Neural network improves voltage quality in three-phase inverters.
problem Achieving high-quality voltage with low THD in three-phase inverters.
method Combining MPC and ANN for voltage tracking.
result ANN-based control outperforms MPC in steady and dynamic performance.
Neural network HDP improves virtual inertia control for non-inductive grids.
problem Traditional virtual inertia controllers are not suitable for non-inductive grids.
method Adaptive neural network heuristic dynamic programming (HDP) for optimal control.
result The proposed HDP controller outperforms traditional controllers in virtual inertia control.
fkcompute calculates a knot invariant from a braid presentation.
problem Computing the Gukov-Manolescu invariant for complex knots and links.
method Three-phase pipeline: braid presentation search, state space encoding, R-matrix multiplication.
result fkcompute efficiently computes the invariant for knots and links up to 12 crossings.
Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering. In the first stage a quaternion extended Kalman filter, which provides a unified…
In this paper a highly abstracted view on the historical development of Genetic Algorithms for the Traveling Salesman Problem is given. In a meta-data analysis three phases in the development can be distinguished. First exponential growth in interest till 1996 can be observed, growth stays linear till 2011 and after th…
Paper revisits five IF paradoxes using differential geometry.
problem Five paradoxes of Instantaneous Frequency in three-phase systems.
method Geometric interpretation of frequency to explain IF paradoxes.
result Revisits and explains five IF paradoxes through a common framework.
EMODM detects abnormal patterns in complex systems.
problem Detecting abnormal patterns in complex systems.
method Probabilistic models and statistical algorithms.
result EMODM detects abnormal patterns in real-time raw data.
In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja's iteration which is an online stochastic gradient descent method for the principal component analysis. Oja's iteration maintains a running estimate of the true principal component from streaming data and enjoys less tempo…
The Frenet frame generalizes the Park transform for multi-phase circuits.
problem Generalizing the Park transform for multi-phase circuits.
method Using the Frenet frame and Cartan's moving frames.
result The Frenet frame provides a new approach to circuit analysis.
We study the stability of partitions in convex domains involving simultaneous coexistence of three phases, viz. triple junctions. We present a careful derivation of the formula for the second variation of area, written in a suitable form with particular attention to boundary and spine terms, and prove, in contrast to t…
New algorithm extracts device profiles for short-term power predictions in commercial buildings.
problem Short-term power prediction in commercial buildings with high accuracy.
method Unsupervised extraction of device profiles from aggregate power measurements, disaggregation using particle swarm optimization, and state changes forecast by artificial neural networks.
result Developed approach outperforms existing methods with high accuracy.
Study on estimating invertible functions with minimax analysis.
problem Minimizing risk of estimating invertible functions on a plane.
method Introduce two types of L2-risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator. result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.
Local invertibility of higher order tensor transforms on compact manifolds.
problem Invertibility of higher order tensor transforms on compact manifolds.
method Local invertibility of transverse and mixed ray transforms of tensors on compact Riemannian manifolds.
result Local invertibility of transverse and mixed ray transforms of tensors for specific dimensions.
Study of strongly invertible Legendrian links in contact 3-space.
problem Characterizing and understanding strongly invertible Legendrian links.
method Equivariant analogs of basic results for strongly invertible and Legendrian links.
result Existence of maximal equivariant Thurston-Bennequin number for strongly invertible links.
Study on invariant Seifert surfaces for strongly invertible knots, showing large gaps in genus.
problem Understanding gaps in genus between strongly invertible knots and their invariant Seifert surfaces.
method Analysis of invariant Seifert surfaces and proof of genus gaps, with variants of Edmonds' theorem.
result Gap between equivariant genus and usual genus can be arbitrarily large for strongly invertible knots.
Dirac operator invertibility proven for specific manifolds.
problem Invertibility of twisted Dirac operator on manifolds.
method Closed connected spin manifold with non-negative scalar curvature, flat Hilbert module bundle.
result Dirac operator is invertible under given conditions.
