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DOE OSTI2026

Intrusive Uncertainty Quantification and Optimal Experiment Design in the Open-Source Pyomo Ecosystem

This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Optical Design of a Compact Imaging Spectrometer for Planetary Mineralogy

We present the design of a compact, wide-angle pushbroom imaging spectrometer suitable for exploration of solar system bodies from low orbit. The spectrometer is based on a single detector array with a broadband response that covers the range 400 to 3000 nm and provides a spectral sampling of 10 nm. The telescope has a 24-deg field of view with 600 spatially resolved elements (detector pixels). A specially designed convex diffraction grating permits optimization of the signal-to-noise ratio through the entire spectral band. Tolerances and design parameters permit the achievement of high uniformity of response through field and wavelength. The spectrometer performance is evaluated in terms of predicted spectral and spatial response functions and from the point of view of minimizing their variation through field and wavelength. The design serves as an example for illustrating the design principles specific to this type of system.

space optics↗

DOE OSTI2019

Optimal Distributed Control of Spatially Invariant Time Varying Linear Systems

In this paper, the optimal distributed linear time varying H2 control problem for cone causal spatially invariant linear time varying (SILTV) systems is considered. This class of systems was initially defined in the work of Voulgaris et al. for cone causal spatially invariant (SI) linear time invariant (LTI) systems. First, the optimal time varying H2 problem is posed using a version of the Youla parameterization. This allows to transform the problem into an affine form which results in a convex but infinite dimensional distributed optimization. Next, the problem is solved by computing an operator projection on a class of time varying Youla parameters with a cone causal distributed structure. The cone causal spatially invariant systems are viewed as input-output multiplicative operators with a mixed causal time varying structure with respect to time, and spatially invariant with respect to the space dimension.

Djouadi, Seddik M.↗

DOE OSTI2022

Market mechanism to enable grid-aware dispatch of Aggregators in radial distribution networks

This paper presents a market-based optimization framework wherein Aggregators can compete for nodal capacity across a distribution feeder and guarantee that allocated flexible capacity cannot cause overloads or congestion. This mechanism, thus, allows Aggregators with allocated capacity to pursue a number of services at the whole-sale market level to maximize revenue of flexible resources. Based on Aggregator bids of capacity (MW) and network access price ($/MW), the distribution system operator (DSO) formulates an optimization problem that prioritizes capacity to the different Aggregators across the network while implicitly considering AC network constraints. This grid-aware allocation is obtained by incorporating a convex inner approximation into the optimization framework that prioritizes hosting capacity to different Aggregators. We adapt concepts from transmission-level capacity market clearing, utility demand charges, and Internet-like bandwidth allocation rules to distribution system operations by incorporating nodal voltage and transformer constraints into the optimization framework. Simulation based results on IEEE distribution networks showcase the effectiveness of the approach.

Nazir, Mohammad Nawaf↗

DOE OSTI2020

Formulation and solution approach for calibrating activity-based travel demand model-system via microsimulation

This study addresses the problem of calibrating utility-maximizing nested logit activity-based travel demand model-systems. After estimation, it is common practice to use aggregate measurements to calibrate the estimated model-system’s parameters prior to their application in transportation planning, policy making, and operations. However, calibration of activity-based model-systems has received much less attention. Existing calibration approaches are myopic heuristics in the sense that they do not consider the fundamental inter-dependencies among choice-models and do not have a systematic way to adjust model parameters. Also, other purely simulation-based approaches do not perform well in large-scale applications. In this study, we focus on utility-maximizing nested logit activity-based model-systems and calibrating aggregate statistics such as activity shares, mode shares, time-dependent & mode-specific OD flows, and time-dependent & mode-specific sensor counts. We formulate the calibration problem as a simulation-based optimization problem and propose a stochastic gradient-based solution procedure to solve it. The solution procedure relies on microsimulation to calculate expectations of the aggregate statistics of interest to the calibration problem. Additionally, we derive approximate analytical expressions for the gradient of the objective function —that are evaluated through microsimulation on mini-batches of the population. The proposed solution procedure is sensitive to the fundamental structure of the activity-based model-system and is non-myopic in considering the dependencies across its model components. The formulated optimization problem is non-convex, highly nonlinear, and potentially has multiple-minima. Lastly, we show —through a real-world application— that the proposed solution procedure outperforms other state-of-the-art purely simulation-based optimization approaches in terms of computational efficiency, stability, and convergence. We also compare various gradient-based solution algorithms to determine the best algorithm to update the parameters. This work has the potential to facilitate wider and easier application of activity-based model-systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Evaluating the effects of real power losses in optimal power flow based storage integration

