Personalising large text-to-image diffusion models with only a handful of images unlocks various applications but exposes a fidelity–forgetting dilemma: models learn new concepts slowly and often erase semantically distant knowledge. We tackle this by injecting discriminative signals into the fine-tuning loop. Our framework, DiffDisReg, couples a Segmentation-Guided Attention Regularizer with a lightweight feature-level head and schedules both through a Semantic-Similarity regularization Scheduler that targets concepts most at risk of being forgotten. Experiments on DreamBooth benchmarks show that DiffDisReg reaches baseline geometric fidelity in under half the training steps while improving final image quality and reducing out-of-domain degradation. Ablation studies confirm the contribution of each component, and qualitative timelines reveal cleaner geometry and color from the earliest iterations. The code is available at: https://github.com/yj373/DiffDisReg.

Diffusion models have rapidly advanced the field of data synthesis as powerful generative models. However, efficiently evaluating their generative capability while reflecting human preferences remains challenging. In contrast, evaluation metrics for discriminative tasks are based on objective truth and can scale across various image domains with negligible cost. On the other hand, recent studies have expanded the application of diffusion models to discriminative tasks, highlighting a promising intersection between generative and discriminative capabilities. Inspired by these, we propose DiffDisEval, a novel benchmark method that assesses the generative ability of diffusion models through the lens of the discriminative segmentation task. DiffDisEval utilizes semantic masks generated by the denoising network in diffusion models, which fuses self-attention and cross-attention maps conditioned on carefully designed textual prompts using the BLIP model, enabling an unbiased evaluation of the model's ability to align images with texts. Additionally, based on DiffDisEval, we introduce an automatic dataset construction pipeline that can mitigate the constraints caused by the predefined label set of an existing image segmentation dataset and generate a dataset to fully characterize the segmentation capability of diffusion models. We formulate a general-purpose evaluation dataset, consisting of 1,000 images from four domains: natural images, medical scans, urban scenes, and aerial views. Evaluating prevalent diffusion models, including Stable Diffusion, Openjourney, and SDXL, reveals a strong correlation between the evaluation results and human preferences, demonstrating the efficacy of assessing generative models through discriminative tasks.

Training deep neural networks (DNNs) rested heavily on efficient local solvers. Due to their local property, local solvers are sensitive to initialization and hyperparameters. In this article, a systematical method for finding multiple high-quality local optimal DNNs, based on the transformation under stability-retaining equilibria characterization (TRUST-TECH) method, is introduced. Our goal is to systematically search for multiple local optimal parameters for large models, such as DNNs, trained on large datasets. To achieve this, a dynamic searching path (DSP) method is proposed to provide improved search guidance used in TRUST-TECH. By integrating the DSP method with the TRUST-TECH (DSP-TT) method, multiple optimal training solutions with higher quality than randomly initialized ones can be obtained. To take advantage of these optimal solutions, a DSP-TT ensemble method is further developed. Experiments on various test cases show that the proposed DSP-TT method achieves considerable improvement over other ensemble methods developed for deep architectures. The DSP-TT ensemble method also shows diversity advantages over other ensemble methods.

In this article, a Trust-Tech source-point method is proposed to systematically compute multiple local optimal solutions (LOSs) for continuous unconstrained nonlinear optimization problems. This proposed method consists of four stages. Stage I finds one LOS (in which existing effective optimizers can be applied), stage II is the stage of escaping an LOS while stage III is the stage for entering the stability region (SR) of another stable equilibrium point (SEP) (i.e., another LOS). Stage IV computes other SEPs (i.e., LOSs) in corresponding SRs. A theoretical foundation for both stages II and III is developed, and these theoretical results are quite general on their own. The proposed method is numerically evaluated to compute multiple LOSs. For instance, a total of 5085 LOSs have been computed by the proposed Trust-Tech source point method on a 50-D test function. In addition, the proposed method can find the global optimal solutions of several test functions with 50 dimensions and 100 dimensions.

