arXiv subjects

Yuxin Xia

Publications and source records attributed to Yuxin Xia.

8 recordsLinked to original sources

arXiv2026

Lifetime Profit-Maximising Co-optimisation of Multi-Service Stacking for Battery Storage

Grid-scale battery energy storage can generate revenue by stacking services across electricity and frequency response markets, yet identifying the lifetime profit-maximising stacking strategy remains challenging. Decisions across services are coupled through shared battery system capacity, constrained by system operator energy management rules, and further shaped by product-specific technical requirements that govern system operation, degradation, and lifetime profitability. This paper presents an ageing-aware receding-horizon framework for co-optimising multi-service stacking that explicitly captures product-specific characteristics and state-of-energy compliance rules. The framework is applied to the Great Britain market, where storage operators can stack electricity trading with multiple dynamic frequency response services procured through the newly introduced 'Enduring Auction Capability' platform under energy management requirements imposed by the National Energy System Operator. Using real market data, we demonstrate that degradation modelling, discount rate, and battery ageing jointly govern both lifetime value and optimal stacking strategy. Accounting for ageing increases lifetime revenue by up to 32% relative to a degradation-agnostic benchmark, while higher-fidelity ageing modelling can provide a further revenue improvement of up to 16% over simpler formulations. Lower discount rates favour strategies that balance calendar and cycling ageing, while higher discount rates favour aggressive operation. Across all strategies, services responding to positive frequency deviations are consistently preferred over those responding to negative deviations. Lifetime profit is maximised by adapting the optimal service mix as the battery ages.

math.OC↗

arXiv2026

HYDRA: Hyperbolic Dynamic Representation Architecture for Kolmogorov-Arnold Networks

Kolmogorov-Arnold Networks (KANs) enhance nonlinear function approximation by replacing scalar weights with learnable univariate functions. However, assigning an independent function to every connection results in substantial parameter redundancy, limiting their scalability and efficiency. To reduce this redundancy, we introduce \textbf{HY}perbolic \textbf{D}ynamic \textbf{R}epresentation \textbf{A}rchitecture (HYDRA), a parameter-efficient hyperbolic extension of KAN that combines spline-based functional learning with representations in the Poincaré ball. HYDRA maps vector-valued inputs into a bounded hyperbolic latent space, performs KAN-style updates in tangent space, and employs a low-rank prototype block to share functional transformations across hidden dimensions. The resulting hyperbolic representations provide a structured radial coordinate for interpretation, while radius control improves training stability by preventing boundary saturation. Extensive experiments across eight benchmark datasets demonstrate that HYDRA consistently achieves competitive or superior predictive performance while improving parameter efficiency and representation interpretability.

cs.LG↗

arXiv2026

Strengthened and Faster Linear Approximation to Joint Chance Constraints with Wasserstein Ambiguity

Many real-world decision-making problems have uncertain parameters in constraints. Wasserstein distributionally robust joint chance constraints (WDRJCC) offer a promising solution by explicitly guaranteeing the probability of the simultaneous constraint satisfaction. However, WDRJCC are computationally demanding, and practical applications often require more tractable approaches, especially for large-scale problems such as power system unit commitment problems and multilevel problems with chance constraints in lower levels. To address this, this paper proposes a convex inner-approximation for WDRJCC with right-hand-side uncertainties (RHS-WDRJCC). We propose a Strengthened and Faster Linear Approximation (SFLA) by strengthening an existing convex inner-approximation. This strengthening process reduces the number of constraints and tightens the feasible region for ancillary variables, leading to significant computational speedup. We prove that the proposed SFLA does not introduce extra conservativeness and can be less conservative compared to common approximations such as W-CVaR. We then extend the proposed SFLA to a more interpretable decision-making paradigm: robustness maximization, where the risk level and the Wasserstein radius are determined by maximizing solution robustness subject to a utility degradation limit. We discuss the connection between risk minimization and radius maximization as two formulations of robustness maximization, and show the advantage of radius maximization. In power system unit commitment, the proposed SFLA achieves up to 10x computational speedup compared to the strengthened and exact reformulation. In a bilevel strategic bidding problem where the exact reformulation is not applicable due to non-convexity, the proposed SFLA leads to 90x speedup than W-CVaR. In robustness maximization, the proposed SFLA demonstrated over 100x speedup.

math.OC↗

arXiv2026

Stochastic Gradient Descent for Nonlinear Inverse Problems in Banach Spaces

Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected randomly at each iteration, SGD scales well to problem size and has been shown to be effective for solving large-scale inverse problems. In this work, we investigate SGD for solving nonlinear inverse problems in Banach spaces through the lens of iterative regularization. Under general assumptions, we prove almost sure convergence of the iterates to the minimum distance solution and show the regularizing property in expectation under an a priori stopping rule. Further, we establish convergence rates under the conditional stability assumptions for both exact and noisy data. Numerical experiments on Schlieren tomography and electrical impedance tomography are presented to show distinct features of the method.

