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Martin Mevissen

Publications and source records attributed to Martin Mevissen.

14 recordsLinked to original sources
arXiv2026

GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysis

Foundation models are transforming business workflows and boosting productivity, yet they remain largely absent from engineering domains such as power system analysis, where strict physical consistency must be enforced. We present GENCO (GEometric Neural Corrective Optimizer), a unified neural solver for steady-state transmission grid analysis that handles power flow (PF), optimal power flow (OPF), and state estimation (SE) within a single architecture and shared grid representation. To support advances in neural power system solvers, we introduce the open-source GridFM Development Framework, which standardizes synthetic data generation and training in a low-code environment. We also release large-scale datasets with millions of PF and OPF scenarios across diverse grid topologies to support reproducible benchmarking. We evaluate GENCO on the PFDelta and OPFData benchmarks against state-of-the-art neural solvers and classical solvers, including Newton-Raphson and IPOPT, as well as on real-world Hydro-Qu\'ebec SCADA data. For large-scale PF, GENCO recovers the full AC operating state, including voltage magnitudes and reactive power that DC-PF cannot provide, while matching DC-PF-level active power-balance residuals. It achieves up to 30x speedups over Newton-Raphson at only 2x the runtime of DC-PF. For OPF, it achieves up to 85x speedups over IPOPT while improving feasibility, optimality, and runtime over DC-OPF. For SE, GENCO is more robust than classical weighted least squares to noisy measurements and grid parameter errors, and always returns a high-quality estimate even when weighted least squares fails to converge. Together, the unified architecture and development framework provide a new approach to large-scale steady-state grid analysis, lowering the barrier to entry for power system engineers and marking a step toward Grid Foundation Models.

cs.AI↗
arXiv2024

Quantum computing in civil engineering: Potentials and Limitations

Quantum computing is a new computational paradigm with the potential to solve certain computationally challenging problems much faster than traditional approaches. Civil engineering encompasses many computationally challenging problems, which leads to the question of how well quantum computing is suitable for solving civil engineering problems and how much impact and implications to the field of civil engineering can be expected when deploying quantum computing for solving these problems. To address these questions, we will, in this paper, first introduce the fundamentals of quantum computing. Thereupon, we will analyze the problem classes to elucidate where quantum computing holds the potential to outperform traditional computers and, focusing on the limitations, where quantum computing is not considered the most suitable solution. Finally, we will review common complex computation use cases in civil engineering and evaluate the potential and the limitations of being improved by quantum computing.

cs.ET↗
arXiv2021

On model selection for scalable time series forecasting in transport networks

The transport literature is dense regarding short-term traffic predictions, up to the scale of 1 hour, yet less dense for long-term traffic predictions. The transport literature is also sparse when it comes to city-scale traffic predictions, mainly because of low data availability. In this work, we report an effort to investigate whether deep learning models can be useful for the long-term large-scale traffic prediction task, while focusing on the scalability of the models. We investigate a city-scale traffic dataset with 14 weeks of speed observations collected every 15 minutes over 1098 segments in the hypercenter of Los Angeles, California. We look at a variety of state-of-the-art machine learning and deep learning predictors for link-based predictions, and investigate how such predictors can scale up to larger areas with clustering, and graph convolutional approaches. We discuss that modelling temporal and spatial features into deep learning predictors can be helpful for long-term predictions, while simpler, not deep learning-based predictors, achieve very satisfactory performance for link-based and short-term forecasting. The trade-off is discussed not only in terms of prediction accuracy vs prediction horizon but also in terms of training time and model sizing.

cs.LG↗
arXiv2021

Quantum Computing for Finance: State of the Art and Future Prospects

This article outlines our point of view regarding the applicability, state-of-the-art, and potential of quantum computing for problems in finance. We provide an introduction to quantum computing as well as a survey on problem classes in finance that are computationally challenging classically and for which quantum computing algorithms are promising. In the main part, we describe in detail quantum algorithms for specific applications arising in financial services, such as those involving simulation, optimization, and machine learning problems. In addition, we include demonstrations of quantum algorithms on IBM Quantum back-ends and discuss the potential benefits of quantum algorithms for problems in financial services. We conclude with a summary of technical challenges and future prospects.

quant-ph↗
arXiv2019

Projections onto the Set of Feasible Inputs and the Set of Feasible Solutions

We study the projection onto the set of feasible inputs and the set of feasible solutions of a polynomial optimisation problem (POP). Our motivation is increasing the robustness of solvers for POP: Without a priori guarantees of feasibility of a particular instance, one should like to perform the projection onto the set of feasible inputs prior to running a solver. Without a certificate of optimality, one should like to project the output of the solver onto the set of feasible solutions subsequently. We study the computational complexity, formulations, and convexifications of the projections. Our results are illustrated on IEEE test cases of Alternating Current Optimal Power Flow (ACOPF) problem.

math.OC↗
arXiv2019

A Fine-Grained Variant of the Hierarchy of Lasserre

There has been much recent interest in hierarchies of progressively stronger convexifications of polynomial optimisation problems (POP). These often converge to the global optimum of the POP, asymptotically, but prove challenging to solve beyond the first level in the hierarchy for modest instances. We present a finer-grained variant of the Lasserre hierarchy, together with first-order methods for solving the convexifications, which allow for efficient warm-starting with solutions from lower levels in the hierarchy.

