arXiv subjects

Julia Kowalski

Publications and source records attributed to Julia Kowalski.

12 recordsLinked to original sources

arXiv2026

FarSky: Task-Aware Latent-Space Coupling for Generative Intra-Hour Solar Forecasting

Accurate solar irradiance forecasting is essential for the reliable integration of photovoltaic power into modern electricity grids. All-sky imagers (ASI) provide high-resolution observations of clouds, making them well suited for intra-hour forecasting. Recent deep learning approaches have substantially improved forecast accuracy but are often limited by deterministic predictions and a reduced capability to anticipate ramp events. This work proposes FarSky, a generative forecasting framework that leverages latent-space coupling to learn task-aware representations of sky images. A multi-task autoencoder first learns a shared latent representation for image reconstruction and irradiance estimation. A latent diffusion model then generates future latent states conditioned on recent observations, from which irradiance forecasts are directly decoded. Probabilistic forecasts are inherently obtained through stochastic sampling. The framework is developed using a multi-year ASI dataset acquired at the Plataforma Solar de Almería, Spain, and evaluated on two independent test datasets against persistence, state-of-the-art end-to-end, and generative forecasting approaches. FarSky achieves the best overall deterministic and probabilistic forecasting performance, improving forecast skill by up to 11 percentage points. Furthermore, it substantially improves ramp event detection over existing methods, achieving F1-scores above 60%. These results demonstrate the potential of combining generative models with task-aware latent-space coupling for solar forecasting.

cs.LG↗

arXiv2026

Zoomy: flexible modeling and simulation software for free-surface flows

Free-surface flow is relevant to many researchers in water resources engineering, geohazard assessment, as well as coastal and river engineering. Many different free-surface models have been proposed, which span modeling complexity from the hydrostatic Saint-Venant equations to the Reynolds-averaged Navier-Stokes equations. Particularly efficient methods can be derived by depth-averaging, resulting in dimensionally reduced models. Typically, this yields hierarchies of models -- models with a variable system structure depending on the polynomial expansion of the flow variables -- that need to be analyzed and numerically solved. This description, analysis, and simulation are challenging, and existing software solutions only cover a specific subset of models generated by these hierarchies. We propose a new software framework to address this issue. Zoomy allows for an efficient description, symbolic analysis, and numerical solution of depth-averaged hierarchies of free-surface flow models. Zoomy handles a numerical discretization in one- and two-dimensional space on unstructured grids. With this framework, systematic evaluation of hierarchies of depth-averaged free-surface flows becomes feasible. Additionally, our open-source framework increases the accessibility of these depth-averaged systems to application engineers interested in efficient methods for free-surface flows.

cs.CE↗

arXiv2025

End-to-End Quantum Algorithm for Topology Optimization in Structural Mechanics

Topology optimization is a key methodology in engineering design for finding efficient and robust structures. Due to the enormous size of the design space, evaluating all possible configurations is typically infeasible. In this work, we present an end-to-end, fault-tolerant quantum algorithm for topology optimization that operates on the exponential Hilbert space representing the design space. We demonstrate the algorithm on the two-dimensional Messerschmitt-Bölkow-Blohm (MBB) beam problem. By restricting design variables to binary values, we reformulate the compliance minimization task as a combinatorial satisfiability problem solved using Grover's algorithm. Within Grover's oracle, the compliance is computed through the finite-element method (FEM) using established quantum algorithms, including block-encoding of the stiffness matrix, Quantum Singular Value Transformation (QSVT) for matrix inversion, Hadamard test, and Quantum Amplitude Estimation (QAE). The complete algorithm is implemented and validated using classical quantum-circuit simulations. A detailed complexity analysis shows that the method evaluates the compliance of exponentially many structures in quantum superposition in polynomial time. In the global search, our approach maintains Grover's quadratic speedup compared to classical unstructured search. Overall, the proposed quantum workflow demonstrates how quantum algorithms can advance the field of computational science and engineering.

quant-ph↗

arXiv2025

Bryne: sustainable prototyping of finite element models

Open-source simulation frameworks are evolving rapidly to provide accessible tools for the numerical solution of partial differential equations. Modern finite element (FEM) software such as FEniCS, Firedrake, or dune-fem alleviates the need for modelers to recode the discretization and linear solver backend for each application and enables rapid prototyping of solvers. However, while it has become easier to build prototype FEM models, creating a solver reusable beyond its specific initial simulation setup remains difficult. Moreover, simulation setups typically cover an ample input parameter space, and tracking complex metadata on research project time scales has become a challenge. This implies the need to supplement model development with a coding-intensive complementary workstream, seldom developed for sustainable reuse. To address these issues, we introduce our open-source Python package Bryne. Bryne is an object-oriented framework for FEM solvers built with the dune-fem Python API. In this article, we describe how it helps to evolve rapid-prototyping solver development into sustainable simulation building. First, we show how to translate a minimal dune-fem solver into a Bryne FEM model to build human-readable, metadata-enriched simulations. Bryne then offers a simulation driver and model coupling interfaces to combine implemented solvers in operator-split multiphysics simulations. The resulting reproducibility-enabled infrastructure allows users to tackle complex simulation setups without sacrificing backend flexibility. We demonstrate the workflow on a convection-coupled phase-change simulation, where a discontinuous Galerkin flow solver is coupled with a solver for solidification phase change.

