increasingly show an ability to improve the efficiency and speed of scientific computing and artificial intelligence applications. Herein, it is proposed that the brain's ubiquitous stochasticity represents an additional source of inspiration for expanding the reach of neuromorphic computing to probabilistic applications. To date, many efforts exploring probabilistic computing have focused primarily on one scale of the microelectronics stack, such as implementing probabilistic algorithms on deterministic hardware or developing probabilistic devices and circuits with the expectation that they will be leveraged by eventual probabilistic architectures. A co‐design vision is described by which large numbers of devices, such as magnetic tunnel junctions and tunnel diodes, can be operated in a stochastic regime and incorporated into a scalable neuromorphic architecture that can impact a number of probabilistic computing applications, such as Monte Carlo simulations and Bayesian neural networks. Finally, a framework is presented to categorize increasingly advanced hardware‐based probabilistic computing technologies.

Misra, Shashank↗

DOE OSTI2021

A Hybrid Energy System Workflow for Energy Portfolio Optimization

This manuscript develops a workflow, driven by data analytics algorithms, to support the optimization of the economic performance of an Integrated Energy System. The goal is to determine the optimum mix of capacities from a set of different energy producers (e.g., nuclear, gas, wind and solar). A stochastic-based optimizer is employed, based on Gaussian Process Modeling, which requires numerous samples for its training. Each sample represents a time series describing the demand, load, or other operational and economic profiles for various types of energy producers. These samples are synthetically generated using a reduced order modeling algorithm that reads a limited set of historical data, such as demand and load data from past years. Numerous data analysis methods are employed to construct the reduced order models, including, for example, the Auto Regressive Moving Average, Fourier series decomposition, and the peak detection algorithm. All these algorithms are designed to detrend the data and extract features that can be employed to generate synthetic time histories that preserve the statistical properties of the original limited historical data. The optimization cost function is based on an economic model that assesses the effective cost of energy based on two figures of merit: the specific cash flow stream for each energy producer and the total Net Present Value. An initial guess for the optimal capacities is obtained using the screening curve method. The results of the Gaussian Process model-based optimization are assessed using an exhaustive Monte Carlo search, with the results indicating reasonable optimization results. The workflow has been implemented inside the Idaho National Laboratory’s Risk Analysis and Virtual Environment (RAVEN) framework. The main contribution of this study addresses several challenges in the current optimization methods of the energy portfolios in IES: First, the feasibility of generating the synthetic time series of the periodic peak data; Second, the computational burden of the conventional stochastic optimization of the energy portfolio, associated with the need for repeated executions of system models; Third, the inadequacies of previous studies in terms of the comparisons of the impact of the economic parameters. The proposed workflow can provide a scientifically defendable strategy to support decision-making in the electricity market and to help energy distributors develop a better understanding of the performance of integrated energy systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Quantum Optimization: Potential, Challenges, and the Path Forward

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of algorithmic approaches, often with little linkage. This is further complicated by the fragmented nature of the field of mathematical optimization, where major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions, have devoted communities. With these aspects in mind, this work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory — highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains – finance and sustainability – as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

A cloud computing approach to massively-parallel distributed stochastic optimization with application to geomechanical reservoir characterization