A novel trajectory-unified (TJU) methodology, enabled by transformation under stability-retraining equilibria characterization (TRUST-TECH, TT) method, is proposed to systematically and deterministically compute a set of multiple local optimal solutions (LOSs), if not all of them, for constrained nonlinear optimization problems. The proposed TT-TJU methodology is composed of two key phases. During Phase I, it robustly computes a LOS; while during Phase II, it systematically computes a set of neighboring LOSs. A theoretical foundation is developed for the proposed TT-TJU methodology. The existence of an optimal solution is shown to be equivalent to the existence of a stable equilibrium point of a class of nonlinear dynamical system derived from the constrained optimization problem under study. From a computational viewpoint, Phase I is numerically implemented in a 3-stage procedure for fast and robust computation of an optimal solution. The second phase makes use of the TRUST-TECH methodology to lead the search away from a computed optimal solution and continue to deterministically compute neighboring LOSs. The proposed methodology has been evaluated on an illustrative bivariate example and a benchmark problem with 110 variables and 55 constraints with promising results.

The convexity property of an AC optimal power flow (AC OPF) problem has attracted significant efforts in conducting numerical studies, but the non-convexity property of general AC OPF has not been shown. This paper develops analytical results showing the non-convex feasible injection region (FIR) of general AC optimal power flow models. This analytical yet general result is illustrated on a 3-bus transmission system and a 33-bus distribution system.

This article presents a two-layer hybrid neural network framework, termed enhanced ELITE (E-ELITE), for short-term load forecasting (STLF) with high-performance forecasting capability and accuracy. The design of the E-ELITE is based on a novel three-stage methodology that is composed of Stage I: optimal structure, Stage II: highly accurate and diverse members of neural network, and Stage III: a neural network-based ensemble. We explore the capability of our proposed consensus-based mixed-integer particle swarm optimization-assisted TRUST-TECH (CMPSOATT) method in each of the three-stage methodology to achieve the following advantages: first high-quality local optimal solutions or even the global optimal solution and second computational speed; consequently, the forecasting accuracy and generalization ability of the E-ELITE is enhanced by CMPSOATT via a training procedure to design a diverse set of optimal ANN forecasting engines in the bottom layer and another training procedure to achieve higher performance results than any engines in the top layer. The resulting E-ELITE is shown to obtain a more accurate, scalable, and better generalization STLF forecasting performance with less computational effort than other powerful forecasting methods through a utility-scale dataset.

A novel user preference enabling (UPE) method is developed to solve general constrained nonlinear multiple objective optimization (MOO) problems. User wish lists on the preferred range of each objective function are introduced and incorporated into the MOO formulation to form a user-preferred (UP) MOO problem. A theoretical foundation of the UP feasible region of MOO problems is developed. The developed theoretical work leads to the development of a UPE method for effectively solving the UP-MOO problems. Distinguishing features of the proposed method include its ability to compute a targeted Pareto solution and to serve as a complement to existing MOO methods, in the sense that the proposed method assists the existing MOO methods in computing the Pareto front by providing feasible solutions and UP feasible solutions. Both proposed UPE method and derived theoretical developments are evaluated on several test systems with promising results.

A comprehensive multi-objective optimization formulation is proposed for multi-period multi-objective look-ahead power dispatch (LA-PD) with renewable uncertainties. User preference over different objectives is incorporated into the model to form a user-preference LA-PD problem. A complete characterization of the user preference-based feasible region is presented. A user preference enabling method is developed based on this characterization. A two-stage solution method is developed to solve the user-preference LA-PD formulation for providing the optimal operation point and optimal participation factors of AGC units, to remain feasible under the uncertainty set and to achieve a targeted Pareto-optimal solution. The performance of the proposed two-stage method is evaluated using the IEEE 30-bus system with promising results.

A novel three-stage methodology, termed the "consensus-based particle swarm optimization (PSO)-assisted Trust-Tech methodology," to find global optimal solutions for nonlinear optimization problems is presented. It is composed of Trust-Tech methods, consensus-based PSO, and local optimization methods that are integrated to compute a set of high-quality local optimal solutions that can contain the global optimal solution. The proposed methodology compares very favorably with several recently developed PSO algorithms based on a set of small-dimension benchmark optimization problems and 20 large-dimension test functions from the CEC 2010 competition. The analytical basis for the proposed methodology is also provided. Experimental results demonstrate that the proposed methodology can rapidly obtain high-quality optimal solutions that can contain the global optimal solution. The scalability of the proposed methodology is promising.

