arXiv subjects

Matthew D. Piggott

Publications and source records attributed to Matthew D. Piggott.

At least 19 recordsLinked to original sources

arXiv2026

Machine Learning Based Mesh Movement for Non-Hydrostatic Tsunami Simulation

This study investigates the use of machine learning based mesh movement method, specifically the Universal Mesh Movement Network (UM2N), with depth integrated non-hydrostatic shallow water models. Motivation for this comes from the need for models which balance efficiency and accuracy for use in probabilistic coastal hazard assessment. Implementations are built on the discontinuous Galerkin finite-element (DG-FE) based software, Thetis, which leverages the partial differential equation (PDE) framework Firedrake for automated code generation. Verification on benchmark test cases and validation against laboratory measurements of coastal hazards, focusing on tsunami propagation, run-up, and inundation is performed. In these tests, the UM2N-driven meshes help resolve key non-hydrostatic dynamics including wave refraction over a conical shoal, run-up with wetting-drying on a conical island, and tsunami inundation in the Monai Valley laboratory benchmark, and yield numerical solutions in close agreement with reference fine-mesh computations and measured data. Notably, in the Monai Valley case, UM2N achieves a ~91% reduction in wave-peak error at the nearshore gauge compared with ~74% for the conventional Monge--Amp\`ere (MA) mesh movement, both relative to the coarse fixed mesh. The UM2N surrogate based approach accelerates the conventional mesh movement step, achieving a ~32% reduction in total runtime and ~2 times speed-up in mesh movement step time over the MA solver on GPU, while offering a significant improvement in robustness over long integration periods and under strongly nonlinear wave conditions.

physics.ao-ph↗

arXiv2025

Geographic variability in reanalysis wind speed biases: A high-resolution bias correction approach for UK wind energy

Reanalysis datasets have become indispensable tools for wind resource assessment and wind power simulation, offering long-term and spatially continuous wind fields across large regions. However, they inherently contain systematic wind speed biases arising from various factors, including simplified physical parameterizations, observational uncertainties, and limited spatial resolution. Among these, low spatial resolution poses a particular challenge for capturing local variability accurately. Whereas prevailing industry practice generally relies on either no bias correction or coarse, nationally uniform adjustments, we extend and thoroughly analyse a recently proposed spatially resolved, cluster-based bias correction framework. This approach is designed to better account for local heterogeneity and is applied to 319 wind farms across the United Kingdom to evaluate its effectiveness. Results show that this method reduced monthly wind power simulation errors by more than 32% compared to the uncorrected ERA5 reanalysis dataset. The method is further applied to the MERRA-2 dataset for comparative evaluation, demonstrating its effectiveness and robustness for different reanalysis products. In contrast to prior studies, which rarely quantify the influence of topography on reanalysis biases, this research presents a detailed spatial mapping of bias correction factors across the UK. The analysis reveals that for wind energy applications, ERA5 wind speed errors exhibit strong spatial variability, with the most significant underestimations in the Scottish Highlands and mountainous areas of Wales. These findings highlight the importance of explicitly accounting for geographic variability when correcting reanalysis wind speeds, and provide new insights into region-specific bias patterns relevant for high-resolution wind energy modelling.

physics.ao-ph↗

arXiv2024

Towards Universal Mesh Movement Networks

Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Ampère PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.

math.NA↗

arXiv2023

Learning to Optimise Wind Farms with Graph Transformers

This work proposes a novel data-driven model capable of providing accurate predictions for the power generation of all wind turbines in wind farms of arbitrary layout, yaw angle configurations and wind conditions. The proposed model functions by encoding a wind farm into a fully-connected graph and processing the graph representation through a graph transformer. The graph transformer surrogate is shown to generalise well and is able to uncover latent structural patterns within the graph representation of wind farms. It is demonstrated how the resulting surrogate model can be used to optimise yaw angle configurations using genetic algorithms, achieving similar levels of accuracy to industrially-standard wind farm simulation tools while only taking a fraction of the computational cost.

cs.LG↗

arXiv2023

Accelerated wind farm yaw and layout optimisation with multi-fidelity deep transfer learning wake models

