A deep learning method speeds up probabilistic optimal power flow calculations.
problem Efficiently solving large-scale nonlinear and nonconvex optimization problems in power systems.
method Developed a SDAE-based OPF using stacked denoising auto encoders to extract system correlations and calculate OPF solutions.
result The trained SDAE network can quickly compute OPF solutions for random system states without optimization.
A new method uses Gaussian Processes to solve power flow problems with uncertain renewable and load inputs.
problem Solving power flow problems with uncertain renewable and load inputs.
method Non-parametric Bayesian inference-based uncertainty propagation using Gaussian Processes.
result The method provides reasonably accurate solutions with fewer samples and time compared to Monte-Carlo simulations.
Paper introduces normalizing flows for accurate probabilistic energy forecasting.
problem Uncertainty in renewable energy forecasting for power systems.
method Normalizing flows for direct learning of multivariate stochastic distributions.
result Normalizing flows outperform other deep learning models in probabilistic forecasting.
Normalizing flows simplify complex distributions through bijective transformations.
problem Defining expressive probability distributions efficiently.
method Bijective transformations on a base distribution.
result Unified perspective on normalizing flows for modeling and inference.
The problem of probabilistic forecasting and online simulation of real-time electricity market with stochastic generation and demand is considered. By exploiting the parametric structure of the direct current optimal power flow, a new technique based on online dictionary learning (ODL) is proposed. The ODL approach inc…
Proposes a method to apply conformal prediction to probabilistic time series forecasting models.
problem Obtaining accurate prediction regions for multi-step time series forecasting with probabilistic models.
method Conformalises conditional normalising flows to generate potentially disjoint prediction regions.
result Improves predictive efficiency in time series forecasting with multimodal distributions.
New probability path model improves flow matching forecasting performance.
problem Impact of probability path model selection on flow matching forecasting performance.
method Proposed a novel probability path model designed to improve forecasting performance.
result Our model achieves faster convergence during training and improved predictive performance compared to existing models.
Cascading flows improve variational inference in structured programs.
problem Challenges in variational inference for complex probabilistic programs.
method Integrates normalizing flows and ASVI to create cascading flows, which embed the forward-pass of probabilistic programs.
result Cascading flows outperform normalizing flows and ASVI in structured inference problems.
MT-SGD samples from multiple target distributions using gradient descent.
problem Sampling from multiple unnormalized target distributions.
method Proposes MT-SGD, a flow of intermediate distributions to sample from multiple target distributions.
result Asymptotic analysis shows MT-SGD reduces to multiple-gradient descent for multi-objective optimization.
We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to the case of optimizing dynamic power flows, i.e., power flows that change with ti…
HCNAF models complex conditional distributions for probabilistic occupancy forecasting.
problem Modeling complex conditional probability density functions for occupancy forecasting.
method Hyper-Conditioned Neural Autoregressive Flow (HCNAF) combining AF and hyper-network.
result HCNAF achieves state-of-the-art performance in self-driving datasets.
Probabilistic Autoencoder learns latent space weights' distribution.
problem Nonlinear model reconstruction error and sample quality.
method Normalizing flow for latent space weights' probability distribution.
result PAE achieves small reconstruction errors, high sample quality, and good performance.
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.
Study uses machine learning to optimize power generation in electrical grids.
problem Optimizing power generation in electrical grids while respecting physical and engineering constraints.
method Two formulations of ACOPF as machine learning problems: direct prediction and constraint prediction.
result Validated machine learning approaches on two benchmark grids.
Paper develops a fast method to find near-optimal power solutions.
problem Solving AC OPF on fast timescales for large networks.
method Leverages machine learning to map system loading to optimal generation values.
result Near-optimal and feasible solutions found on milliseconds timescales.