Power systems subjected to large disturbances may become transiently unstable, which can lead to uncontrolled system separation and cascading outages. An important goal of developing the smart grids is to maintain high-level system stability. Controlled islanding is a corrective measure that can efficiently attenuate the detrimental impact of large disturbances by splitting the system into self-healing islands. This paper is devoted to a quantitative study of unstable equilibrium points on the stability boundary, which gives an estimate for the number of possible system separations and provides useful guideline for the strategy design of controlled islanding.

The integration of renewable energies requests smart power grids to be capable of supporting various power flow patterns, and thus urgently needs the development of smart and robust power flow solvers. However, there are several great challenges, as the problem of power flow divergence and the issue of multi-solution. Homotopy methodology is commonly utilized to deal with these issues. This paper proposes a set of sufficiently conditions for the uniqueness of power flow solution, by showing the uniqueness of continuation path in a homotopy method, which can serve as the condition for controlling when to apply the costly global-searching techniques for finding multiple power flow solutions. Theoretical results are illustrated by simulations on the IEEE 1123-bus distribution network with distributed generation.

Nonlinear integer programming has not reached the same level of maturity as linear programming, and is still difficult to solve, especially for large-scale systems. Branch-and-bound ( B&B) and its variants are widely used methods for integer programming, and numerical solutions obtained by them still can be far away from the global optimum. In this paper, we propose a novel approach to guide the deterministic/heuristic methods and the commercial solvers for nonlinear integer programming, and aim at improving the solution quality by taking advantage of transformation under stability-retraining equilibrium characterization (TRUST-TECH) method. Moreover, we examine the effectiveness by developing and simulating TRUST-TECH guided B&B and TRUST-TECH guided commercial solver(s), and compare their performance with that of the original methods/solvers (e.g., GAMS (General Algebraic Modeling System)/ BARON, GAMS/SCIP, and LINDO (Linear, INteractive, Discrete Optimizer)/MINLP) and also with that of recently-reported evolutionary-algorithm (EA)-based methods. Simulation results provide evidence that, the solution quality is substantially improved, and the global-optimal solutions are usually obtained after the application of TRUST-TECH. The proposed approach can be immediately utilized to guide other EA-based methods and commercial solvers which incorporate intelligent searching components.

Implicit Z-bus distribution power flow method may encounter divergence problems when applied to distribution systems with distributed generators (DGs) modeled as P-V nodes. In this paper, analysis of divergence problems associated with the Implicit Z-bus method is performed. We illustrate the derived analytical results to conduct divergence analysis on the IEEE 13-bus, and a practical 1101-node distribution networks.

The controlling unstable equilibrium point (CUEP) method is a reliable direct method for stability analysis of electrical power systems. In this paper, the foundations of the CUEP method, initially developed for network-reduced power system models, are extended to network-preserving power system models, which are represented by a set of differential-algebraic equations (DAEs). This extension explores the relationship between equilibrium points on the stability boundary of DAE systems and those of their associated singularly perturbed systems (SPS).

Power flow study is a fundamental task of power system operation and planning. Of the several methods developed in commercial package for power flow study, the Newton-Raphson method is the most successful one. It is however well recognized that the NR method may diverge in power flow study. In this paper, we numerically study the convergence regions of power flow solutions using Newton-Raphson(NR) method. This study of convergence region is motivated by the need to determine an initial guess which converges to one of the power flow solution. It will be numerically shown that the convergence region of NR method, if exist, has a fractal boundary and is hence sensitive to initial conditions. Several fractal features will be investigated considering the convergence regions of power flow at the base case and at various loading conditions, and with different load models. An IEEE 14-bus system will be used to illustrate the fractal boundary via numerical results.

This paper presents a method to compute the saddle-node bifurcation points (SNB) of distribution networks and verifies the existence of saddle-node bifurcations in 3-phase distribution networks with distributed generators (DGs). Numerical studies were performed on the IEEE 13-bus distribution test feeder and on a practical 1123-nodes distribution system. These numerical results indicate that SNB occurs due to load variation and the penetration of DGs. Physically speaking, the SNB indicates the limitation of power delivery capability of distribution networks in delivering power from DGs and substation to loads.

