arXiv subjects

Mihai Anitescu

Publications and source records attributed to Mihai Anitescu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Recovering sparse DFT from missing signals via interior point method on GPU

We propose a method to recover the sparse discrete Fourier transform (DFT) of a signal that is both noisy and potentially incomplete, with missing values. The problem is formulated as a penalized least-squares minimization based on the inverse discrete Fourier transform (IDFT) with an $\ell_1$-penalty term, reformulated to be solvable using a primal-dual interior point method (IPM). Although Krylov methods are not typically used to solve Karush-Kuhn-Tucker (KKT) systems arising in IPMs due to their ill-conditioning, we employ a tailored preconditioner and establish new asymptotic bounds on the condition number of preconditioned KKT matrices. Thanks to this dedicated preconditioner -- and the fact that FFT and IFFT operate as linear operators without requiring explicit matrix materialization -- KKT systems can be solved efficiently at large scales in a matrix-free manner. Numerical results from a Julia implementation leveraging GPU-accelerated interior point methods, Krylov methods, and FFT toolkits demonstrate the scalability of our approach on problems with hundreds of millions of variables, inclusive of real data obtained from the diffuse scattering from a slightly disordered Molybdenum Vanadium Dioxide crystal.

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arXiv2025

Near-Optimal Performance of Stochastic Model Predictive Control

This article presents a dynamic regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. While this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: Under stabilizability and detectability conditions, the dynamic regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.

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arXiv2025

Floodgates up to contain the DeePC and limit extrapolation

Behavioral data-enabled control approaches typically assume data-generating systems of linear dynamics. This may result in false generalization if the newly designed closed-loop system results in input-output distributional shifts beyond learning data. These shifts may compromise safety by activating harmful nonlinearities in the data-generating system not experienced previously in the data and/or not captured by the linearity assumption inherent in these approaches. This paper proposes an approach to slow down the distributional shifts and therefore enhance the safety of the data-enabled methods. This is achieved by introducing quadratic regularization terms to the data-enabled predictive control formulations. Slowing down the distributional shifts comes at the expense of slowing down the exploration, in a trade-off resembling the exploration vs exploitation balance in machine learning.

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arXiv2024

A Framework for Balancing Power Grid Efficiency and Risk with Bi-objective Stochastic Integer Optimization

Power grid expansion planning requires making large investment decisions in the present that will impact the future cost and reliability of a system exposed to wide-ranging uncertainties. Extreme temperatures can pose significant challenges to providing power by increasing demand and decreasing supply and have contributed to recent major power outages. We propose to address a modeling challenge of such high-impact, low-frequency events with a bi-objective stochastic integer optimization model that finds solutions with different trade-offs between efficiency in normal conditions and risk to extreme events. We propose a conditional sampling approach paired with a risk measure to address the inherent challenge in approximating the risk of low-frequency events within a sampling based approach. We present a model for spatially correlated, county-specific temperatures and a method to generate both unconditional and conditionally extreme temperature samples from this model efficiently. These models are investigated within an extensive case study with realistic data that demonstrates the effectiveness of the bi-objective approach and the conditional sampling technique. We find that spatial correlations in the temperature samples are essential to finding good solutions and that modeling generator temperature dependence is an important consideration for finding efficient, low-risk solutions.

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arXiv2024

Scalable Multi-Period AC Optimal Power Flow Utilizing GPUs with High Memory Capacities

This paper demonstrates the scalability of open-source GPU-accelerated nonlinear programming (NLP) frameworks -- ExaModels.jl and MadNLP.jl -- for solving multi-period alternating current (AC) optimal power flow (OPF) problems on GPUs with high memory capacities (e.g., NVIDIA GH200 with 480 GB of unified memory). There has been a growing interest in solving multi-period AC OPF problems, as the increasingly fluctuating electricity market requires operation planning over multiple periods. These problems, formerly deemed intractable, are now becoming technologically feasible to solve thanks to the advent of high-memory GPU hardware and accelerated NLP tools. This study evaluates the capability of these tools to tackle previously unsolvable multi-period AC OPF instances. Our numerical experiments, run on an NVIDIA GH200, demonstrate that we can solve a multi-period OPF instance with more than 10 million variables up to $10^{-4}$ precision in less than 10 minutes. These results demonstrate the efficacy of the GPU-accelerated NLP frameworks for the solution of extreme-scale multi-period OPF. We provide ExaModelsPower.jl, an open-source modeling tool for multi-period AC OPF models for GPUs.

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arXiv2024

Extended Kalman filter -- Koopman operator for tractable stochastic optimal control

The theory of dual control was introduced more than seven decades ago. Although it has provided rich insights to the fields of control, estimation, and system identification, dual control is generally computationally prohibitive. In recent years, however, the use of Koopman operator theory for control applications has been emerging. This paper presents a new reformulation of the stochastic optimal control problem that, employing the Koopman operator, yields a standard LQR problem with the dual control as its solution. We provide a numerical example that demonstrates the effectiveness of the proposed approach compared with certainty equivalence control, when applied to systems with varying observability.