Wind farm modelling has been an area of rapidly increasing interest with numerous analytical as well as computational-based approaches developed to extend the margins of wind farm efficiency and maximise power production. In this work, we present the novel ML framework WakeNet, which can reproduce generalised 2D turbine wake velocity fields at hub-height over a wide range of yaw angles, wind speeds and turbulence intensities (TIs), with a mean accuracy of 99.8% compared to the solution calculated using the state-of-the-art wind farm modelling software FLORIS. As the generation of sufficient high-fidelity data for network training purposes can be cost-prohibitive, the utility of multi-fidelity transfer learning has also been investigated. Specifically, a network pre-trained on the low-fidelity Gaussian wake model is fine-tuned in order to obtain accurate wake results for the mid-fidelity Curl wake model. The robustness and overall performance of WakeNet on various wake steering control and layout optimisation scenarios has been validated through power-gain heatmaps, obtaining at least 90% of the power gained through optimisation performed with FLORIS directly. We also demonstrate that when utilising the Curl model, WakeNet is able to provide similar power gains to FLORIS, two orders of magnitude faster (e.g. 10 minutes vs 36 hours per optimisation case). The wake evaluation time of wakeNet when trained on a high-fidelity CFD dataset is expected to be similar, thus further increasing computational time gains. These promising results show that generalised wake modelling with ML tools can be accurate enough to contribute towards active yaw and layout optimisation, while producing realistic optimised configurations at a fraction of the computational cost, hence making it feasible to perform real-time active yaw control as well as robust optimisation under uncertainty.

cs.LG↗

arXiv2022

End-to-end Wind Turbine Wake Modelling with Deep Graph Representation Learning

Wind turbine wake modelling is of crucial importance to accurate resource assessment, to layout optimisation, and to the operational control of wind farms. This work proposes a surrogate model for the representation of wind turbine wakes based on a state-of-the-art graph representation learning method termed a graph neural network. The proposed end-to-end deep learning model operates directly on unstructured meshes and has been validated against high-fidelity data, demonstrating its ability to rapidly make accurate 3D flow field predictions for various inlet conditions and turbine yaw angles. The specific graph neural network model employed here is shown to generalise well to unseen data and is less sensitive to over-smoothing compared to common graph neural networks. A case study based upon a real world wind farm further demonstrates the capability of the proposed approach to predict farm scale power generation. Moreover, the proposed graph neural network framework is flexible and highly generic and as formulated here can be applied to any steady state computational fluid dynamics simulations on unstructured meshes.

cs.LG↗

arXiv2022

Parallel Metric-Based Mesh Adaptation in PETSc using ParMmg

This research note documents the integration of the MPI-parallel metric-based mesh adaptation toolkit ParMmg into the solver library PETSc. This coupling brings robust, scalable anisotropic mesh adaptation to a wide community of PETSc users, as well as users of downstream packages. We demonstrate the new functionality via the solution of Poisson problems in three dimensions, with both uniform and spatially-varying right-hand sides.

cs.MS↗

arXiv2022

E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation

Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the finite element method. By decomposing the error estimates into contributions from individual elements, it is possible to formulate adaptation methods, which modify the mesh with the objective of minimising the resulting QoI error. However, the standard error estimate formulation involves the true adjoint solution, which is unknown in practice. As such, it is common practice to approximate it with an 'enriched' approximation (e.g. in a higher order space or on a refined mesh). Doing so generally results in a significant increase in computational cost, which can be a bottleneck compromising the competitiveness of (goal-oriented) adaptive simulations. The central idea of this paper is to develop a "data-driven" goal-oriented mesh adaptation approach through the selective replacement of the expensive error estimation step with an appropriately configured and trained neural network. In doing so, the error estimator may be obtained without even constructing the enriched spaces. An element-by-element construction is employed here, whereby local values of various parameters related to the mesh geometry and underlying problem physics are taken as inputs, and the corresponding contribution to the error estimator is taken as output. We demonstrate that this approach is able to obtain the same accuracy with a reduced computational cost, for adaptive mesh test cases related to flow around tidal turbines, which interact via their downstream wakes, and where the overall power output of the farm is taken as the QoI. Moreover, we demonstrate that the element-by-element approach implies reasonably low training costs.

cs.LG↗

arXiv2022

Learning to Estimate and Refine Fluid Motion with Physical Dynamics

Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion, and thus struggle if applied to fluid motion estimation directly. Further, optical flow methods only focus on two consecutive frames without utilising historical temporal information, while the fluid motion (velocity field) can be considered a continuous trajectory constrained by time-dependent partial differential equations (PDEs). This discrepancy has the potential to induce physically inconsistent estimations. Here we propose an unsupervised learning based prediction-correction scheme for fluid flow estimation. An estimate is first given by a PDE-constrained optical flow predictor, which is then refined by a physical based corrector. The proposed approach outperforms optical flow methods and shows competitive results compared to existing supervised learning based methods on a benchmark dataset. Furthermore, the proposed approach can generalize to complex real-world fluid scenarios where ground truth information is effectively unknowable. Finally, experiments demonstrate that the physical corrector can refine flow estimates by mimicking the operator splitting method commonly utilised in fluid dynamical simulation.

