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At least 37 records · Page 2

Towards Robustness Guarantees for Feedback-Based Optimization

Feedback-based online optimization algorithms have gained traction in recent years because of their simple implementation, their ability to reject disturbances in real time, and their increased robustness to model mismatch. While the robustness properties have been observed both in simulation and experimental results, the theoretical analysis in the literature is mostly limited to nominal conditions. In this work, we propose a framework to systematically assess the robust stability of feedback-based online optimization algorithms. We leverage tools from monotone operator theory, variational inequalities and classical robust control to obtain tractable numerical tests that guarantee robust convergence properties of online algorithms in feedback with a physical system, even in the presence of disturbances and model uncertainty. The results are illustrated via an academic example and a case study of a power distribution system.

approximation algorithms↗

Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

The theory of open quantum systems lays the foundation for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this Letter, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure, we compactly represent quantum states with autoregressive neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of string states to partially restore the symmetry of the autoregressive neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one-dimensional and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo method to sample restricted Boltzmann machines. Our Letter provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Practical Application of Model-based Programming and State-based Architecture to Space Missions

A viewgraph presentation to develop models from systems engineers that accomplish mission objectives and manage the health of the system is shown. The topics include: 1) Overview; 2) Motivation; 3) Objective/Vision; 4) Approach; 5) Background: The Mission Data System; 6) Background: State-based Control Architecture System; 7) Background: State Analysis; 8) Overview of State Analysis; 9) Background: MDS Software Frameworks; 10) Background: Model-based Programming; 10) Background: Titan Model-based Executive; 11) Model-based Execution Architecture; 12) Compatibility Analysis of MDS and Titan Architectures; 13) Integrating Model-based Programming and Execution into the Architecture; 14) State Analysis and Modeling; 15) IMU Subsystem State Effects Diagram; 16) Titan Subsystem Model: IMU Health; 17) Integrating Model-based Programming and Execution into the Software IMU; 18) Testing Program; 19) Computationally Tractable State Estimation & Fault Diagnosis; 20) Diagnostic Algorithm Performance; 21) Integration and Test Issues; 22) Demonstrated Benefits; and 23) Next Steps

Mission Data System (MDS)↗

Bayesian Analysis of the Power Spectrum of the Cosmic Microwave Background

There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background. The sky, when viewed in the microwave, is very uniform, with a nearly perfect blackbody spectrum at 2.7 degrees. Very small amplitude brightness fluctuations (to one part in a million!!) trace small density perturbations in the early universe (roughly 300,000 years after the Big Bang), which later grow through gravitational instability to the large-scale structure seen in redshift surveys... In this talk, I will discuss a Bayesian formulation of this problem; discuss a Gibbs sampling approach to numerically sampling from the Bayesian posterior, and the application of this approach to the first-year data from the Wilkinson Microwave Anisotropy Probe. I will also comment on recent algorithmic developments for this approach to be tractable for the even more massive data set to be returned from the Planck satellite.

Bayesian inference↗

Benchmark solutions for the galactic ion transport equations with spatial and energy coupling

In order to anticipate future space shielding requirements, NASA has initiated an effort to formulate computational methods to simulate radiation effects in space. As part of the program, numerical transport algorithms have been developed for the deterministic Boltzman equation describing galactic cosmic ray (GCR) interactions with matter. It thus becomes necessary to assess the accuracy of proposed deterministic algorithms. For this reason, analytical benchmark solutions to mathematically tractable galactic cosmic ray equations have recently been obtained. Even though these problems involve simplifying assumptions of the associated physics, they still contain the essential features of the basic transport processes. The solutions obtained are features of the basic transport processes. The solutions obtained are compared to results from numerical algorithms in order to ensure proper coding and to provide a measure of the accuracy of the numerical methods used in the algorithm. For the first time, mathematical methods have been applied to the galactic ion transport (GIT) equations in the straight ahead approximation with constant nuclear properties. The approach utilizes a Laplace transforms inversion yielding a closed form benchmark solution which is also computationally efficient.