Invertible networks help explain decisions and identify important features.
problem Interpreting and explaining the decisions of black-box neural networks.
method Two-stage approach: invertible transformation to feature space and linear classifier. Determining decision boundaries and feature importance using local linear models.
result Ability to explain decisions and identify important features in neural networks.
Table of symmetric diagrams for knots up to 10 crossings.
problem Finding symmetric diagrams for strongly invertible knots.
method Compilation of symmetric diagrams for knots up to 10 crossings.
result Similarity of transversal diagrams to symmetric union diagrams for strongly invertible knots.
Global invertibility proven for orientation-preserving maps without homeomorphic extension.
problem Global invertibility of orientation-preserving Sobolev maps.
method Avoiding homeomorphic extension, study of strictly orientation-preserving maps.
result Global invertibility can be achieved without homeomorphic extension.
Invertible neural networks with masked convolutions improve classification and generative models.
problem Building robust invertible neural networks for better model interpretability and generative tasks.
method Combining masked convolutions and iterative inversion methods to create invertible architectures.
result Invertible neural networks achieve competitive performance in classification and generative tasks.
HINT improves invertible neural networks for better density estimation and Bayesian inference.
problem Sparse Jacobians limit expressiveness in invertible neural architectures.
method Recursive hierarchical coupling within subsets of variables leads to dense, triangular Jacobian.
result HINT allows efficient sampling from joint and posterior distributions using a single network.
ISR creates analytical relationships from data via invertible maps.
problem Creating analytical relationships from datasets.
method Combines INNs and EQL, using invertible maps and sparsity promoting regularization.
result ISR can serve as a normalizing flow for density estimation and solve inverse problems.
Local invertibility of ray transforms on convex manifolds.
problem Invertibility of ray transforms on compact Riemannian manifolds with strictly convex boundary.
method Local invertibility results for transverse and mixed ray transforms of 1 and 1+1 tensors.
result Local invertibility of ray transforms near boundary points, leading to global results.
Deep invertible networks decode EEG signals better than chance.
problem Decoding brain signals from EEG data.
method Deep invertible networks for generating and classifying brain signals.
result Deep invertible networks generate realistic EEG signals and classify novel signals above chance.
This work tackles exploding inverses in INNs, revealing and mitigating their numerical non-invertibility.
problem Exploding inverses in INNs cause numerical non-invertibility, leading to failures in various tasks.
method Derived bi-Lipschitz properties of INN building blocks, proposed regularizers for local invertibility, and stable INN designs for global invertibility.
result Bi-Lipschitz properties and stable INN designs are crucial for addressing numerical non-invertibility.
Neural ODEs and i-ResNets can't approximate all continuous invertible functions.
problem Neural ODEs and i-ResNets' limitations in approximating continuous invertible functions.
method Proving the approximation capabilities of Neural ODEs and i-ResNets.
result Neural ODEs and i-ResNets can approximate homeomorphisms on a p-dimensional Euclidean space.
CF-INNs can approximate any invertible function, resolving a long-standing problem.
problem Whether CF-INNs can approximate any invertible function.
method Demonstrated CF-INNs are universal approximators for invertible functions by showing a convenient criterion.
result CF-INNs are universal approximators for invertible functions.
This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.
problem Training invertible linear layers during optimization with gradient-based methods is challenging.
method Train rank-one perturbations and add them to weight matrices infrequently, keeping track of inverses and determinants.
result Invertible linear layers improve mixing and mode separation in normalizing flows.
Spaces of metrics with invertible Dirac operator are homotopy equivalent for cobordant manifolds.
problem Proving homotopy equivalence of spaces of metrics with invertible Dirac operator.
method Using cobordism theory and properties of Dirac operators.
result Spaces of metrics with invertible Dirac operator are homotopy equivalent for cobordant manifolds.
Develops equivariant grid homology for strongly invertible knots.
problem Invariants of strongly invertible knots.
method Equivariant grid diagrams and mapping cones.
result Equivariant unknotting numbers and genus bounds.
New findings on knot genera using advanced techniques.
problem Understanding the 4-genus of knots, especially strongly invertible and periodic ones.
method Innovative concordance group invariants, Donaldson's theorem, and g-signature.
result Many new examples showing the equivariant 4-genus is larger than the 4-genus.
