Develops a machine learning approach for solving AC-OPF problems.
problem Nonlinear and computationally demanding AC chance-constrained OPF problem.
method Uses Gaussian process regression to approximate AC power flow equations.
result Demonstrates competitive and promising results compared to state-of-the-art approaches.
DNN policies improve stochastic AC OPF for power grid optimization.
problem Optimizing power grid operations under uncertainty.
method Deep neural network (DNN) policies for real-time generator dispatch decisions.
result DNN policies enforce feasibility constraints and produce near optimal solutions.
Paper uses Gaussian processes to solve AC-OPF with renewable uncertainty.
problem Optimizing power grids with fluctuating renewable sources.
method Data-driven approach using Gaussian processes.
result Efficiently solves chance-constrained AC-OPF with uncertainty.
This work uses a SI-DNN to predict AC-OPF solutions efficiently.
problem Efficiently predicting AC-OPF solutions in real-time power systems.
method Sensitivity-Informed Deep Neural Network (SI-DNN) for AC-OPF.
result SI-DNN can predict AC-OPF solutions with better generalization and constraint satisfaction.
The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often needed to be solved repeatedly under various conditions, either in rea…
MI-GAN solves OPF with renewable uncertainty using model-informed layers.
problem Optimal Power Flow (OPF) under renewable uncertainty.
method Model-Informed Generative Adversarial Network (MI-GAN) framework with three layers.
result MI-GAN improves solution feasibility and optimality.
Paper proposes a fast data-driven AC-OPF method using sparse hybrid Gaussian processes.
problem Optimizing electricity generation and delivery under generation uncertainty in modern power grids.
method Data-driven approach using sparse hybrid Gaussian processes to model power flow equations.
result Shows up to two times faster and more accurate solutions compared to state-of-the-art methods.
DiffOPF solves multi-valued OPF problems by sampling from system history.
problem Multi-valued and non-convex OPF problems due to system parameter variability.
method DiffOPF treats OPF as a conditional sampling problem, learning from historical data.
result DiffOPF enables statistically credible warm starts with favorable cost and constraint satisfaction trade-offs.
GP CC-OPF solves uncertain power grid optimization with Gaussian Process.
problem Uncertainty in power grid operations due to high renewables integration.
method Data-driven Gaussian Process regression for solving non-convex CC-OPF problem.
result Effective economic dispatch optimization in uncertain power grids.
Paper develops robust OPF method using contextual information.
problem Optimal Power Flow problem under incomplete uncertainty knowledge.
method Distributionally robust chance-constrained formulation with probability trimmings and optimal transport.
result Distributional robustness improves expected cost and system reliability.
In this paper, we develop an online method that leverages machine learning to obtain feasible solutions to the AC optimal power flow (OPF) problem with negligible optimality gaps on extremely fast timescales (e.g., milliseconds), bypassing solving an AC OPF altogether. This is motivated by the fact that as the power gr…
Probabilistic-driven classification techniques extend the role of traditional approaches that output labels (usually integer numbers) only. Such techniques are more fruitful when dealing with problems where one is not interested in recognition/identification only, but also into monitoring the behavior of consumers and/…
The implementation of optimal power flow (OPF) methods to perform voltage and power flow regulation in electric networks is generally believed to require extensive communication. We consider distribution systems with multiple controllable Distributed Energy Resources (DERs) and present a data-driven approach to learn c…
Probabilistic optimal power flow (POPF) is an important analytical tool to ensure the secure and economic operation of power systems. POPF needs to solve enormous nonlinear and nonconvex optimization problems. The huge computational burden has become the major bottleneck for the practical application. This paper presen…
This paper develops an ensemble learning-based linearization approach for power flow, which differs from the network-parameter based direct current (DC) power flow or other extended versions of linearization. As a novel data-driven linearization through data mining, it firstly applies the polynomial regression (PR) as …
This paper proposes a cascading failure mitigation strategy based on Reinforcement Learning (RL) method. Firstly, the principles of RL are introduced. Then, the Multi-Stage Cascading Failure (MSCF) problem is presented and its challenges are investigated. The problem is then tackled by the RL based on DC-OPF (Optimal P…
Paper proposes OPF policy for fair resource allocation with sublinear regret.
problem Fair resource allocation in an online setting against an unrestricted adversary.
method Online Proportional Fair (OPF) policy achieving approximate sublinear regret.
result OPF policy achieves cα-approximate sublinear regret with cα≤1.445. Improves neural network performance by enriching training dataset.
problem Achieving worst-case performance guarantees in neural networks.
method Adapting training dataset during training to reduce worst-case violations.
result Improved worst-case performance guarantees in neural networks.
Study finds cherry-picking load shaping strategies outperforms others in reducing grid CO2 emissions.
problem Lack of detailed counterfactual data makes it hard to assess load shaping strategies' effectiveness.
method Calibrated granular ERCOT simulations for counterfactual analysis of load shaping strategies.
result LMP-based load shaping outperforms other strategies in reducing grid CO2 emissions.
Paper corrects and expands stochastic Lie systems theory.
problem Stochastic Lie systems and their properties.
method Corrected stochastic Lie theorem, introduced new stochastic Lie systems.
result Stochastic Lie systems can differ significantly between Stratonovich and Itô approaches.
The study analyzes stochastic Lie systems and their applications in various models.
problem Analyzing stochastic differential equations on manifolds.
method Coalgebra method for Hamiltonian stochastic Lie systems.
result New examples of stochastic Lie systems and Hamiltonian stochastic Lie systems are analyzed.