physics.comp-ph↗

arXiv2022

A scale-coupled numerical method for transient close-contact melting

We introduce a numerical workflow to model and simulate transient close-contact melting processes based on the space-time finite element method. That is, we aim at computing the velocity at which a forced heat source melts through a phase-change material. Existing approaches found in the literature consider a thermo-mechanical equilibrium in the contact melt film, which results in a constant melting velocity of the heat source. This classical approach, however, cannot account for transient effects in which the melting velocity adjusts itself to equilibrium conditions. With our contribution, we derive a model for the transient melting process of a planar heat source. We iteratively cycle between solving for the heat equation in the solid material and updating the melting velocity. The latter is computed based on the heat flux in the vicinity of the heat source. The motion of the heated body is simulated via the moving mesh strategy referred to as the Virtual Region Shear-Slip Mesh Update Method, which avoids remeshing and is particularly efficient in representing unidirectional movement. We show numerical examples to validate our methodology and present two application scenarios, a 2D planar thermal melting probe and a 2D hot-wire cutting machine.

math.NA↗

arXiv2021

A level-set based space-time finite element approach to the modelling of solidification and melting processes

We present a strategy for the numerical solution of convection-coupled phase-transition problems, with focus on solidification and melting. We solve for the temperature and flow fields over time. The position of the phase-change interface is tracked with a level-set method, which requires knowledge of the heat-flux discontinuity at the interface. In order to compute the heat-flux jump, we build upon the ghost-cell approach and extend it to the space-time finite element method. This technique does not require a local enrichment of the basis functions, such as methods like extended finite elements, and it can be easily implemented in already existing finite element codes. Verification cases for the 1D Stefan problem and the lid-driven cavity melting problem are provided. Furthermore, we show a more elaborate 2D case in view of complex applications.

math.NA↗

arXiv2020

Emulator-based global sensitivity analysis for flow-like landslide run-out models

Landslide run-out modeling involves various uncertainties originating from model input data. It is therefore desirable to assess the model's sensitivity. A global sensitivity analysis that is capable of exploring the entire input space and accounts for all interactions, often remains limited due to computational challenges resulting from a large number of necessary model runs. We address this research gap by integrating Gaussian process emulation into landslide run-out modeling and apply it to the open-source simulation tool r.avaflow. The feasibility and efficiency of our approach is illustrated based on the 2017 Bondo landslide event. The sensitivity of aggregated model outputs, such as the apparent friction angle, impact area, as well as spatially resolved maximum flow height and velocity, to the dry-Coulomb friction coefficient, turbulent friction coefficient and the release volume are studied. The results of first-order effects are consistent with previous results of common one-at-a-time sensitivity analyses. In addition to that, our approach allows to rigorously investigate interactions. Strong interactions are detected on the margins of the flow path where the expectation and variation of maximum flow height and velocity are small. The interactions generally become weak with increasing variation of maximum flow height and velocity. Besides, there are stronger interactions between the two friction coefficients than between the release volume and each friction coefficient. In the future, it is promising to extend the approach for other computationally expensive tasks like uncertainty quantification, model calibration, and smart early warning.

physics.flu-dyn↗

arXiv2020

Mixed finite elements for convection-coupled phase-change in enthalpy form: Open software verified and applied to 2D benchmarks

Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate this convection-coupled phase-change problem on a single computational domain. The governing equations can be solved accurately with a monolithic approach using mixed finite elements and Newton's method. Previously, the monolithic approach has relied on adaptive mesh refinement to regularize local nonlinearities at phase interfaces. This contribution instead separates mesh refinement from nonlinear problem regularization and provides a continuation procedure which robustly obtains accurate solutions on the tested 2D uniform meshes. A flexible and extensible open source implementation is provided. The code is formally verified to accurately solve the governing equations in time and in 2D space, and convergence rates are shown. Two benchmark simulations are presented in detail with comparison to experimental data sets and corresponding results from the literature, one for the melting of octadecane and another for the freezing of water. Sensitivities to key numerical parameters are presented. For the case of freezing water, effective reduction of numerical errors from these key parameters is successfully demonstrated. Two more simulations are briefly presented, one for melting at a higher Rayleigh number and one for melting gallium.

physics.comp-ph↗

arXiv2019

Topographic uncertainty quantification for flow-like landslide models via stochastic simulations