Ganapol, Barry D.↗

Co-evolution for Problem Simplification

This paper explores a co-evolutionary approach applicable to difficult problems with limited failure/success performance feedback. Like familiar "predator-prey" frameworks this algorithm evolves two populations of individuals - the solutions (predators) and the problems (prey). The approach extends previous work by rewarding only the problems that match their difficulty to the level of solut,ion competence. In complex problem domains with limited feedback, this "tractability constraint" helps provide an adaptive fitness gradient that, effectively differentiates the candidate solutions. The algorithm generates selective pressure toward the evolution of increasingly competent solutions by rewarding solution generality and uniqueness and problem tractability and difficulty. Relative (inverse-fitness) and absolute (static objective function) approaches to evaluating problem difficulty are explored and discussed. On a simple control task, this co-evolutionary algorithm was found to have significant advantages over a genetic algorithm with either a static fitness function or a fitness function that changes on a hand-tuned schedule.

Haith, Gary L.↗

Dynamic remapping of parallel computations with varying resource demands

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity.

Nicol, D. M.↗

Tractable Goal Selection with Oversubscribed Resources

We describe an efficient, online goal selection algorithm and its use for selecting goals at runtime. Our focus is on the re-planning that must be performed in a timely manner on the embedded system where computational resources are limited. In particular, our algorithm generates near optimal solutions to problems with fully specified goal requests that oversubscribe available resources but have no temporal flexibility. By using a fast, incremental algorithm, goal selection can be postponed in a "just-in-time" fashion allowing requests to be changed or added at the last minute. This enables shorter response cycles and greater autonomy for the system under control.

Rabideau, Gregg↗

Reveal, A General Reverse Engineering Algorithm for Inference of Genetic Network Architectures

Given the immanent gene expression mapping covering whole genomes during development, health and disease, we seek computational methods to maximize functional inference from such large data sets. Is it possible, in principle, to completely infer a complex regulatory network architecture from input/output patterns of its variables? We investigated this possibility using binary models of genetic networks. Trajectories, or state transition tables of Boolean nets, resemble time series of gene expression. By systematically analyzing the mutual information between input states and output states, one is able to infer the sets of input elements controlling each element or gene in the network. This process is unequivocal and exact for complete state transition tables. We implemented this REVerse Engineering ALgorithm (REVEAL) in a C program, and found the problem to be tractable within the conditions tested so far. For n = 50 (elements) and k = 3 (inputs per element), the analysis of incomplete state transition tables (100 state transition pairs out of a possible 10(exp 15)) reliably produced the original rule and wiring sets. While this study is limited to synchronous Boolean networks, the algorithm is generalizable to include multi-state models, essentially allowing direct application to realistic biological data sets. The ability to adequately solve the inverse problem may enable in-depth analysis of complex dynamic systems in biology and other fields.