Many search strategies used to optimize parameters during hydrologic model calibration are inherently limited in that simulations must be performed sequentially in order for the algorithm to converge. As a result, the overall time required to reach a solution increases linearly with the number of steps necessary. In contrast, sampling strategies that attempt to approximate the posterior distribution of the parameters do not require the model simulations to be run in sequence and therefore invite the use of a massively parallel approach across heterogeneous computing environments. We apply a cloud computing methodology to this problem where a head node running on Amazon Web Services continuously produces candidate models that are distributed to arbitrary compute environments to run the simulation, in our case Clemson’s Palmetto cluster computer. Thus the time required to obtain a sufficient number of samples to produce an adequate approximation of the posterior distribution of the parameters is limited by the number of available compute sites. Monte Carlo sampling of the posterior space would be duplicative and inefficient, thus we combine Latin hypercube methods with genetic algorithms to ensure that no large regions of the parameter space are left unexplored, and that high probability regions are investigated thoroughly. We independently assess the fit to different types of data sets without the need to construct a single objective function. Sets of Pareto optimal models are particularly valuable when the quality and information content of data is poorly known or conceptual model errors exist in our simulation. We illustrate our approach for a problem where in situ strain data are used to calibrate the parameters of an oil reservoir in the Avant oil field in Oklahoma. We use well injection and shut-in to stress a deep (500m) confined formation, and observe the geomechanical response using borehole strainmeters installed in the shallow subsurface (30m). These data were then used to calibrate the poroelastic properties of the reservoir and caprock along with the geometry of an elliptic channel associated with the formation. Using our approach we are able to identify issues with model error as well as substantial tradeoffs that occur within the parameters.

inversion, stochastic, geomechanics, poroelastic, ↗

DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Path-accelerated stochastic molecular dynamics: Parallel-in-time integration using path integrals

Massively parallel computer architectures create new opportunities for the performance of long-time scale molecular dynamics (MD) simulations. Here, we introduce the path-accelerated molecular dynamics method that takes advantage of distributed computing to reduce the wall-clock time of MD simulation via parallelization with respect to stochastic MD time steps. The marginal distribution for the time evolution of a system is expressed in terms of a path integral, enabling the use of path sampling techniques to numerically integrate MD trajectories. By parallelizing the evaluation of the path action with respect to time and by initializing the path configurations from a nonequilibrium distribution, the algorithm enables significant speedups in terms of the length of MD trajectories that can be integrated in a given amount of wall-clock time. The method is demonstrated for Brownian dynamics, although it is generalizable to other stochastic equations of motion including open systems. We apply the method to two simple systems, a harmonic oscillator and a Lennard-Jones liquid, and we show that in comparison to the conventional Euler integration scheme for Brownian dynamics, the new method can reduce the wall-clock time for integrating trajectories of a given length by more than three orders of magnitude in the former system and more than two in the latter. This new method for parallelizing MD in the dimension of time can be trivially combined with algorithms for parallelizing the MD force evaluation to achieve further speedup.

Rosa-Raíces, Jorge L.↗

DOE OSTI2024

A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the “noise-aware numerical optimization” literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. In conclusion, we study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in scikit-quant.

classical optimizers↗

DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A Distributionally Robust Resilience Enhancement Strategy for Distribution Networks Considering Decision-Dependent Contingencies

When performing the resilience enhancement for distribution networks, there are two obstacles to reliably model the uncertain contingencies: 1) decision-dependent uncertainty (DDU) due to various line hardening decisions, and 2) distributional ambiguity due to limited outage information during extreme weather events (EWEs). Here, to address these two challenges, this paper develops scenario-wise decision-dependent ambiguity sets (SWDD-ASs), where the DDU and distributional ambiguity inherent in EWE-induced contingencies are simultaneously captured for each possible EWE scenario. Then, a two-stage tri-level decision-dependent distributionally robust resilient enhancement (DD-DRRE) model is formulated, whose outputs include the optimal line hardening, distributed generation (DG) allocation, and proactive network reconfiguration strategy under the worst-case distributions in SWDD-ASs. Subsequently, the DD-DRRE model is equivalently recast to a mixed-integer linear programming (MILP)-based master problem and multiple scenario-wise subproblems, facilitating the adoption of a customized column-and-constraint generation (C&CG) algorithm. Finally, case studies demonstrate a remarkable improvement in the out-of-sample performance of our model, compared to its prevailing stochastic and robust counterparts. Moreover, the potential values of incorporating the ambiguity and distributional information are quantitatively estimated, providing a useful reference for planners with different budgets and risk-aversion levels.