Optimizes power systems with energy storage under uncertainty using scenario-based method.
problem Optimizing power systems with energy storage, intermittent renewable generation, and uncontrollable loads under uncertainty.
method Developed a novel solution method based on scenario optimization and strategic sampling to solve the chance-constrained optimal power system operation problem.
result The strategic sampling method significantly improves computational efficiency and data-driven convex approximation of power flow.
Injective flows for star-like manifolds improve variational inference efficiency.
problem Efficiently modeling densities on star-like manifolds with exact Jacobian computation.
method Proposed injective flows for star-like manifolds with exact Jacobian computation.
result Exact Jacobian computation for star-like manifolds reduces computational cost to NFs.
Paper presents a deep learning approach to AC Optimal Power Flow.
problem Nonlinear and nonconvex OPF problem in power systems.
method Combines deep learning with Lagrangian dual methods.
result Deep learning model achieves highly accurate predictions.
Normalizing flows optimize Jacobian determinant for unique likelihood objective.
problem Optimizing normalizing flows for unique likelihood.
method Showed Jacobian determinant is unique for given distributions, leading to a unique global optimum. Used eigenvalues of auto-correlation matrix for explicit likelihood expression.
result Explicit expression of likelihood for flows, independent of neural network parameterization, with theoretical optimal value.
DIN framework directly models hydraulic conductivity and uncertainty.
problem Modeling hydraulic conductivity and uncertainty in groundwater flow.
method DIN utilizes DDPM as a prior learner, incorporating observational data through conditional injection mechanisms.
result DIN generates multiple constraint-satisfying realizations and accurate uncertainty quantification.
Probabilistic programming languages (PPLs) are a powerful modeling tool, able to represent any computable probability distribution. Unfortunately, probabilistic program inference is often intractable, and existing PPLs mostly rely on expensive, approximate sampling-based methods. To alleviate this problem, one could tr…
This paper introduces a new probabilistic model for online learning which dynamically incorporates information from stochastic gradients of an arbitrary loss function. Similar to probabilistic filtering, the model maintains a Gaussian belief over the optimal weight parameters. Unlike traditional Bayesian updates, the m…
We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and on the Good-Turing missing mass estimator. We prove two different regret bounds on t…
Paper uses ensemble learning for more accurate power flow modeling.
problem Improving accuracy and efficiency of power flow modeling.
method Applies polynomial regression and ensemble learning (GB, bagging) to create a more accurate linear power flow model.
result Data-driven model outperforms traditional methods in accuracy and speed.
Improved time series forecasting with multivariate probabilistic models.
problem Improving accuracy in forecasting time series with statistical dependencies.
method Conditioned Normalizing Flows for autoregressive deep learning models.
result Improved performance over state-of-the-art models on real-world data sets.
DIGRAC clusters directed graphs using flow imbalance, outperforming existing methods.
problem Clustering directed networks without label supervision.
method DIGRAC uses a graph neural network with a novel imbalance loss for directed flow imbalance.
result DIGRAC outperforms 10 state-of-the-art methods on directed graph clustering.
iEFM trains CNF models from unnormalized densities efficiently.
problem Training generators from energy functions or unnormalized densities.
method Iterated energy-based flow matching (iEFM) with simulation-free objective.
result iEFM outperforms existing methods in probabilistic modeling.
Synthesizes static analysis for probabilistic programs.
problem Optimize learning process, verify models, improve programming interface.
method Organize and analyze static analysis techniques for probabilistic programming.
result Future directions for improvement in statistical machine learning.
Flow adjusts curvature to avoid a fixed region, proving bounds and regularity.
problem Adjusting curvature flow to avoid a fixed region.
method Flow by powers of Gauss curvature, proving optimal curvature bounds and regularity.
result Proves optimal curvature bounds and long time existence for all dimensions and powers.
Electronic power inverters are capable of quickly delivering reactive power to maintain customer voltages within operating tolerances and to reduce system losses in distribution grids. This paper proposes a systematic and data-driven approach to determine reactive power inverter output as a function of local measuremen…
FMOPF generates diverse near-optimal power flow solutions.
problem Generating diverse near-optimal power flow solutions for risk quantification.
method Decouples compression from generation through latent flow matching and explicitly models load-state coupling.
result FMOPF provides the most effective Newton-Raphson warm starts and lowest tail risk.