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independe…
Bayesian neural networks can be partially stochastic without losing predictive power.
problem The necessity of fully stochastic parameters in Bayesian neural networks.
method Theoretical and empirical investigation of partially stochastic networks compared to fully stochastic ones.
result Expressive predictive distributions require only small amounts of stochasticity, and partially stochastic networks can match or outperform fully stochastic networks.
Stochastic approximation algorithms show exponential progress bounds.
problem Analyzing the convergence of stochastic approximation algorithms.
method Developed geometric ergodicity proofs to establish exponential concentration bounds.
result Proved faster convergence rates for specific algorithms.
Stochastic gradient methods can converge in expectation under heavy-tailed noise.
problem Convergence of stochastic gradient methods under heavy-tailed noise.
method Comprehensive study of stochastic optimization under heavy-tailed noise for extsfSGD, extsfSMD, extsfASMD, extsfSGDM in convex and nonconvex optimization. result Established in-expectation convergence results for various stochastic gradient methods.
Study on stochastic mean curvature flow on networks using Ito calculus.
problem Understanding the dynamics of network structures under random influences.
method Application of Ito calculus to derive a stochastic differential equation (SDE) for network edges.
result New insights into the stability, long-term behavior, and pattern formation of complex networks under stochastic influences.
New method reveals insights about stochastic optimization methods using modified equations.
problem Understanding the qualitative behavior of stochastic optimization algorithms.
method Developed a class of stochastic differential equations to approximate the dynamics of stochastic optimization methods.
result Mean-square stability of the modified equation provides qualitative insights about stochastic coordinate descent.
New method uses backward SDEs for deep learning uncertainty.
problem Uncertainty quantification in deep learning models.
method Probabilistic machine learning with stochastic neural networks and stochastic optimal control.
result Effectiveness validated through numerical experiments.
The article reviews how to set stochastic volatility model parameters.
problem Choosing parameters for stochastic volatility models.
method Examines existing literature on various methods.
result Different approaches to setting stochastic volatility parameters.
We extend Dupire's formula for stochastic interest rates and local volatility.
problem Deriving formulas for stochastic interest rates and local volatility.
method Generalizations of Dupire's formula for stochastic drift and local volatility.
result Validated the limits of the generalized Dupire formulae for specific cases.
This paper studies a non-stochastic version of Fernholz's stochastic portfolio theory for a simple model of stock markets with continuous price paths. It establishes non-stochastic versions of the most basic results of stochastic portfolio theory and discusses connections with Stroock-Varadhan martingales.
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with small noise parameters. We prove that this approximation can be understood math…
New theorem handles stochastic Volterra semimartingales.
problem Classic Fubini theorem restrictions for Volterra semimartingales.
method Introduced measure-valued stochastic integration.
result Proved new stochastic Fubini theorem.
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
problem Predicting and capturing long-term behaviors of stochastic dynamical systems.
method Data-driven framework combining Reservoir Computing and Normalizing Flow, integrating error modeling and both approaches virtues.
result Successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
We introduce a stochastic model for noisy vector fields on manifolds.
problem Noisy vector fields violate the assumption of parallel transport in stochastic analysis.
method We define a stochastic Lie bracket that induces torsion and analyze its consequences.
result The stochastic Lie bracket induces torsion in expectation.
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
Survey of methods for solving smooth stochastic variational inequalities.
problem Solving smooth (strongly) monotone stochastic variational inequalities.
method Deterministic foundation, general stochastic formulation, finite sum setup, recent advances.
result Review of various methods for solving smooth stochastic variational inequalities.
This paper provides a unifying theoretical framework for stochastic optimization algorithms by means of a latent stochastic variational problem. Using techniques from stochastic control, the solution to the variational problem is shown to be equivalent to that of a Forward Backward Stochastic Differential Equation (FBS…
The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.
problem Comparing and characterizing random outcomes in risk assessment.
method Exploring the equivalence between higher order risk measures and stochastic dominance, using stochastic optimization and expectiles as examples.
result Higher order risk measures and stochastic dominance are equivalent and can be used to characterize random outcomes.
In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The sto…
Algorithm samples constrained stochastic differential equations.
problem Sampling stochastic differential equations with complex constraints.
method Pathspace Metropolis-adjusted manifold sampling.
result Demonstrated effectiveness in various constrained conditions.
New algorithm solves stochastic optimization problems with unknown gradients.
problem Solving nonlinear optimization problems with stochastic objectives and deterministic constraints.
method Adaptive SQP with differentiable exact augmented Lagrangian and stochastic line search.
result Global convergence established for both non-adaptive and adaptive SQP methods.
Paper uses second-order differential geometry to study stochastic mechanics.
problem Stochastic differential equations and their symmetries.
method Develops second-order differential geometry to study symmetries of SDEs and constructs stochastic mechanics.
result Establishes stochastic Lagrangian and Hamiltonian mechanics and their relations with HJB equations.
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together with optimal control theory to derive novel adaptive hyper-parameter adjustment po…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several e…
Bayesian inference using stochastic neural networks ensembles.
problem Approximating Bayesian posterior distributions.
method Formulate stochastic ensembles of neural networks, train with variational inference, and evaluate using Monte Carlo dropout.
result Stochastic ensembles provide more accurate posterior estimates than other methods.