math.OC↗
arXiv2018

Transmission-Constrained Unit Commitment

The unit commitment with transmission constraints in the alternating-current (AC) model is a challenging mixed-integer non-linear optimisation problem. We present an approach based on decomposition of a Mixed-Integer Semidefinite Programming (MISDP) problem into a mixed-integer quadratic (MIQP) master problem and a semidefinite programming (SDP) sub-problem. Between the master problem and the sub-problem, we pass novel classes of cuts. We analyse finite convergence to the optimum of the MISDP and report promising computational results on a test case from the Canary Islands, Spain.

math.OC↗
arXiv2018

A Hidden Markov Model for Route and Destination Prediction

We present a simple model and algorithm for predicting driver destinations and routes, based on the input of the latest road links visited as part of an ongoing trip. The algorithm may be used to predict any clusters previously observed in a driver's trip history. It assumes that the driver's historical trips are grouped into clusters sharing similar patterns. Given a new trip, the algorithm attempts to predict the cluster in which the trip belongs. The proposed algorithm has low temporal complexity. In addition, it does not require the transition and emission matrices of the Markov chain to be computed. Rather it relies on the frequencies of co-occurrences of road links and trip clusters. We validate the proposed algorithm against an experimental dataset. We discuss the success and convergence of the algorithm and show that our algorithm has a high prediction success rate.

physics.soc-ph↗
arXiv2016

Power Flow as an Algebraic System

Steady states of alternating-current (AC) circuits have been studied in considerable detail. In 1982, Baillieul and Byrnes derived an upper bound on the number of steady states in a loss-less AC circuit [IEEE TCAS, 29(11): 724--737] and conjectured that this bound holds for AC circuits in general. We prove this is indeed the case, among other results, by studying a certain multi-homogeneous structure in an algebraisation.

math.OC↗
arXiv2016

MINLP in Transmission Expansion Planning

Transmission expansion planning requires forecasts of demand for electric power and a model of the underlying physics, i.e., power flows. We present three approaches to deriving exact solutions to the transmission expansion planning problem in the alternating-current model, for a given load.

math.OC↗
arXiv2012

Mean squared error minimization for inverse moment problems

We consider the problem of approximating the unknown density $u\in L^2(Ω,λ)$ of a measure $μ$ on $Ω\subset\R^n$, absolutely continuous with respect to some given reference measure $λ$, from the only knowledge of finitely many moments of $μ$. Given $d\in\N$ and moments of order $d$, we provide a polynomial $p_d$ which minimizes the mean square error $\int (u-p)^2dλ$ over all polynomials $p$ of degree at most $d$. If there is no additional requirement, $p_d$ is obtained as solution of a linear system. In addition, if $p_d$ is expressed in the basis of polynomials that are orthonormal with respect to $λ$, its vector of coefficients is just the vector of given moments and no computation is needed. Moreover $p_d\to u$ in $L^2(Ω,λ)$ as $d\to\infty$. In general nonnegativity of $p_d$ is not guaranteed even though $u$ is nonnegative. However, with this additional nonnegativity requirement one obtains analogous results but computing $p_d\geq0$ that minimizes $\int (u-p)^2dλ$ now requires solving an appropriate semidefinite program. We have tested the approach on some applications arising from the reconstruction of geometrical objects and the approximation of solutions of nonlinear differential equations. In all cases our results are significantly better than those obtained with the maximum entropy technique for estimating $u$.

math.OC↗
arXiv2010

Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations

Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of problems involving nonlinear differential equations. Given a system of nonlinear differential equations, we apply a technique based on finite differences and sparse SDP relaxations for polynomial optimization problems (POP) to obtain a discrete approximation of its solution. In a second step we apply maximum entropy estimation (using moments of a Borel measure associated with the discrete solution) to obtain a smooth closed-form approximation. The approach is illustrated on a variety of linear and nonlinear ordinary differential equations (ODE), partial differential equations (PDE) and optimal control problems (OCP), and preliminary numerical results are reported.

math.OC↗
arXiv2008

Solutions of Polynomial Systems Derived from the Steady Cavity Flow Problem

We propose a general algorithm to enumerate all solutions of a zero-dimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady cavity flow problem in two dimensions. The key technique on which our algorithm is based is to solve polynomial optimization problems via sparse semidefinite programming relaxations (SDPR), which has been adopted successfully to solve reaction-diffusion boundary value problems recently. The cost function to be minimized is derived from discretizing the fluid's kinetic energy. The enumeration algorithm's solutions are shown to converge to the minimal kinetic energy solutions for SDPR of increasing order. We demonstrate the algorithm with SDPR of first and second order on polynomial systems for different scenarios of the cavity flow problem and succeed in deriving the $k$ smallest kinetic energy solutions. The question whether these solutions converge to solutions of the steady cavity flow problem is discussed, and we pose a conjecture for the minimal energy solution for increasing Reynolds number.

math.NA↗