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arXiv2024

Accelerating Optimal Power Flow with GPUs: SIMD Abstraction of Nonlinear Programs and Condensed-Space Interior-Point Methods

This paper introduces a framework for solving alternating current optimal power flow (ACOPF) problems using graphics processing units (GPUs). While GPUs have demonstrated remarkable performance in various computing domains, their application in ACOPF has been limited due to challenges associated with porting sparse automatic differentiation (AD) and sparse linear solver routines to GPUs. We address these issues with two key strategies. First, we utilize a single-instruction, multiple-data abstraction of nonlinear programs. This approach enables the specification of model equations while preserving their parallelizable structure and, in turn, facilitates the parallel AD implementation. Second, we employ a condensed-space interior-point method (IPM) with an inequality relaxation. This technique involves condensing the Karush--Kuhn--Tucker (KKT) system into a positive definite system. This strategy offers the key advantage of being able to factorize the KKT matrix without numerical pivoting, which has hampered the parallelization of the IPM algorithm. By combining these strategies, we can perform the majority of operations on GPUs while keeping the data residing in the device memory only. Comprehensive numerical benchmark results showcase the advantage of our approach. Remarkably, our implementations -- MadNLP.jl and ExaModels.jl -- running on NVIDIA GPUs achieve an order of magnitude speedup compared with state-of-the-art tools running on contemporary CPUs.

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arXiv2024

Data-Driven Estimation of Failure Probabilities in Correlated Structure-Preserving Stochastic Power System Models

We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed line energy probability density function is derived from the Fokker--Planck equation of the full-order continuous Markov process. Our method consists of estimates produced by numerically integrating this reduced equation. Numerical experiments for scalar- and vector-valued energy functions are conducted using the classical multimachine model under spatiotemporally correlated noise perturbation. The method demonstrates a more sample-efficient approach for computing probabilities of tail events when compared with kernel density estimation. Moreover, it produces vastly more accurate estimates of joint event occurrence when compared with independent models.

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arXiv2023

Voltage-Dependent Electromechanical Wave Propagation Modeling for Dynamic Stability Analysis in Power Systems

Accurate dynamic modeling of power systems is essential to assess the stability of electrical power systems when faced with disturbances, which can trigger cascading failures leading to blackouts. A continuum model proves to be effective in capturing Electromechanical Wave (EMW) propagation characteristics, including its velocity, arrival time, and deviations. Analyzing these characteristics enables the assessment of the impacts of EMW on the performance of the protection system. Prior research has often modeled nonlinear EMW propagation through Partial Differential Equations (PDEs) within a homogeneous and uniform frame structure, assuming constant bus voltages across the entire power system. However, this assumption can produce inaccurate results. In this paper, we relax this assumption by introducing a second-order nonlinear hyperbolic EMW propagation equation model that accounts for voltage variations. Additionally, we present numerical solutions for the EMW propagation equation using the Lax-Wendroff integration method. To validate our approach, we conduct simulations on two test systems: a two-bus one-machine system and the New England 39-bus 10-machine system. The simulation results demonstrate the effectiveness of our proposed model and emphasize the importance of including the bus voltage equations in the analysis.

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arXiv2023

Centralized calibration of power system dynamic models using variational data assimilation

This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based resources, assessing power systems' dynamic performance under disturbances has become challenging, necessitating robust model calibration methods. The proposed approach expands on previous Bayesian frameworks by establishing a posterior distribution of parameters using an approximation around the maximum a posteriori value. We illustrate the efficacy of our method by generating events of varying intensity, highlighting its ability to capture the systems' evolution accurately and with associated uncertainty estimates. This research improves the precision of dynamic performance assessments in modern power systems, with potential applications in managing uncertainties and optimizing system operations.

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arXiv2023

Network Cascade Vulnerability using Constrained Bayesian Optimization

Measures of power grid vulnerability are often assessed by the amount of damage an adversary can exact on the network. However, the cascading impact of such attacks is often overlooked, even though cascades are one of the primary causes of large-scale blackouts. This paper explores modifications of transmission line protection settings as candidates for adversarial attacks, which can remain undetectable as long as the network equilibrium state remains unaltered. This forms the basis of a black-box function in a Bayesian optimization procedure, where the objective is to find protection settings that maximize network degradation due to cascading. Notably, our proposed method is agnostic to the choice of the cascade simulator and its underlying assumptions. Numerical experiments reveal that, against conventional wisdom, maximally misconfiguring the protection settings of all network lines does not cause the most cascading. More surprisingly, even when the degree of misconfiguration is limited due to resource constraints, it is still possible to find settings that produce cascades comparable in severity to instances where there are no resource constraints.

cs.SI↗

arXiv2023

A Fast Temporal Decomposition Procedure for Long-horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian, provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit stepsize is accepted locally for the approximate search direction, and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme by Na et al., 2022. However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, while we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

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arXiv2023

Application of probabilistic modeling and automated machine learning framework for high-dimensional stress field