Topography representing digital elevation models (DEMs) are essential inputs for computational models capable of simulating the run-out of flow-like landslides. Yet, DEMs are often subject to error, a fact that is mostly overlooked in landslide modeling. We address this research gap and investigate the impact of topographic uncertainty on landslide-run-out models. In particular, we will describe two different approaches to account for DEM uncertainty, namely unconditional and conditional stochastic simulation methods. We investigate and discuss their feasibility, as well as whether DEM uncertainty represented by stochastic simulations critically affects landslide run-out simulations. Based upon a historic flow-like landslide event in Hong Kong, we present a series of computational scenarios to compare both methods using our modular Python-based workflow. Our results show that DEM uncertainty can significantly affect simulation-based landslide run-out analyses, depending on how well the underlying flow path is captured by the DEM, as well as further topographic characteristics and the DEM error's variability. We further find that in the absence of systematic bias in the DEM, a performant root mean square error based unconditional stochastic simulation yields similar results than a computationally intensive conditional stochastic simulation that takes actual DEM error values at reference locations into account. In all other cases the unconditional stochastic simulation overestimates the variability of the DEM error, which leads to an increase of the potential hazard area as well as extreme values of dynamic flow properties.

physics.geo-ph↗

arXiv2018

Moment Approximations and Model Cascades for Shallow Flow

Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates depth-averaging. While the shallow flow formulation is advantageous in terms of computational efficiency, it also comes at the price of losing vertical information such as the flow's velocity profile. This gives rise to a model error, which limits the shallow flow model's predictive power and is often not explicitly quantifiable. We propose the use of vertical moments to overcome this problem. The shallow moment approximation preserves information on the vertical flow structure while still making use of the simplifying framework of depth-averaging. In this article, we derive a generic shallow flow moment system of arbitrary order starting from a set of balance laws, which has been reduced by scaling arguments. The derivation is based on a fully vertically resolved reference model with the vertical coordinate mapped onto the unit interval. We specify the shallow flow moment hierarchy for kinematic and Newtonian flow conditions and present 1D numerical results for shallow moment systems up to third order. Finally, we assess their performance with respect to both the standard shallow flow equations as well as with respect to the vertically resolved reference model. Our results show that depending on the parameter regime, e.g. friction and slip, shallow moment approximations significantly reduce the model error in shallow flow regimes and have a lot of potential to increase the predictive power of shallow flow models, while keeping them computationally cost efficient.

physics.comp-ph↗

arXiv2018

Melting probe technology for subsurface exploration of extraterrestrial ice - Critical refreezing length and the role of gravity

The 'Ocean Worlds' of our Solar System are covered with ice, hence the water is not directly accessible. Using melting probe technology is one of the promising technological approaches to reach those scientifically interesting water reservoirs. Melting probes basically consist of a heated melting head on top of an elongated body that contains the scientific payload. The traditional engineering approach to design such melting probes starts from a global energy balance around the melting head and quantifies the power necessary to sustain a specific melting velocity while preventing the probe from refreezing and stall in the channel. Though this approach is sufficient to design simple melting probes for terrestrial applications, it is too simplistic to study the probe's performance for environmental conditions found on some of the Ocean's Worlds, e.g. a lower value of the gravitational acceleration. This will be important, however, when designing exploration technologies for extraterrestrial purposes. We tackle the problem by explicitly modeling the physical processes in the thin melt film between the probe and the underlying ice. Our model allows to study melting regimes on bodies of different gravitational acceleration, and we explicitly compare melting regimes on Europa, Enceladus and Mars. In addition to that, our model allows to quantify the heat losses due to convective transport around the melting probe. We discuss to which extent these heat losses can be utilized to avoid the necessity of a side wall heating system to prevent stall, and introduce the notion of the 'Critical Refreezing Length'. Our results allow to draw important conclusions towards the design of melting probe technology for future missions to icy bodies in our Solar System.

physics.flu-dyn↗

arXiv2018

Monolithic simulation of convection-coupled phase-change - verification and reproducibility

Phase interfaces in melting and solidification processes are strongly affected by the presence of convection in the liquid. One way of modeling their transient evolution is to couple an incompressible flow model to an energy balance in enthalpy formulation. Two strong nonlinearities arise, which account for the viscosity variation between phases and the latent heat of fusion at the phase interface. The resulting coupled system of PDE's can be solved by a single-domain semi-phase-field, variable viscosity, finite element method with monolithic system coupling and global Newton linearization. A robust computational model for realistic phase-change regimes furthermore requires a flexible implementation based on sophisticated mesh adaptivity. In this article, we present first steps towards implementing such a computational model into a simulation tool which we call Phaseflow. Phaseflow utilizes the finite element software FEniCS, which includes a dual-weighted residual method for goal-oriented adaptive mesh refinement. Phaseflow is an open-source, dimension-independent implementation that, upon an appropriate parameter choice, reduces to classical benchmark situations including the lid-driven cavity and the Stefan problem. We present and discuss numerical results for these, an octadecane PCM convection-coupled melting benchmark, and a preliminary 3D convection-coupled melting example, demonstrating the flexible implementation. Though being preliminary, the latter is, to our knowledge, the first published 3D result for this method. In our work, we especially emphasize reproducibility and provide an easy-to-use portable software container using Docker.

physics.flu-dyn↗