This study proposes a DC optimal power flow (DCOPF) with losses formulation (the `-DCOPF+S problem) and uses it to investigate the role of real power losses in OPF based grid-scale storage integration. We derive the `- DCOPF+S problem by augmenting a standard DCOPF with storage (DCOPF+S) problem to include quadratic real power loss approximations. This procedure leads to a multi-period nonconvex quadratically constrained quadratic program, which we prove can be solved to optimality using either a semidefinite or second order cone relaxation. Our approach has some important benefits over existing models. It is more computationally tractable than ACOPF with storage (ACOPF+S) formulations and the provably exact convex relaxations guarantee that an optimal solution can be attained for a feasible problem. Adding loss approximations to a DCOPF+S model leads to a more accurate representation of locational marginal prices, which have been shown to be critical to determining optimal storage dispatch and siting in prior ACOPF+S based studies. Case studies demonstrate the improved accuracy of the `-DCOPF+S model over a DCOPF+S model and the computational advantages over an ACOPF+S formulation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2015

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by three steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Nonconvex regularization for sparse neural networks

Convex ℓ 1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in this paper, a nonconvex regularization method is investigated in the context of shallow ReLU networks: We prove that in contrast to the convex approach, any resulting (locally optimal) network is finite even in the presence of infinite data (i.e., if the data distribution is known and the limiting case of infinite samples is considered). Moreover, here we show that approximation guarantees and existing bounds on the network size for finite data are maintained.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

Abstract ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. If the plasma temperature were to inadvertently rise in this burning regime, the positive correlation between temperature and the fusion reaction rate would establish a destabilizing positive feedback loop. Careful regulation of the plasma’s temperature and density, or burn control, is required to prevent these potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. An adaptive estimator manages destabilizing uncertainties in the plasma confinement properties and the particle recycling conditions (caused by plasma–wall interactions). The controller regulates the plasma density with requests for deuterium and tritium particle injections. In ITER-like plasmas, the fusion-born alpha particles will primarily heat the plasma electrons, resulting in different electron and ion temperatures in the core. By considering separate response models for the electron and ion energies, the proposed controller can independently regulate the electron and ion temperatures by requesting that different amounts of auxiliary power be delivered to the electrons and ions. These two commands for a specific control effort (electron and ion heating) are sent to an actuator allocation module that optimally maps them to the heating actuators available to ITER: an electron cyclotron heating system (20 MW), an ion cyclotron heating system (20 MW), and two neutral beam injectors (16.5 MW each). Two different actuator allocators are presented in this work. The first actuator allocator finds the optimal mapping by solving a convex quadratic program that includes actuator saturation and rate limits. It is nonadaptive and assumes that the mapping between the commanded control efforts and the allocated actuators (i.e. the effector model) contains no uncertainties. The second actuator allocation module has an adaptive estimator to handle uncertainties in the effector model. This uncertainty includes actuator efficiencies, the fractions of neutral beam heating that are deposited into the plasma electrons and ions, and the tritium concentration of the fueling pellets. Furthermore, the adaptive allocator considers actuator dynamics (actuation lag) that contain uncertainty. This adaptive allocation algorithm is more computationally efficient than the aforementioned nonadaptive allocator because it is computed using dynamic update laws so that finding the solution to a static optimization problem is not required at every time step. A simulation study assesses the performance of the proposed adaptive burn controller augmented with each of the actuator allocation modules.

Physics↗

DOE OSTI2021

Analysis of the ratio of ℓ 1 and ℓ 2 norms in compressed sensing

We study the ratio of ℓ 1 and ℓ 2 norms ( ℓ 1 / ℓ 2 ) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ 1 / ℓ 2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ 1 / ℓ 2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ 1 / ℓ 2 algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Efficient numerical methods to solve sparse linear equations with application to PageRank

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. Here, we propose three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks

To fit sparse linear associations, a LASSO sparsity inducing penalty with a single hyperparameter provably allows to recover the important features (needles) with high probability in certain regimes even if the sample size is smaller than the dimension of the input vector (haystack). More recently learners known as artificial neural networks (ANN) have shown great successes in many machine learning tasks, in particular fitting nonlinear associations. Small learning rate, stochastic gradient descent algorithm and large training set help to cope with the explosion in the number of parameters present in deep neural networks. Yet few ANN learners have been developed and studied to find needles in nonlinear haystacks. Driven by a single hyperparameter, our ANN learner, like for sparse linear associations, exhibits a phase transition in the probability of retrieving the needles, which we do not observe with other ANN learners. To select our penalty parameter, we generalize the universal threshold of Donoho and Johnstone (Biometrika 81(3):425–455, 1994) which is a better rule than the conservative (too many false detections) and expensive cross-validation. In the spirit of simulated annealing, we propose a warm-start sparsity inducing algorithm to solve the high-dimensional, non-convex and non-differentiable optimization problem. We perform simulated and real data Monte Carlo experiments to quantify the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A Peer-to-Peer Market-Based Control Strategy for a Smart Residential Community with Behind-the-Meter Distributed Energy Resources

This paper presents a distributed peer-to-peer market control strategy to manage and to enable resource sharing of behind-the-meter distributed energy resources in a residential community. In the proposed strategy, each consumer or prosumer determines the flexibility of their point of connection to the power network such that the obtained flexibility is network-feasible. Based on the feasible flexibility, the consumers and the prosumers trade power among each other at each time instance to fulfill their preferred load requirements while maximizing their payoffs and helping to regulate node voltages inside the community. Because the problem to be solved is non-convex, a distributed particle swarm optimization algorithm is used to coordinate the consumers/prosumers in a fully autonomous manner without any centralized or hierarchical coordination. Numerical simulations performed on a community of 48 homes demonstrate the efficacy of the proposed approach.

