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Yilu Liu

Publications and source records attributed to Yilu Liu.

At least 19 recordsLinked to original sources
arXiv2026

Critical Inertia Estimation for the Three U.S. Interconnections

The rapid integration of inverter-based resources (IBRs) is reducing system inertia across U.S. power grids, raising concerns about frequency stability following large contingencies. This paper presents a simulation-based assessment of critical inertia--the minimum system inertia required to prevent first-stage under-frequency load shedding (UFLS) after the largest credible contingency--across the three major U.S. interconnections: Eastern Interconnection (EI), WECC, and ERCOT. Reduced-inertia scenarios are created by progressively replacing synchronous generators with IBRs, and dynamic simulations are performed using full-scale PSS(R)E and PowerWorld models. The results show that ERCOT reaches critical inertia at approximately 20% IBR penetration under the strict first-stage UFLS criterion--or approximately 58% if only the final UFLS stage must be avoided--compared with above 90% for EI and approximately 67%-68% for WECC. IBR shares in 2024 in the U.S. portions of EI, WECC, and ERCOT were 16%, 33%, and 44%, respectively, indicating varying proximity to critical inertia thresholds. These findings highlight the importance of full dynamic simulations to accurately estimate critical inertia and guide transmission planning under high renewable penetration scenarios.

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arXiv2026

Measurement-Based Assessment of Decadal Inertia and Primary Frequency Response Trends in the US Eastern Interconnection

Changes in the generation mix of the U.S. Eastern Interconnection (EI) raise questions about long-term frequency performance, particularly inertia and primary frequency response (PFR). This paper jointly examines these characteristics using synchronized FNET/GridEye frequency measurements and confirmed generation-trip events from 2013 to 2025. A representative EI frequency trajectory is constructed using the median of geographically distributed measurements. Effective inertia is estimated quarterly from the early post-disturbance rate of change of frequency (RoCoF), using a 3-second window and least-squares fitting. PFR is evaluated using the beta metric, which measures aggregate frequency response from disturbance size and the A-to-B frequency deviation. Annual beta estimates are obtained after filtering events by starting frequency and disturbance size to improve comparability across years. Results show that EI effective inertia varies seasonally and follows a non-monotonic trend rather than a uniform long-term decline. Over the same period, coal generation decreased while natural gas, wind, and solar generation increased. Changes in synchronous generator commitment and operating conditions may have offset some expected inertia reductions. Filtered beta generally increased from the mid-2010s to the early 2020s, with year-to-year variability thereafter. The different trends show that early inertial behavior and broader aggregate frequency response have not evolved in parallel. Joint analysis of inertia and beta offers a more complete measurement-based assessment of EI frequency performance during the generation transition.

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arXiv2026

PMU Foundation Model Bridge: A Tool for Connecting Synchrophasor Streams to Time Series Foundation Models

This paper presents PMU Foundation Model Bridge, an open source tool that connects online phasor measurement unit (PMU) or phasor data concentrator (PDC) streams to publicly available time series foundation models (TSFM). Through a desktop interface or command line interface, users can select measurement channels, define preprocessing, choose TSFMs, and configure outputs. In the initial release, 4 publicly available TSFMs were supported, including Chronos-2, TimesFM 2.5, Timestral, and TimesFM-3. The tool supports both file and synchrophasor streaming outputs, therefore enabling both offline use and integration into C37.118-based online workflow applications. In addition to supporting raw synchrophasor data, the framework provides a preprocessing layer for deriving customized additional quantities for forecasting. The tool is validated using a virtual PMU and real-time laboratory measurements from a frequency disturbance recorder (FDR). The tool aims to support community research on combining synchrophasor technology with TSFMs.

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arXiv2026

Few-for-Many Best-Arm Identification in Multi-Objective Bandits

Real-world systems often serve many objectives but can deploy only a few options, whose performance must be learned from noisy feedback. Modeling each option as an arm in a multi-objective bandit, we introduce \emph{few-for-many best-arm identification}, which seeks a small set of arms minimizing the worst weighted degradation from the objective-wise optima, rather than the best arm for every objective. We consider both known objective groups and latent groups specified only by a representative budget, and propose \textsc{GFM-Elim} and \textsc{AFM-Elim} with instance-dependent sample-complexity guarantees. For Gaussian rewards, we further derive a lower bound for the latent-group setting and show that it is asymptotically attainable with high probability by an oracle-based Track-and-Stop procedure. Our results show that sharing observations across objectives and ignoring irrelevant objective-wise distinctions can substantially reduce the sampling cost, as confirmed by experiments on synthetic and real-world tasks.