cs.LG↗

arXiv2022

M2N: Mesh Movement Networks for PDE Solvers

Mainstream numerical Partial Differential Equation (PDE) solvers require discretizing the physical domain using a mesh. Mesh movement methods aim to improve the accuracy of the numerical solution by increasing mesh resolution where the solution is not well-resolved, whilst reducing unnecessary resolution elsewhere. However, mesh movement methods, such as the Monge-Ampere method, require the solution of auxiliary equations, which can be extremely expensive especially when the mesh is adapted frequently. In this paper, we propose to our best knowledge the first learning-based end-to-end mesh movement framework for PDE solvers. Key requirements of learning-based mesh movement methods are alleviating mesh tangling, boundary consistency, and generalization to mesh with different resolutions. To achieve these goals, we introduce the neural spline model and the graph attention network (GAT) into our models respectively. While the Neural-Spline based model provides more flexibility for large deformation, the GAT based model can handle domains with more complicated shapes and is better at performing delicate local deformation. We validate our methods on stationary and time-dependent, linear and non-linear equations, as well as regularly and irregularly shaped domains. Compared to the traditional Monge-Ampere method, our approach can greatly accelerate the mesh adaptation process, whilst achieving comparable numerical error reduction.

cs.LG↗

arXiv2020

Unsupervised Learning of Particle Image Velocimetry

Particle Image Velocimetry (PIV) is a classical flow estimation problem which is widely considered and utilised, especially as a diagnostic tool in experimental fluid dynamics and the remote sensing of environmental flows. Recently, the development of deep learning based methods has inspired new approaches to tackle the PIV problem. These supervised learning based methods are driven by large volumes of data with ground truth training information. However, it is difficult to collect reliable ground truth data in large-scale, real-world scenarios. Although synthetic datasets can be used as alternatives, the gap between the training set-ups and real-world scenarios limits applicability. We present here what we believe to be the first work which takes an unsupervised learning based approach to tackle PIV problems. The proposed approach is inspired by classic optical flow methods. Instead of using ground truth data, we make use of photometric loss between two consecutive image frames, consistency loss in bidirectional flow estimates and spatial smoothness loss to construct the total unsupervised loss function. The approach shows significant potential and advantages for fluid flow estimation. Results presented here demonstrate that our method outputs competitive results compared with classical PIV methods as well as supervised learning based methods for a broad PIV dataset, and even outperforms these existing approaches in some difficult flow cases. Codes and trained models are available at https://github.com/erizmr/UnLiteFlowNet-PIV.

cs.CV↗

arXiv2018

An investigation into the accuracy of the depth-averaging used in tidal turbine array optimisation

Depth-averaged shallow water models are widely used for the large-scale simulation of tidal turbine arrays. The relatively low computational complexity of this approach allows for layout optimisations aimed at improving the total array power output as well as an assessment of large-scale environmental impacts. In order to assess the suitability of using depth-averaged models to optimise array configurations, a comprehensive comparison between the wake profiles and power outputs predicted by a 2D shallow water model and a 3D actuator disc momentum (ADM) model is presented. Initially, a viscosity sensitivity analysis is presented to outline the limitations associated with using a constant eddy viscosity in the depth-averaged model and to outline the importance of correctly calibrating this value in line with the freestream velocity magnitude. Thereafter, the depth-averaged OpenTidalFarm (OTF) tool is used to optimise the positions of an array of 32 turbines in an ideal channel and the 3D Fluidity ADM-RANS model is used to assess the accuracy of the OTF predictions for the first time. It is shown that with the help of corrected power calculations a good agreement between the two models can be achieved, thus demonstrating the value of the eddy viscosity calibration implemented in the depth-averaged model.

physics.flu-dyn↗

arXiv2018

Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.

physics.ao-ph↗

arXiv2018

Mesh-adaptive simulations of horizontal-axis turbine arrays using the actuator line method

Numerical models of the flow and wakes due to turbines operating within a real-scale offshore wind farm can lead to a prohibitively large computational cost, particularly when considering blade-resolved simulations. With the introduction of turbine parametrizations such as the actuator disk (AD) or the actuator line (AL) models, this problem has been partially addressed, yet the computational cost associated with these simulations remains high. In this work, we present an implementation and validation of an AL model within the mesh-adaptive three-dimensional fluid dynamics solver, Fluidity, under a unsteady Reynolds-averaged Navier-Stokes based turbulence modelling approach. A key feature of this implementation is the use of mesh optimization techniques, which allow for the automatic refinement or coarsening of the mesh locally according to the resolution needed by the fluid flow solver. The model is first validated against experimental data from wind tunnel tests. Finally, we demonstrate the benefits of mesh-adaptivity by considering flow past the Lillgrund offshore wind farm.