Defines knot signature invariant using G-signature theorem.
problem No specific problem stated; focuses on knot theory.
method Uses G-signature theorem to define knot invariant.
result Defines an invariant for strongly invertible knots.
Paper shows invertibility of tensor X-ray transform on certain manifolds.
problem Invertibility of tensor X-ray transform on asymptotically conic manifolds.
method Used 1-cusp pseudodifferential operator algebra and modified solenoidal gauge condition.
result Invertibility of tensor X-ray transform up to natural obstruction.
For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones wer…
The paper proposes a data-driven method for optimal power flow and voltage regulation in distribution grids.
problem Optimal power flow and voltage regulation in decentralized power grids.
method The approach uses a network model, historic data, and regression to find functions approximating optimal reactive power injections for inverters.
result The method achieves near-optimal results in voltage- and capacity-constrained loss minimization and voltage flattening.
New invertible transformations improve flow-based generative models.
problem Improving flow-based generative models for better performance.
method Proposed new invertible transformations and coupling layers.
result New coupling layers achieve better results in IDF.
We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple …
Proposes a constant memory iterative inverse model using invertible networks.
problem Memory limitations in iterative learning approaches for inverse problems.
method Invertible networks to avoid storing intermediate activations, constant memory model.
result Trains 400-layer models on 3D MRI volumes, achieving state-of-the-art image reconstruction.
ButterflyFlow uses butterfly matrices for efficient invertible layers in normalizing flows.
problem Building efficient invertible layers for complex probability distributions.
method Proposes butterfly layers for invertible linear layers, leveraging their ability to capture complex structures.
result ButterflyFlow achieves strong density estimation and significantly better log-likelihoods on various datasets.
By using parity arguments we prove that free knots are, generally, not invertible.
Invertible DenseNets improve model efficiency and performance.
problem Improving model efficiency and performance in neural networks.
method Enforcing invertibility in DenseNets by satisfying the Lipschitz constraint and proposing a learnable concatenation.
result i-DenseNets outperform Residual Flows in negative log-likelihood on various datasets.
Two knots with unique surgery properties.
problem Characterizing strongly invertible L-space knots.
method Examined surgeries and knot properties.
result Found knots whose surgeries are never Khovanov thin.
Generative model for 3D point clouds using invertible flows.
problem Generating realistic 3D point clouds.
method Invertible flow-based models for point cloud generation with parameter sharing and embedding vectors.
result The model generates high-quality 3D point clouds with good similarity.
New spectral sequences define knot invariants.
problem Understanding strongly invertible knots.
method Two spectral sequences in knot Floer homology.
result Numerical invariant defined for strongly invertible knots.
Residual Flows improve flow-based models for density estimation.
problem Density estimation using flow-based models with biased log-density estimates.
method Proposed a Russian roulette estimator for unbiased log-density estimation and used an alternative infinite series for gradient calculation. Improved invertible residual blocks with activation functions avoiding derivative saturation and generalized Lipschitz condition to induced mixed norms.
result Residual Flows achieve state-of-the-art performance on density estimation and outperform coupling block networks in joint generative and discriminative modeling.
New findings on knot operations challenge a long-standing conjecture.
problem Understanding equivariant unknotting numbers of strongly invertible knots.
method Study of symmetric crossing change operations for strongly invertible knots.
result The equivariant unknotting number is not additive under connected sum.
We study invertible generating pairs of fundamental groups of graph manifolds, that is, pairs of elements (g,h) for which the map g --> g^{-1}, h --> h^{-1} extends to an automorphism. We show in particular that a graph manifold is of Heegaard genus 2 if and only if its fundamental group has an invertible generating pa…
Study on equivariant Q-sliceness for strongly invertible knots.
problem Understanding Q-sliceness for strongly invertible knots.
method Constructive and obstructive approaches using Fox-Milnor condition and equivariant concordance.
result Klein amphichiral knots are equivariant Q-slice in a single Q-homology 4-ball.