Gianmarco Mengaldo

• PhD - Imperial College London
• Professor (Assistant) at National University of Singapore

This paper investigates the connections between many popular variants of the well-established discontinuous Galerkin method and the recently developed high-order flux reconstruction approach on irregular tensor-product grids. We explore these connections by analysing three nodal versions of tensor-product discontinuous Galerkin spectral element app...

Counterfactual reasoning typically involves considering alternatives to actual events. While often applied to understand past events, a distinct form-forward counterfactual reasoning-focuses on anticipating plausible future developments. This type of reasoning is invaluable in dynamic financial markets, where anticipating market developments can po...

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales. Classical approaches based on the Lyapunov spectrum rely on the knowledge of the dynamic forward operator, or of a...

Accurate assessments of extreme weather events are vital for research and policy, yet localized and granular data remain scarce in many parts of the world. This data gap limits our ability to analyze potential outcomes and implications of extreme weather events, hindering effective decision-making. Large Language Models (LLMs) can process vast amou...

In machine learning forecasting, standard error metrics such as mean absolute error (MAE) and mean squared error (MSE) quantify discrepancies between predictions and target values. However, these metrics do not directly evaluate the physical and/or dynamical consistency of forecasts, an increasingly critical concern in scientific and engineering ap...

The success of artificial intelligence (AI), and deep learning models in particular, has led to their widespread adoption across various industries due to their ability to process huge amounts of data and learn complex patterns. However, due to their lack of explainability, there are significant concerns regarding their use in critical sectors, suc...

This paper introduces a methodology leveraging Large Language Models (LLMs) for sector-level portfolio allocation through systematic analysis of macroeconomic conditions and market sentiment. Our framework emphasizes top-down sector allocation by processing multiple data streams simultaneously, including policy documents, economic indicators, and s...

Extreme weather events are increasing in frequency and intensity due to climate change. This, in turn, is exacting a significant toll in communities worldwide. While prediction skills are increasing with advances in numerical weather prediction and artificial intelligence tools, extreme weather still present challenges. More specifically, identifyi...

Visual foundation models (VFMs) have become increasingly popular due to their state-of-the-art performance. However, interpretability remains crucial for critical applications. In this sense, self-explainable models (SEM) aim to provide interpretable classifiers that decompose predictions into a weighted sum of interpretable concepts. Despite their...

Sustainability reports are key for evaluating companies' environmental, social and governance, ESG performance, but their content is increasingly obscured by greenwashing - sustainability claims that are misleading, exaggerated, and fabricated. Yet, existing NLP approaches for ESG analysis lack robustness against greenwashing risks, often extractin...

Accurate and efficient climate simulations are crucial for understanding Earth's evolving climate. However, current general circulation models (GCMs) face challenges in capturing unresolved physical processes, such as cloud and convection. A common solution is to adopt cloud resolving models, that provide more accurate results than the standard sub...

Evaluating corporate sustainability performance is essential to drive sustainable business practices, amid the need for a more sustainable economy. However, this is hindered by the complexity and volume of corporate sustainability data (i.e. sustainability disclosures), not least by the effectiveness of the NLP tools used to analyse them. To this e...

Geophysical systems are inherently complex and span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially pronounced for extreme events, which are primarily governed by their instantaneous properties rather than their average characteristics. Advances in dynamical systems the...

The Pacific Walker circulation and the closely connected El Niño/Southern Oscillation influence the climate and weather of the tropical Indo-Pacific region. They specifically exert a strong control on the regional occurrence of weather extremes, such as heatwaves, heavy precipitation and prolonged dry spells, which are becoming increasingly frequen...

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales. Classical approaches based on the Lyapunov spectrum rely on the knowledge of the dynamic forward operator, or of a...

Extreme weather can lead to weather-induced disasters. These have a profound impact on communities worldwide, causing loss of life, damage to properties and infrastructure, and disruption of daily activities. In alignment with the United Nations Sustainable Development Goals, addressing the increasing frequency and severity of these events, exacerb...

Post-hoc interpretability methods play a critical role in explainable artificial intelligence (XAI), as they pinpoint portions of data that a trained deep learning model deemed important to make a decision. However, different post-hoc interpretability methods often provide different results, casting doubts on their accuracy. For this reason, severa...

Climate change is a global challenge with multiple far-reaching consequences, including the intensification and increased frequency of many extreme-weather events. In response to this pressing issue, we present ClimaMeter, a platform designed to assess and contextualize extreme-weather events relative to climate change. The platform offers near-rea...