The ensemble of optimal input-pruned neural networks using TRUST-TECH (ELITE) method for constructing high-quality ensemble through an optimal linear combination of accurate and diverse neural networks is developed. The optimization problems in the proposed methodology are solved by a global optimization a global optimization method called TRansformation Under Stability-reTraining Equilibrium Characterization (TRUST-TECH), whose main features include its capability in identifying multiple local optimal solutions in a deterministic, systematic, and tier-by-tier manner. ELITE creates a diverse population via a feature selection procedure of different local optimal neural networks obtained using tier-1 TRUST-TECH search. In addition, the capability of each input-pruned network is fully exploited through a TRUST-TECH-based optimal training. Finally, finding the optimal linear combination weights for an ensemble is modeled as a nonlinear programming problem and solved using TRUST-TECH and the interior point method, where the issue of non-convexity can be effectively handled. Extensive numerical experiments have been carried out for pattern classification on the synthetic and benchmark datasets. Numerical results show that ELITE consistently outperforms existing methods on the benchmark datasets. The results show that ELITE can be very promising for constructing high-quality neural network ensembles.

The BCU method has been confirmed as an important on-line tool for direct transient stability assessment of power systems. The boundary property, which guarantees the controlling UEP of the original model and that of the reduced-state model, is a key issue in the BCU method. Instead of one-parameter transversality conditions proposed earlier, analytical results on the boundary property will be explored. We have applied the self-indexing energy function and the structural stability to analyze boundary properties of simple power systems. We have shown that, under certain mild conditions, the original system and the reduced-state system share the same UEPs on stability boundaries. Numerical studies confirm theoretical developments.

The PJM Interconnection has successfully designed and implemented a Transient Stability Analysis & Control (TSA&C) system at the PJM system control center using new techniques. TEPCO-BCU was selected as a fast screening tool to improve the performance of the PJM TSA system. This paper presents an evaluation study of TEPCO-BCU in a real-time environment as a transient stability analysis (TSA) screening tool. This evaluation study is the largest in terms of system size for a practical application of the theory of the stability regions.

Power distribution systems are now integrating Smart Grid technologies allowing for widespread implementation of demand response and direct load control. This paper will present a service restoration problem formulation and solution algorithm for power distribution systems which incorporates load curtailment. A ranking based heuristic search algorithm is proposed which prioritizes the multi-objective service restoration problem and returns a new system configuration and load curtailment scheme to restore power to out-of-service customers following fault isolation. A numerical example is presented to illustrate the mechanics of the proposed algorithm.

In spite of the initialization problem, the Expectation-Maximization (EM) algorithm is widely used for estimating the parameters of finite mixture models. Most popular model-based clustering techniques might yield poor clusters if the parameters are not initialized properly. To reduce the sensitivity of initial points, a novel algorithm for learning mixture models from multivariate data is introduced in this paper. The proposed algorithm takes advantage of TRUST-TECH (TRansformation Under STability-reTaining Equilibra CHaracterization) to compute neighborhood local maxima on likelihood surface using stability regions. Basically, our method coalesces the advantages of the traditional EM with that of the dynamic and geometric characteristics of the stability regions of the corresponding nonlinear dynamical system of the log-likelihood function. Two phases namely, the EM phase and the stability region phase, are repeated alternatively in the parameter space to achieve improvements in the maximum likelihood. The EM phase obtains the local maximum of the likelihood function and the stability region phase helps to escape out of the local maximum by moving towards the neighboring stability regions. The algorithm has been tested on both synthetic and real datasets and the improvements in the performance compared to other approaches are demonstrated. The robustness with respect to initialization is also illustrated experimentally.

Efficient training in a neural network plays a vital role in deciding the network architecture and the accuracy of these classifiers. Most popular local training algorithms tend to be greedy and hence get stuck at the nearest local minimum of the error surface and this corresponds to suboptimal network model. Stochastic approaches in combination with local methods are used to obtain an effective set of training parameters. Due to the lack of effective fine-tuning capability, these algorithms often fail to obtain such an optimal set of parameters and are computationally expensive. As a trade-off between computational expense and accuracy required, a novel method to improve the local search capability of training algorithms is proposed in this paper. This approach takes advantage of TRUST-TECH (TRansformation Under STability-reTaining Equilibrium CHaracterization) to compute neighborhood local minima on the error surface surrounding the current solution in a systematic manner. Empirical results on different real world datasets indicate that the proposed algorithm is computationally effective in obtaining promising solutions.