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arXiv2026

Relative isoperimetry in the three-dimensional cube: classification and quantitative stability

We determine the complete relative isoperimetric profile of the three-dimensional unit cube and classify all minimizing sets, including the equality cases at both transition volumes. Up to cube isometries and complementation, the minimizers are corner eighth-balls, edge quarter-cylinders, and coordinate slabs, with transitions at $4π/81$ and $1/π$. Building on this classification, we prove that the perimeter deficit at each fixed volume controls the squared $L^1$ distance to the full minimizing family, with optimal exponent two. Near either transition, a uniform estimate combines the distance to each adjacent phase with its excess perimeter and identifies the linear degeneration, at neighboring volumes, of the best constant for distance to the actual minimizers. As consequences, we resolve the isoperimetric conjecture in Milman's formulation (Conjecture~1.1) for all cuboids $(0,β)\times(0,1)^2$, $0<β\leq1$, and the three-dimensional case of Brezis's Open Problem~10.1.

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arXiv2026

Budget-Aware LLM Discovery via Cost-Calibrated Frontier Utility

Large language models increasingly support scientific and algorithmic discovery through inference-time search over evaluated candidates. Existing adaptive discovery controllers assign credit based only on score progress, even though prompt length, retries, and guidance calls cause search actions to incur different token costs. Under a fixed search budget, the controller must decide which frontier to develop and whether its gain justifies the realized cost before the budget is exhausted. We prove that, in the worst case, cost-blind control can forfeit all but a vanishing fraction of attainable quality as frontier count and cost heterogeneity grow. To address this limitation, we introduce \textbf{CostAda}, an adaptive controller built on \emph{cost-calibrated frontier utility}. By valuing progress relative to realized action cost and conditioning credit on the remaining budget, CostAda coordinates local exploration intensity, frontier allocation, and budgeted tactic intervention. Realized action cost and remaining budget therefore shape the search rather than serving only as accounting variables or a stopping rule. Across eight benchmarks with GLM-5 and GPT-5.4, CostAda reaches the strongest baseline's full-budget quality with at most half the budget on thirteen of sixteen benchmark--backbone pairs and achieves the strongest final quality on all sixteen pairs.

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arXiv2026

Isolated singularities of the capillary equation with negative gravity

We classify isolated singularities of classical solutions to the capillary equation with negative gravity, \[ \operatorname{div}\frac{Du}{\sqrt{1+|Du|^2}}=-u \qquad\text{in }B_R\setminus\{0\}\subset\mathbb R^n, \qquad n\ge2, \] without a priori assumptions on symmetry, sign, one-sided boundedness, or blow-up rate. Every such solution is either bounded near the puncture or tends uniformly to $+\infty$ or $-\infty$. In the bounded case, the solution extends across the puncture as a $W^{1,1}_{\mathrm{loc}}$ distributional solution; this extension has a unique continuous representative when $2\le n\le7$. In the unbounded case, for some $\varepsilon\in\{-1,1\}$, \[ u(x)=\varepsilon\left(\frac{n-1}{|x|} -\frac{n+3}{2(n-1)^2}|x|^3\right)+O(|x|^5), \] uniformly in the angular variable. In every fixed smaller ball, all sufficiently high level sets of $\varepsilon u$ are connected, smooth, strictly convex hypersurfaces enclosing the puncture. The corresponding pressure-rescaled graphs converge smoothly with multiplicity one to the round cylinder $\partial B_{n-1}\times\mathbb R$. Nonradial examples form infinite-dimensional families that agree with the radial pole to every algebraic order, so the complete asymptotic expansion does not determine the singular solution germ. The proof of the classification combines critical tail estimates and logarithmic $BV$ compactness with level-set rigidity and the translation identities of the capillary equation. The critical two-dimensional case requires an additional finite-height analysis to exclude a translation defect.