Liang, Shoudan↗

Motion Planning Algorithms for Safety and Quantum Computing Efficiency

Motion planning remains a fundamental problem in robotics. Sampling-based algorithms use randomization to allow efficient solutions to this complex problem. As mobile robots and autonomous vehicles become more prevalent in everyday life, motion planning must be applied to increasingly challenging scenarios. Safety has become a paramount concern in motion planning for ensuring robotic applications enrich human lives. To date, many motion planning techniques to increase safety in the face of uncertain and dynamic environments have been developed. This dissertation first addresses distributional safety of Rapidly-Exploring Random Trees (RRT) through our algorithm W-Safe RRT. To acknowledge distributional uncertainty and poor modeling, W-Safe RRT uses the Wasserstein metric to provide a probabilistic bound on the distributional distance between a robot and obstacles. Human-interpretable environmental agent classification allows online safety margin adaptation. We propose and analyze an integrating region method for online classification that increases actor labeling accuracy based on behavioral feature values when compared to state of the art methods. The method performs class assignments based on local maximum likelihood in a created behavioral feature-space, allowing a notion of classification uncertainty. Model-based methods with safety guarantees can quickly become computationally in tractable, especially with multiple agents, higher dimensions, and plentiful unknowns. Sampling based algorithms have been parallelized for computation with multi-core computers and GPUs. We consider the use of quantum algorithms and computers for sampling-based motion planning for the first time. Quantum computing performs operations on superpositions of states and can solve certain problems much more efficiently than classical computers, but introduces previously unseen challenges. With Quantum-RRT, we recast the motion planning problem into a database-search structure and use Quantum Amplitude Amplification to find reachable states in the database with a quadratic performance increase over classical methods. We address two error sources with this method: quantum measurement and quantum oracle errors. We then extend this method to Parallel Quantum-RRT, which uses a manager-worker architecture with multiple parallel quantum workers to increase database search efficiency. We compare algorithm architectures and characterize probabilities of multiple workers finding solutions. Lastly, we test in simulation the quantum algorithms against classical versions in a wide variety of scenarios, concluding that a similar parallelization improvement is to be found in the quantum case as was found in the parallelization of classical RRT.

97 MATHEMATICS AND COMPUTING↗

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗

Adding GPU Support to the Markov Chain Monte Carlo Code Catmip

In geophysics, we are confronted with many under-determined inverse problems. For example, all of our observations of earthquakes are made at the Earth’s surface. So, when we try to infer how slip during an earthquake evolves in space and time, we find that there are many potential slip histories that are consistent with our limited observations and our understanding of earthquake physics. One way to approach these problems is with Bayesian analysis which allows us to infer the ensemble of all potential slip models that satisfy the observations and our prior knowledge of earthquake physics. In Bayesian analysis, our prior knowledge is known as the prior probability density function or prior PDF, the fit to the data is known as the data likelihood, and the target PDF that satisfies both the prior PDF and data likelihood is known as the posterior PDF. However, simulating the posterior PDF typically requires using Markov Chain Monte Carlo (MCMC) to draw tens of billions of random realizations of earthquake slip models, which may not be computationally feasible. To make this and similar geophysical inversions computationally tractable, we developed the Cascading Adaptive Transitional Metropolis In Parallel (CATMIP) algorithm. CATMIP is an efficient parallel Markov Chain Monte Carlo (MCMC) sampler that is used for model fitting and uncertainty quantification in geophysics. Example use cases are earthquake rupture modeling, determining mineral composition on Mars, reconstructing the history of ocean salinity, and historical earthquake relocation. CATMIP employs many parallel instances of the Metropolis algorithm for sampling in a transitioning framework. Transitioning is a process in which a set of random samples at equilibrium with a known probability density function (PDF) are used as seeds for the Markov chains to sample successive target PDFs that incrementally move the distribution from the starting seeds to the final desired PDF that describes the relative plausibility of potential values for the model parameters. The algorithm is implemented as a Master-Worker model employing MPI for communication. The worker processes are loosely coupled with global parameters periodically optimized by the master process. This provides a very high amount of parallelism with little communication between updates. During the presentation we will discuss the history of the algorithm and elaborate the earthquake rupture modeling use case for the CATMIP package. Our first step toward GPU optimization was to optimize the code for the CPU. CPU profiling revealed that most of the compute time is spent in calls to level 2 BLAS routines and calls to GSL random number generators. We revised the algorithm to employ level 3 BLAS routines instead. In our presentation we will describe how this was accomplished. Adding GPU support to CATMIP consisted mostly of replacing the calls to GSL with calls to GPU vendor-provided library routines. A small number of loops were directly implemented in CUDA. In the presentation will provide implementation details. Finally, we will discuss methods for profiling and opportunities for further optimizing GPU execution. By creating a code with the flexibility to run on either a CPU or GPU architecture, CATMIP can be used on systems ranging from large CPU-based HPC environments to single servers with GPU acceleration and everything in between.