Simple probabilistic solution for optimal liquidation with linear price impact.
problem Maximizing expected terminal wealth in a setup with quadratic transaction costs.
method Provided a simple probabilistic solution to the problem.
result Simple and probabilistic form of the solution not previously published.
The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. While the general form of the reinforcement learning problem enables effective reasoning about uncertainty, the connection between reinforcement learni…
VFG model embeds flow-based models with hierarchical structures using variational inference.
problem Flow-based models struggle with high-dimensional latent spaces and lack of tractable inference for graphical structures.
method Integrates flow-based functions through variational inference with aggregation nodes for hierarchical information integration.
result VFG models achieve improved ELBO and likelihood values on multiple datasets.
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.
Paper uses RL to mitigate cascading failures in power systems.
problem Mitigating multi-stage cascading failures in power grids.
method Reinforcement Learning applied to DC-OPF for power flow optimization.
result Reduced system collapse rates through RL-based optimization.
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.
The increasing complexity of the power grid, due to higher penetration of distributed resources and the growing availability of interconnected, distributed metering devices re- quires novel tools for providing a unified and consistent view of the system. A computational framework for power systems data fusion, based on…
A new KDE model prevents singular solutions and accelerates optimization for probabilistic modeling.
problem Adapting to varying densities in data regions for probabilistic modeling.
method Adaptive KDE model with individual bandwidths, LOO-MLL criterion, and modified EM algorithm.
result The proposed models prevent singular solutions and have promising performance.
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.
Neural network predicts daily power consumption with high accuracy.
problem Middle-term power consumption prediction in the energy sector.
method Incorporates trend, seasonality, and weather conditions in a shallow Neural Network.
result Excellent density forecast results on one-year test set.
New model predicts radiative properties of nanoparticle layers with high accuracy and uncertainty.
problem Predicting radiative properties of nanoparticle embedded layers accurately and with uncertainty.
method Conditional normalizing flows learn conditional distributions of optical outputs given input parameters.
result The model achieves high predictive accuracy and reliable uncertainty estimates.
Transformers model contextual relations using probabilistic measures, revealing their expressive power.
problem Lack of clear understanding of Transformer's ability to model contextual relations.
method Introduced a measure-theoretic framework connecting softmax attention and entropy-regularized optimal transport.
result Transformer architectures can approximate arbitrary contextual relations, and the choice of normalization affects how these relations are represented.
Diffusion LLMs can efficiently generate harmful prompts for adversarial testing.
problem Generating harmful prompts for adversarial testing is resource-intensive and costly.
method Transformed adversarial prompt optimization into an efficient inference task using pretrained Diffusion LLMs.
result Only a few conditional samples are required to generate harmful prompts with high reward.
Improved normalising flows using Student's t-distribution for robust training.
problem Training deep probabilistic models with robust statistics.
method Propose Student's t-distribution as a robust alternative to Gaussian in normalising flows.
result Improved robustness and reduced generalization gap with Student's t-distribution.
MPF method improves parameter estimation in probabilistic models.
problem Difficulty in fitting probabilistic models due to intractable partition function.
method Minimum Probability Flow (MPF) method for parameter estimation.
result MPF outperforms existing techniques in convergence time and accuracy.
Paper proposes a method for weather-informed probabilistic forecasting and scenario generation in power systems.
problem Challenges of integrating renewable energy sources into power grids due to their stochasticity and uncertainty.
method Combines probabilistic forecasting and Gaussian copula for day-ahead prediction and scenario generation of load, wind, and solar power.
result Demonstrates superior performance of the proposed weather-informed Temporal Fusion Transformer (WI-TFT) model.
In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important geometric quantities under the…