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arXiv2026

The Sharp $C^{1,1}$ Target Threshold for Minimizing Constraint Maps

Let $K\subset\R^m$ be the closure of a bounded domain whose boundary is a compact embedded hypersurface, and let \( \overline M=\R^m\setminus\operatorname{int}K \) be the allowed target. We prove that if $\partial K$ is of class $C^{1,1}$, then every $\overline M$-valued local minimizer of the Dirichlet energy $E(u;B):=\int_B|Du|^2\dd x$ is locally $W^{2,\infty}$, and hence locally $C^{1,1}$, on its continuity set. For every $0<α<1$, we also construct a convex body with $C^{1,α}$ boundary and an everywhere continuous global minimizer that is not $C^{1,1}$. Thus $C^{1,1}$ is the sharp target regularity threshold in the Hölder scale.

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arXiv2026

A Model-threshold Dimension Bound and Sharp Critical Ends for Smooth Singular Sets of Constant Positive $σ_k$-curvature Metrics

Let $k\in\mathbb N$ satisfy $1 0$ must obey \[ p\leq p_k(n), \] where $p_k$ is the model threshold determined by $\Hh^{p+1}\times\Sn^{n-p-1}$. When $k=2$ and $n=m^2$, we construct a smooth complete equality example on $\Sn^n\setminus\Sn^{(m^2-m-2)/2}$. We also prove that the strict inequality $p<p_k(n)$ holds under a finite positive linear-contact hypothesis.

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arXiv2026

The Higher-Dimensional Nitsche Conjecture: Sharp Bounds and Rigidity

Let $n\ge3$ and let $h:\A(r,1)\to\A(R,1)\subset\mathbb R^n$ be an onto homeomorphism with harmonic coordinate functions. We prove the sharp Nitsche bound \[ R\le R_{n,+}(r):=\frac{nr}{n-1+r^n}, \] and, when $h$ interchanges the two ends, the strictly stronger sharp bound \[ R\le R_{n,-}(r):=\frac{nr^{n-1}}{1+(n-1)r^n}. \] Both critical cases are rigid: equality forces, up to an orthogonal transformation, the corresponding end-preserving or end-reversing radial harmonic homeomorphism. No continuous extension to the closed annulus, boundary homeomorphism, boundary Jacobian, or sign condition on the Jacobian is assumed. The proof converts the nonzero degree of each interior direction map into a probability coupling and establishes a sharp contraction principle for vector measures under positive zonal kernels, using the strict concavity of spherical-cap barycenters. At either critical value, a second-order endpoint defect forces equality for a limiting transfer kernel, whose equality classification yields an orthogonal coupling graph. The remaining trace is locked by a Dirichlet-to-Neumann spectral gap in the end-preserving case and by endpoint Hölder regularity and uniform convergence of the direction maps in the end-reversing case.

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arXiv2026

Global Minimality and Rigidity of the Constraint Map Vortex

We consider the minimization problem \[ \min\left\{\int_{B_1}|Du|^2:\ u\in W^{1,2}(B_1;\mathbb R^n),\quad u=x\ \text{on }\partial B_1,\quad |u|\ge a\right\}, \quad 0<a<1. \] Figalli, Guerra, Kim, and Shahgholian proved that the canonical radial vortex is the unique global minimizer for $n\ge7$, and asked whether the same holds in dimensions \(3\le n \le6\). We answer this question affirmatively, thereby completing the global minimality and rigidity of the constraint map vortex in every dimension \(n\ge3\).

math.AP↗
arXiv2026

Time Distribution Principle Using Measured Traveling Waves in Power Grid

Accurate time synchronization is essential for distributed systems. Conventional methods, such as satellite-based synchronization and communication-based approaches, face challenges including signal vulnerability and dependence on communication delay symmetry. This paper proposes a novel time synchronization principle based on traveling wave (TW) measurements in power grids. By leveraging the inherent symmetry of forward and backward TW propagation, the proposed method achieves high-precision time distribution without relying on external time references. The methodology is validated through electromagnetic transient simulations on a modified IEEE 14-bus system. The results demonstrate that under normal conditions, the proposed approach achieves microsecond-level synchronization accuracy. These findings suggest that the TW-based time synchronization principle is a potential alternative to traditional methods, offering improved security and reduced dependence on communication quality.

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arXiv2026

Nonconvex Sublevel Sets For The Planar Translating Mean Curvature Equation

Translating solitons arise as models for type~II singularities of mean-convex mean curvature flow. We construct a smooth bounded uniformly convex domain \(\Om\Subset\R^2\) such that the zero-Dirichlet solution of the planar translating mean curvature equation has a nonconvex sublevel set. The construction is based on a corrected near-critical grim-reaper profile and explicit barriers on a long convex channel.