math.NA↗

arXiv2025

Bilevel Transmission Expansion Planning with Joint Chance-Constrained Dispatch

In transmission expansion planning (TEP), network planners make long-term investment decisions while anticipating market clearing outcomes that are increasingly affected by renewable generation uncertainty. Additionally, market participants' sensitivity to network charges and the requirement for cost recovery by the network planner introduce further complexity. Since the day-ahead market clears before uncertainty realizes, explicitly modelling these uncertainties at the lower-level market clearing becomes important in bilevel TEP problems. In this paper, we introduce a novel bilevel TEP framework with lower-level joint chance-constrained market clearing that manages line flow constraints under wind uncertainty and accounts for the effect of network tariffs on participants' actual marginal costs and utility. To solve this complex problem, we propose a Strengthened Linear Approximation (SLA) technique for handling Wasserstein distributionally robust joint chance constraints with right-hand-side uncertainties (RHS-WDRJCC). The proposed method offers more efficient approximations without additional conservativeness and avoids the numerical issues encountered in existing approaches by introducing valid inequalities. The case study demonstrates that the proposed model achieves the desired out-of-sample constraint satisfaction probability. Moreover, the numerical results highlight the significant computational advantage of SLA, achieving up to a 26x speedup compared to existing methods such as worst-case conditional value-at-risk, while maintaining high solution quality.

math.OC↗

arXiv2025

Scalable Multi-Level Optimization for Sequentially Cleared Energy Markets with a Case Study on Gas and Carbon Aware Unit Commitment

This paper examines Mixed-Integer Multi-Level problems with Sequential Followers (MIMLSF), a specialized optimization model aimed at enhancing upper-level decision-making by incorporating anticipated outcomes from lower-level sequential market-clearing processes. We introduce a novel approach that combines lexicographic optimization with a weighted-sum method to asymptotically approximate the MIMLSF as a single-level problem, capable of managing multi-level problems exceeding three levels. To enhance computational efficiency and scalability, we propose a dedicated Benders decomposition method with multi-level subproblem separability. To demonstrate the practical application of our MIMLSF solution technique, we tackle a unit commitment problem (UC) within an integrated electricity, gas, and carbon market clearing framework in the Northeastern United States, enabling the incorporation of anticipated costs and revenues from gas and carbon markets into UC decisions. This ensures that only profitable gas-fired power plants (GFPPs) are committed, allowing system operators to make informed decisions that prevent GFPP economic losses and reduce total operational costs under stressed electricity and gas systems. The case study not only demonstrates the applicability of the MIMLSF model but also highlights the computational benefits of the dedicated Benders decomposition technique, achieving average reductions of 32.23% in computing time and 94.23% in optimality gaps compared to state-of-the-art methods.

math.OC↗

arXiv2024

An Incentive Regulation Approach for Balancing Stakeholder Interests in Transmission Investment

The merchant-regulatory mechanism represents a promising tool that combines the benefits of merchant investment and regulated investment, thereby providing efficient incentives for merchant Transmission Companies (Transcos) subject to regulatory compliance. However, one of the drawbacks of the H-R-G-V merchant-regulated mechanism is that it allows the Transco to capture the entire surplus increase resulting from investment, without any economic benefits for consumers and generators. To address this issue, we propose an incentive tuning parameter, which is incorporated into the calculation of the incentive fee for the Transco. Accordingly, the regulatory framework can effectively manage the Transco's profit and allow market participants to access economic benefits, thus ensuring a fair distribution of economic advantages among the stakeholders, while the impact on overall social welfare remains relatively modest.

math.OC↗

arXiv2024

Visual Harmony: Text-Visual Interplay in Circular Infographics

Infographics are visual representations designed for efficient and effective communication of data and knowledge. One crucial aspect of infographic design is the interplay between text and visual elements, particularly in circular visualizations where the textual descriptions can either be embedded within the graphics or placed adjacent to the visual representation. While several studies have examined text layout design in visualizations in general, the text-visual interplay in infographics and its subsequent perceptual effects remain underexplored. To address this, our study investigates how varying text placement and descriptiveness impact pleasantness, comprehension and overall memorability in the infographics viewing experience. We recruited 30 participants and presented them with a collection of 15 infographics across a diverse set of topics, including media and public events, health and nutrition, science and research, and sustainability. The text placement (embed, side-to-side) and descriptiveness (simplistic, normal, descriptive) were systematically manipulated, resulting in a total of six experimental conditions. Our key findings indicate that text placement can significantly influence the memorability of infographics, whereas descriptiveness can significantly impact the pleasantness of the viewing experience. Embedding text placement and simplistic text can potentially contribute to more effective infographic designs. These results offer valuable insights for infographic designers, contributing to the creation of more effective and memorable visual representations.

cs.HC↗