decision-dependent uncertainty↗

DOE OSTI2024

Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Characterization of single-shot attosecond pulses with angular streaking photoelectron spectra

Most of the traditional attosecond pulse retrieval algorithms are based on a so-called attosecond streak camera technique, in which the momentum of the electron is shifted by an amount depending on the relative time delay between the attosecond pulse and the streaking infrared pulse. Thus, temporal information of the attosecond pulse is encoded in the amount of momentum shift in the streaked photoelectron momentum spectrogram S(p,τ), where p is the momentum of the electron along the polarization direction and τ is the time delay. An iterative algorithm is then employed to reconstruct the attosecond pulse from the streaking spectrogram. This method, however, cannot be applied to attosecond pulses generated from free-electron x-ray lasers where each single shot is different and stochastic in time. However, using a circularly polarized infrared laser as the streaking field, a two (or three)-dimensional angular streaking electron spectrum can be used to retrieve attosecond pulses for each shot, as well as the time delay with respect to the circularly polarized IR field. Here we show that a retrieval algorithm previously developed for the traditional streaking spectrogram can be modified to efficiently characterize single-shot attosecond pulses. The methods have been applied to retrieve 188 single shots from recent experiments. We analyze the statistical behavior of these 188 pulses in terms of pulse duration, bandwidth, pulse peak energy, and time delay with respect to the IR field. Furthermore, the retrieval algorithm is efficient and can be easily used to characterize a large number of shots in future experiments for attosecond pulses at free-electron x-ray laser facilities.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Quantum-assisted associative adversarial network: applying quantum annealing in deep learning

Abstract Generative models have the capacity to model and generate new examples from a dataset and have an increasingly diverse set of applications driven by commercial and academic interest. In this work, we present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted by the discriminator. A quantum processor can be used to sample from the model to train the Boltzmann machine. This novel hybrid quantum-classical algorithm joins a growing family of algorithms that use a quantum processor sampling subroutine in deep learning, and provides a scalable framework to test the advantages of quantum-assisted learning. For the latent space model, fully connected, symmetric bipartite and Chimera graph topologies are compared on a reduced stochastically binarized MNIST dataset, for both classical and quantum sampling methods. The quantum-assisted associative adversarial network successfully learns a generative model of the MNIST dataset for all topologies. Evaluated using the Fréchet inception distance and inception score, the quantum and classical versions of the algorithm are found to have equivalent performance for learning an implicit generative model of the MNIST dataset. Classical sampling is used to demonstrate the algorithm on the LSUN bedrooms dataset, indicating scalability to larger and color datasets. Though the quantum processor used here is a quantum annealer, the algorithm is general enough such that any quantum processor, such as gate model quantum computers, may be substituted as a sampler.

Wilson, Max (ORCID:0000000207983391)↗

DOE OSTI2022

A hybrid robust-stochastic optimization approach for day-ahead scheduling of cascaded hydroelectric system in restructured electricity market

Uncertainties arising from complicated natural and market environments pose great challenges for the efficient operation of cascaded hydroelectric systems. To overcome these challenges, this paper studies the day-ahead scheduling of cascaded hydroelectric systems in a restructured electricity market with the presence of uncertainties in electricity price and natural water inflow. To properly model the uncertainty, we consider the unique characteristics of these two types of uncertainties and capture them via the uncertainty set and stochastic scenarios, respectively. Further, a hybrid robust-stochastic optimization model is developed to simultaneously hedge against these two types of uncertainties, which is formulated as a large-scale non-convex optimization problem with mixed integer recourse. After introducing linearization of nonlinear terms, a tailored hybrid decomposition scheme combining Lagrangian relaxation and Dantzig-Wolfe decomposition is adopted to achieve efficient computation of the proposed model. Two real-world cases are conducted to demonstrate the capability and characteristics of the proposed model and algorithms.

13 HYDRO ENERGY↗

DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