physics.flu-dyn↗

arXiv2018

Turbulence-resolving simulations of wind turbine wakes

Turbulence-resolving simulations of wind turbine wakes are presented using a high--order flow solver combined with both a standard and a novel dynamic implicit spectral vanishing viscosity (iSVV and dynamic iSVV) model to account for subgrid-scale (SGS) stresses. The numerical solutions are compared against wind tunnel measurements, which include mean velocity and turbulent intensity profiles, as well as integral rotor quantities such as power and thrust coefficients. For the standard (also termed static) case the magnitude of the spectral vanishing viscosity is selected via a heuristic analysis of the wake statistics, while in the case of the dynamic model the magnitude is adjusted both in space and time at each time step. The study focuses on examining the ability of the two approaches, standard (static) and dynamic, to accurately capture the wake features, both qualitatively and quantitatively. The results suggest that the static method can become over-dissipative when the magnitude of the spectral viscosity is increased, while the dynamic approach which adjusts the magnitude of dissipation locally is shown to be more appropriate for a non-homogeneous flow such that of a wind turbine wake.

physics.flu-dyn↗

arXiv2016

Anisotropic mesh adaptation in Firedrake with PETSc DMPlex

Despite decades of research in this area, mesh adaptation capabilities are still rarely found in numerical simulation software. We postulate that the primary reason for this is lack of usability. Integrating mesh adaptation into existing software is difficult as non-trivial operators, such as error metrics and interpolation operators, are required, and integrating available adaptive remeshers is not straightforward. Our approach presented here is to first integrate Pragmatic, an anisotropic mesh adaptation library, into DMPlex, a PETSc object that manages unstructured meshes and their interactions with PETSc's solvers and I/O routines. As PETSc is already widely used, this will make anisotropic mesh adaptation available to a much larger community. As a demonstration of this we describe the integration of anisotropic mesh adaptation into Firedrake, an automated Finite Element based system for the portable solution of partial differential equations which already uses PETSc solvers and I/O via DMPlex. We present a proof of concept of this integration with a three-dimensional advection test case.

math.NA↗

arXiv2016

Design optimisation and resource assessment for tidal-stream renewable energy farms using a new continuous turbine approach

This paper presents a new approach for optimising the design of tidal stream turbine farms. In this approach, the turbine farm is represented by a turbine density function that specifies the number of turbines per unit area and an associated continuous locally-enhanced bottom friction field. The farm design question is formulated as a mathematical optimisation problem constrained by the shallow water equations and solved with efficient, gradient-based optimisation methods. The resulting method is accurate, computationally efficient, allows complex installation constraints, and supports different goal quantities such as to maximise power or profit. The outputs of the optimisation are the optimal number of turbines, their location within the farm, the overall farm profit, the farm's power extraction, and the installation cost. We demonstrate the capabilities of the method on a validated numerical model of the Pentland Firth, Scotland. We optimise the design of four tidal farms simultaneously, as well as individually, and study how farms in close proximity may impact upon one another.

cs.CE↗

arXiv2016

On the validity of tidal turbine array configurations obtained from steady-state adjoint optimisation

Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation of high-resolution and ideally 3D transient models is generally a very computationally expensive problem. As a result, existing work on the adjoint optimisation of tidal turbine placement has been mostly limited to steady-state simulations in which very high, non-physical values of the background viscosity are required to ensure that a steady-state solution exists. However, such compromises may affect the reliability of the modelled turbines, their wakes and interactions, and thus bring into question the validity of the computed optimal turbine positions. This work considers a suite of idealised simulations of flow past tidal turbine arrays in a 2D channel. It compares four regular array configurations, detailed by Divett et al. (2013), with the configuration found through adjoint optimisation in a steady-state, high-viscosity setup. The optimised configuration produces considerably more power. The same configurations are then used to produce a suite of transient simulations that do not use constant high-viscosity, and instead use large eddy simulation (LES) to parameterise the resulting turbulent structures. It is shown that the LES simulations produce less power than that predicted by the constant high-viscosity runs. Nevertheless, they still follow the same trends in the power curve throughout time, with optimised layouts continuing to perform significantly better than simplified configurations.

physics.flu-dyn↗