behind-the-meter↗

DOE OSTI2022

A Peer-to-Peer Market-Based Control Strategy for a Smart Residential Community with Behind-the-Meter Distributed Energy Resources: Preprint

behind-the-meter↗

DOE OSTI2023

A Peer-to-Peer Market-Based Control Strategy for a Smart Residential Community with Behind-the-Meter Distributed Energy Resources

This paper presents a distributed peer-to-peer market control strategy to manage and to enable resource sharing of behind-the-meter distributed energy resources in a residential community. In the proposed strategy, each consumer or prosumer determines the flexibility of their point of connection to the power network such that the obtained flexibility is network-feasible. Based on the feasible flexibility, the consumers and the prosumers trade power among each other at each time instance to fulfil their preferred load requirements while maximizing their payoffs and helping to regulate node voltages inside the community. Because the problem to be solved is non-convex, a distributed particle swarm optimization algorithm is used to coordinate the consumers/prosumers in a fully autonomous manner without any centralized or hierarchical coordination. Numerical simulations performed on a community of 48 homes demonstrate the efficacy of the proposed approach.

distributed energy resource↗

DOE OSTI2019

SUSPECT: MINLP special structure detector for Pyomo

We present SUSPECT, an open source toolkit that symbolically analyzes mixed-integer nonlinear optimization problems formulated using the Python algebraic modeling library Pyomo. We present the data structures and algorithms used to implement SUSPECT. SUSPECT works on a directed acyclic graph representation of the optimization problem to perform: bounds tightening, bound propagation, monotonicity detection, and convexity detection. We show how the tree-walking rules in SUSPECT balance the need for lightweight computation with effective special structure detection. SUSPECT can be used as a standalone tool or as a Python library to be integrated in other tools or solvers. Here, we highlight the easy extensibility of SUSPECT with several recent convexity detection tricks from the literature. We also report experimental results on the MINLPLib 2 dataset.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

MO-AB-BRA-01: A Global Level Set Based Formulation for Volumetric Modulated Arc Therapy

Purpose: The current clinical Volumetric Modulated Arc Therapy (VMAT) optimization is formulated as a non-convex problem and various greedy heuristics have been employed for an empirical solution, jeopardizing plan consistency and quality. We introduce a novel global direct aperture optimization method for VMAT to overcome these limitations. Methods: The global VMAT (gVMAT) planning was formulated as an optimization problem with an L2-norm fidelity term and an anisotropic total variation term. A level set function was used to describe the aperture shapes and adjacent aperture shapes were penalized to control MLC motion range. An alternating optimization strategy was implemented to solve the fluence intensity and aperture shapes simultaneously. Single arc gVMAT plans, utilizing 180 beams with 2° angular resolution, were generated for a glioblastoma multiforme (GBM), lung (LNG), and 2 head and neck cases—one with 3 PTVs (H&N3PTV) and one with 4 PTVs (H&N4PTV). The plans were compared against the clinical VMAT (cVMAT) plans utilizing two overlapping coplanar arcs. Results: The optimization of the gVMAT plans had converged within 600 iterations. gVMAT reduced the average max and mean OAR dose by 6.59% and 7.45% of the prescription dose. Reductions in max dose and mean dose were as high as 14.5 Gy in the LNG case and 15.3 Gy in the H&N3PTV case. PTV coverages (D95, D98, D99) were within 0.25% of the prescription dose. By globally considering all beams, the gVMAT optimizer allowed some beams to deliver higher intensities, yielding a dose distribution that resembles a static beam IMRT plan with beam orientation optimization. Conclusions: The novel VMAT approach allows for the search of an optimal plan in the global solution space and generates deliverable apertures directly. The single arc VMAT approach fully utilizes the digital linacs’ capability in dose rate and gantry rotation speed modulation. Varian Medical Systems, NIH grant R01CA188300, NIH grant R43CA183390.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Local Feature Sufficiency Exploration for Predicting Security-constrained Generation Dispatch in Multi-Area Power Systems

Deriving generation dispatch is essential for efficient and secure operation of electric power systems. This is usually achieved by solving a security-constrained optimal power flow(SCOPF) problem, which is by nature non-convex, nonlinear and thus computational intensive. The state-of-the-art optimization approaches are not able to solve this problem for large-scale power systems within power system operation time window (usually 5 minutes). In this work, we developed supervised learning approaches to determine security-constrained generation dispatch within much shorter time window. More importantly, the physical constrain of only accessing to local measurements and other information in most utilities’ real-time operation can not be ignored for the predictive models.The feasibility and accuracy of utilizing only local features(measurements and grid information in one area) to predict optimal local generation dispatch (dispatch of all generators in the corresponding area) in multi-area power systems has been explored. The results showed optimal local generation dispatch can be predicted with local features with high accuracy, which is comparable to the results obtained with global features.

Sun, Yixuan↗