HECC↗

Automated Adversary Emulation for Cyber-Physical Systems via Reinforcement Learning

Adversary emulation is an offensive exercise that provides a comprehensive assessment of a system’s resilience against cyber attacks. However, adversary emulation is typically a manual process, making it costly and hard to deploy in cyber-physical systems (CPS) with complex dynamics, vulnerabilities, and operational uncertainties. In this paper, we develop an automated, domain-aware approach to adversary emulation for CPS. We formulate a Markov Decision Process (MDP) model to determine an optimal attack sequence over a hybrid attack graph with cyber (discrete) and physical (continuous) components and related physical dynamics. We apply model-based and model-free reinforcement learning (RL) methods to solve the discrete-continuous MDP in a tractable fashion. As a baseline, we also develop a greedy attack algorithm and compare it with the RL procedures. We summarize our findings through a numerical study on sensor deception attacks in buildings to compare the performance and solution quality of the proposed algorithms.

Bhattacharya, Arnab↗

A graph-based network for predicting chemical reaction pathways in solid-state materials synthesis

Abstract Accelerated inorganic synthesis remains a significant challenge in the search for novel, functional materials. Many of the principles which enable “synthesis by design” in synthetic organic chemistry do not exist in solid-state chemistry, despite the availability of extensive computed/experimental thermochemistry data. In this work, we present a chemical reaction network model for solid-state synthesis constructed from available thermochemistry data and devise a computationally tractable approach for suggesting likely reaction pathways via the application of pathfinding algorithms and linear combination of lowest-cost paths in the network. We demonstrate initial success of the network in predicting complex reaction pathways comparable to those reported in the literature for YMnO 3 , Y 2 Mn 2 O 7 , Fe 2 SiS 4 , and YBa 2 Cu 3 O 6.5 . The reaction network presents opportunities for enabling reaction pathway prediction, rapid iteration between experimental/theoretical results, and ultimately, control of the synthesis of solid-state materials.

36 MATERIALS SCIENCE↗

Advanced data analysis in inertial confinement fusion and high energy density physics

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

47 OTHER INSTRUMENTATION↗

Tractable minor-free generalization of planar zero-field Ising models

In this work, we present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive 'gluing' of planar and O(1)-sized components and subsets of at most three vertices into a tree. The polynomial time algorithm of the dynamic programming type for solving exact inference (computing partition function) and exact sampling (generating i.i.d. samples) consists of sequential application of an efficient (for planar) or brute-force (for O(1)-sized) inference and sampling to the components as a black box. To illustrate the utility of the new family of tractable graphical models, we first build a polynomial algorithm for inference and sampling of zero-field Ising models over K 33 -minor-free topologies and over K 5 -minor-free topologies—both of which are extensions of the planar zero-field Ising models—which are neither genus- nor treewidth-bounded. Second, we empirically demonstrate an improvement in the approximation quality of the NP-hard problem of inference over the square-grid Ising model in a node-dependent nonzero 'magnetic' field.

97 MATHEMATICS AND COMPUTING↗

Temporal Constraint Reasoning With Preferences

A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time (specifically, associated with durations or orderings of events) on the basis of preferences. For example. a pair of events might be constrained to occur in a certain order, and, in addition. it might be preferable that the delay between them be as large, or as small, as possible. This paper explores problems in which a set of temporal constraints is specified, where each constraint is associated with preference criteria for making local decisions about the events involved in the constraint, and a reasoner must infer a complete solution to the problem such that, to the extent possible, these local preferences are met in the best way. A constraint framework for reasoning about time is generalized to allow for preferences over event distances and durations, and we study the complexity of solving problems in the resulting formalism. It is shown that while in general such problems are NP-hard, some restrictions on the shape of the preference functions, and on the structure of the preference set, can be enforced to achieve tractability. In these cases, a simple generalization of a single-source shortest path algorithm can be used to compute a globally preferred solution in polynomial time.

Khatib, Lina↗