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer models makes it computationally intensive to query them hundreds of times for optimization and one usually relies on a simplified model albeit at the cost of losing predictive accuracy and precision. Towards this, data-driven surrogate modeling methods have shown a lot of promise in emulating the behavior of the expensive computer models. However, a major bottleneck in such methods is the inability to deal with high input dimensionality and the need for relatively large datasets. With such problems, the input and output quantity of interest are tensors of high dimensionality. Commonly used surrogate modeling methods for such problems, suffer from requirements like high number of computational evaluations that precludes one from performing other numerical tasks like uncertainty quantification and statistical analysis. In this work, we propose an end-to-end approach that maps a high-dimensional image like input to an output of high dimensionality or its key statistics. Our approach uses two main framework that perform three steps: a) reduce the input and output from a high-dimensional space to a reduced or low-dimensional space, b) model the input-output relationship in the low-dimensional space, and c) enable the incorporation of domain-specific physical constraints as masks. In order to accomplish the task of reducing input dimensionality we leverage principal component analysis, that is coupled with two surrogate modeling methods namely: a) Bayesian hybrid modeling, and b) DeepHyper's deep neural networks. We demonstrate the applicability of the approach on a problem of a linear elastic stress field data.

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arXiv2023

Scalable Physics-based Maximum Likelihood Estimation using Hierarchical Matrices

Physics-based covariance models provide a systematic way to construct covariance models that are consistent with the underlying physical laws in Gaussian process analysis. The unknown parameters in the covariance models can be estimated using maximum likelihood estimation, but direct construction of the covariance matrix and classical strategies of computing with it requires $n$ physical model runs, $n^2$ storage complexity, and $n^3$ computational complexity. To address such challenges, we propose to approximate the discretized covariance function using hierarchical matrices. By utilizing randomized range sketching for individual off-diagonal blocks, the construction process of the hierarchical covariance approximation requires $O(\log{n})$ physical model applications and the maximum likelihood computations require $O(n\log^2{n})$ effort per iteration. We propose a new approach to compute exactly the trace of products of hierarchical matrices which results in the expected Fischer information matrix being computable in $O(n\log^2{n})$ as well. The construction is totally matrix-free and the derivatives of the covariance matrix can then be approximated in the same hierarchical structure by differentiating the whole process. Numerical results are provided to demonstrate the effectiveness, accuracy, and efficiency of the proposed method for parameter estimations and uncertainty quantification.

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arXiv2023

Efficient Computation of Power System Maximum Transient Linear Growth

Existing methods to determine the stability of a power system to small perturbations are based on eigenvalue analysis and focus on the asymptotic (long-term) behavior of the power grid. During the preasymptotic (short-term) transient, however, the system can exhibit large growth that is not explained by eigenvalues alone. In this paper we propose a new framework to determine the maximum (optimal) preasymptotic growth using the singular value decomposition. The approach is tailored to the analysis of quantities of interest in power system dynamics, such as the set of rotor speed deviations. Matrix-free techniques are developed to avoid the explicit formation of dense matrices and enable the analysis of large-scale systems without reaching memory bounds. Extensive results carried out from small to very large-scale systems (e.g., 70k-bus system) verify the theoretical aspects of the technique.

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arXiv2023

Graph Neural Network-Inspired Kernels for Gaussian Processes in Semi-Supervised Learning

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a promising class of models for graph-structured data in semi-supervised learning and beyond. Their competitive performance is often attributed to a proper capturing of the graph inductive bias. In this work, we introduce this inductive bias into GPs to improve their predictive performance for graph-structured data. We show that a prominent example of GNNs, the graph convolutional network, is equivalent to some GP when its layers are infinitely wide; and we analyze the kernel universality and the limiting behavior in depth. We further present a programmable procedure to compose covariance kernels inspired by this equivalence and derive example kernels corresponding to several interesting members of the GNN family. We also propose a computationally efficient approximation of the covariance matrix for scalable posterior inference with large-scale data. We demonstrate that these graph-based kernels lead to competitive classification and regression performance, as well as advantages in computation time, compared with the respective GNNs.

cs.LG↗

arXiv2023

Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming

We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. We propose an active-set stochastic sequential quadratic programming (StoSQP) algorithm that utilizes a differentiable exact augmented Lagrangian as the merit function. The algorithm adaptively selects the penalty parameters of the augmented Lagrangian and performs a stochastic line search to decide the stepsize. The global convergence is established: for any initialization, the KKT residuals converge to zero almost surely. Our algorithm and analysis further develop the prior work of Na et al., (2022). Specifically, we allow nonlinear inequality constraints without requiring the strict complementary condition; refine some of the designs in Na et al., (2022) such as the feasibility error condition and the monotonically increasing sample size; strengthen the global convergence guarantee; and improve the sample complexity on the objective Hessian. We demonstrate the performance of the designed algorithm on a subset of nonlinear problems collected in CUTEst test set and on constrained logistic regression problems.

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arXiv2023

Parallel Interior-Point Solver for Block-Structured Nonlinear Programs on SIMD/GPU Architectures

We investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses a SIMD/GPU accelerator locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations, to a dense matrix encoding the sensitivities of the problem's degrees of freedom, drastically minimizing the memory exchange. We demonstrate the method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the method can achieve a 50x speed-up compared to the state-of-the-art method.

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