In spite of the initialization problem, the expectation-maximization (EM) algorithm is widely used for estimating the parameters in several data mining related tasks. Most popular model-based clustering techniques might yield poor clusters if the parameters are not initialized properly. To reduce the sensitivity of initial points, a novel algorithm for learning mixture models from multivariate data is introduced in this paper. The proposed algorithm takes advantage of TRUST-TECH (TRansformation Under STability- reTaining Equilibra CHaracterization) to compute neighborhood local maxima on likelihood surface using stability regions. Basically, our method coalesces the advantages of the traditional EM with that of the dynamic and geometric characteristics of the stability regions of the corresponding nonlinear dynamical system of the log-likelihood function. Two phases namely, the EM phase and the stability region phase, are repeated alternatively in the parameter space to achieve improvements in the maximum likelihood. Though applied to Gaussian mixtures in this paper, our technique can be easily generalized to any other parametric finite mixture model. The algorithm has been tested on both synthetic and real datasets and the improvements in the performance compared to other approaches are demonstrated. The robustness with respect to initialization is also illustrated experimentally.

The concept of a stability region (region of attraction) of nonlinear dynamical systems is widely used in many fields such as engineering and the sciences. In this paper, we study the notion of stability regions for a class of non-hyperbolic dynamical systems. A complete characterization of the stability boundary is presented for a fairly large class of non-hyperbolic dynamical systems. Several necessary and sufficient conditions for an equilibrium manifold (the generalized concept of an equilibrium point) to lie on the stability boundary are derived. It is shown that the stability boundary of this class of systems consists of the union of the stable manifolds of the equilibrium manifolds on the stability boundary. In addition, an effective scheme to estimate stability regions by using an energy function is developed. It is shown that the scheme can optimally estimate stability regions for a class of non-hyperbolic dynamical systems. Two examples are given to illustrate the theoretical prediction.

This paper introduces the concept of the convergent region of the Newton homotopy method. It is shown that convergent regions of the Newton homotopy method are equal to the stability regions for the Newton flow x/spl dot/=-adj(DF(x))F(x). A quite complete algebraic characterization of a convergent region and its boundary for a large class of nonlinear systems is derived and this characterization, which is explicit and computationally feasible, leads to the development of a numerical method to determine the convergent region and to the construction of simple criteria to avoid revisitations of the same solutions from different initial guesses. Two examples are given to illustrate the theoretical prediction.

A comprehensive analysis of homotopy methods on the computation of all DC operating points of nonlinear circuits and systems is conducted. Several sufficient conditions for the connectivity of all the solutions along a single homotopy path are derived. These conditions offer criteria to determine a starting point from which one can find all the solutions along one homotopy path. For the class of nonlinear circuits and systems in which all the solutions lie on several homotopy paths, a new systematic method to explicitly construct a starting point for each homotopy path is developed, From a practical viewpoint, the constructive method developed does not require the difficult task of finding a good initial guess and is applicable to general nonlinear circuits and systems. From a methodological viewpoint, the constructive method developed is applicable to general homotopy methods with different homotopy functions.

In recent developments of direct methods for power system transient stability analysis, the task of finding the controlling unstable equilibrium point (u.e.p.) of the original system is performed on an artificial, dimension-reduction system for easily computing the controlling u.e.p. It has been shown that if the stable and unstable manifolds of a family of parametrized systems, which relates the original power system and an artificial, dimension-reduction system, satisfy the transversality condition as the parameter varies, then the artificial, dimension-reduction system contains the same set of u.e.p.'s on the stability boundary. In this paper, instead of direct verification of the transversality conditions, we show that under small mechanical power injections, the original power system model and the artificial, dimension-reduction system contain the same unstable equilibrium points on the stability boundary for one machine and two machine power system models.

We propose a systematic method to find several local optimal solutions for a general nonlinear optimization problem. Analytical results for quasi-gradient systems and reflected gradient systems are developed and applied to explore the topological and geometric aspects of the critical points of the objective function. A mechanism is devised to escape from a local optimal solution and proceed into another local optimal solution by locating the decomposition point. By properly switching between quasi-gradient systems and reflected gradient systems, our proposed method can obtain a set of local optimal solutions and decomposition points. This algorithm also can find the global optimal solution. It depends on its ability to find all the decomposition points. The main algorithm contains two levels: the lower level is continuous while the upper level is discrete in nature. Further improvements in the algorithm to locate all decomposition points are desirable. The proposed method is applied to one test example with encouraging results.>