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arXiv2026

Keeping Data Centers Online in Weak Grids: PLL-Free VM-DPC With Adaptive Reactive-Power Support for Centralized UPS Systems

Data center power systems are increasingly exposed to weak-grid conditions due to the rapid growth of converter-dominated networks and highly dynamic artificial intelligence (AI) workloads. In centralized uninterruptible power supply (UPS) architectures, the front-end rectifier continuously processes the incoming facility power, making its dynamic performance critical for ensuring stable operation and reliable power delivery to information technology (IT) equipment. Under weak-grid conditions, conventional phase-locked loop (PLL)-based proportional-integral (PI) rectifier controllers may exhibit instability due to strong interactions between converter control dynamics and grid impedance. This paper investigates the stability of centralized UPS data center systems operating under weak-grid conditions using a detailed switching-level model developed in MATLAB/Simulink and validated in real time using an OPAL-RT platform. To enhance weak-grid stability and improve converter-grid interaction, a voltage-modulated direct power control (VM-DPC) strategy with adaptive reactive power support is applied to the front-end rectifier. The proposed approach directly regulates active and reactive power without PLL synchronization while dynamically supporting the point of common coupling (PCC) voltage during rapid IT load variations. Results demonstrate that conventional PI-based rectifier control becomes unstable under SCR<=2 conditions, leading to dc-link oscillations and degradation of downstream power delivery. In contrast, the proposed VM-DPC strategy restores stable operation, improves system damping, and maintains reliable power transfer to highly dynamic IT loads under weak-grid operation.

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arXiv2026

Frequency Response of Windowed DFT Phasor Estimation: Impact on Oscillation Observability

Phasor measurement units (PMUs) are widely used for sub-synchronous oscillation monitoring, yet the effect of windowed discrete Fourier transform (DFT)-based phasor estimation on oscillation observability is not fully characterized. This letter derives the complete complex-valued frequency response of the windowed DFT phasor estimator under both magnitude and phase modulation. The analysis shows that the estimation window introduces both frequency-dependent magnitude attenuation and phase shift to oscillation components, governed by the complex gain. A simple recovery method is also proposed to restore the true oscillation amplitude and phase from PMU data using the analytically known complex gain. The results are validated through time-domain simulations and provide guidance for industry practitioners on interpreting PMU-based oscillation measurements and selecting appropriate window lengths.

eess.SP↗
arXiv2026

FoMEMO: Towards Foundation Models for Expensive Multi-objective Optimization

Expensive multi-objective optimization is a prevalent and crucial concern in many real-world scenarios, where sample-efficiency is vital due to the limited evaluations to recover the true Pareto front for decision making. Existing works either involve rebuilding Gaussian process surrogates from scratch for each objective in each new problem encountered, or rely on extensive past domain experiments for pre-training deep learning models, making them hard to generalize and impractical to cope with various emerging applications in the real world. To address this issue, we propose a new paradigm named FoMEMO (Foundation Models for Expensive Multi-objective Optimization), which enables the establishment of a foundation model conditioned on any domain trajectory and user preference, and facilitates fast in-context optimization based on the predicted preference-wise aggregated posteriors. Rather than accessing extensive real-world domain experiments for training, we demonstrate that pre-training the foundation model with a diverse set of hundreds of millions of synthetic data can lead to superior generalization and optimization performance to unknown problems, without necessitating any subsequent model training or updates in the following optimization process.

cs.LG↗
arXiv2026

Quality-Diversity Optimization as Multi-Objective Optimization

The Quality-Diversity (QD) optimization aims to discover a collection of high-performing solutions that simultaneously exhibit diverse behaviors within a user-defined behavior space. This paradigm has stimulated significant research interest and demonstrated practical utility in domains including robot control, creative design, and adversarial sample generation. A variety of QD algorithms with distinct design principles have been proposed in recent years. Instead of proposing a new QD algorithm, this work introduces a novel reformulation by casting the QD optimization as a multi-objective optimization (MOO) problem with a huge number of optimization objectives. By establishing this connection, we enable the direct adoption of well-established MOO methods, particularly set-based scalarization techniques, to solve QD problems through a collaborative search process. We further provide a theoretical analysis demonstrating that our approach inherits theoretical guarantees from MOO while providing desirable properties for the QD optimization. Experimental studies across several QD applications confirm that our method achieves performance competitive with state-of-the-art QD algorithms.

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