Plain Language Summary Earthquakes are natural phenomena resulting from the Earth's crust cyclically loading and unloading. The unpredictability of seismic events, combined with the large energy they release during the co‐seismic phase, poses not only scientific challenges but also significant threats to numerous populated regions at risk. Numerica...

Sustainability commonly refers to entities, such as individuals, companies, and institutions, having a non-detrimental (or even positive) impact on the environment, society, and the economy. With sustainability becoming a synonym of acceptable and legitimate behaviour, it is being increasingly demanded and regulated. Several frameworks and standard...

The scientific method is the cornerstone of human progress across all branches of the natural and applied sciences, from understanding the human body to explaining how the universe works. The scientific method is based on identifying systematic rules or principles that describe the phenomenon of interest in a reproducible way that can be validated...

Prototypical networks aim to build intrinsically explainable models based on the linear summation of concepts. However, important challenges remain in the transparency, compactness, and meaningfulness of the explanations provided by these models. This work demonstrates how frozen pre-trained ViT backbones can be effectively turned into prototypical...

Underwater soft robots are typically constructed from soft and flexible materials, which enable them to adapt to aquatic environments where the terrain can be complex. They are often inspired by soft-bodied aquatic animals and can be used for a range of tasks, such as underwater exploration, environmental monitoring, and rescue operations. However,...

The detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems. Here, changepoints indicate instances in time when the underlying dynamical system has a fundamentally differen...

Wildfires are among the most threatening hazards to life, property, well-being, and the environment. Studying public opinions about wildfires can help monitor the perception of the impacted communities. Nevertheless, wildfire research is relatively limited compared to other climate-related hazards. This article presents our data mining work on publ...

The detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems. Here, changepoints indicate instances in time when the underlying dynamical system has a fundamentally differen...

Post-hoc interpretability methods are critical tools to explain neural-network results. Several post-hoc methods have emerged in recent years but they produce different results when applied to a given task, raising the question of which method is the most suitable to provide accurate post-hoc interpretability. To understand the performance of each...

This paper presents a novel approach for explainability in financial analysis by deriving financially-explainable statistical relationships through aspect-based sentiment analysis, Pearson correlation, Granger causality & uncertainty coefficient. The proposed methodology involves constructing an aspect list from financial literature and applying as...

We analyze frictional motion for a laboratory fault as it passes through the stability transition from stable sliding to unstable motion. We study frictional stick-slip events, which are the lab equivalent of earthquakes, via dynamical system tools in order to retrieve information on the underlying dynamics and to assess whether there are dynamical...

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations discretised with the Discontinuous Galerkin method. On the other side, from a numerical modelling point of view,...

In this paper, we present recent efforts to develop reduced order modeling (ROM) capabilities for spectral element methods (SEM). Namely, we detail the implementation of ROM for both continuous Galerkin and discontinuous Galerkin methods in the spectral/hp element library Nektar++. The ROM approaches adopted are intrusive methods based on the prope...

In recent years, different dispersion-diffusion (eigen)analyses have been developed and used to assess various spectral element methods (SEMs) with regards to accuracy and stability, both of which are very important aspects for under-resolved computations of transitional and turbulent flows. Not surprisingly, eigenanalysis has been used recurrently...

Embodied intelligence (intelligence that requires and leverages a physical body) is a well-known paradigm in soft robotics, but its mathematical description and consequent computational modelling remain elusive, with a need for models that can be used for design and control purposes. We argue that filling this gap will enable full uptake of embodie...

We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapsho...

Data assimilation (DA) in geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variation...

Laboratory earthquakes exhibit characteristics of a low dimensional random attractor with a dimension similar to that of natural slow earthquakes. A model of stochastic differential equations based on rate and state-dependent friction explains the laboratory observations. We study the transition from stable sliding to stickslip events and find that...

The current work aims to present a quasi-static model of a soft robot arm configuration, inspired by octopus arm. The arm is assumed under the water and hence the main goal is to study the impacts of hydrostatic force, tangential and normal forces of the water imposed to the arm as the environmental interactions, where the arm is driven by tensions...

Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a vari...

This study presents a comprehensive spatial eigenanalysis of fully-discrete discontinuous spectral element methods, now generalizing previous spatial eigenanalysis that did not include time integration errors. The influence of discrete time integration is discussed in detail for different explicit Runge-Kutta (1st to 4th order accurate) schemes com...

We aim to reconstruct the latent space dynamics of high dimensional systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent...

In recent years, different dispersion-diffusion (eigen)analyses have been developed and used to assess various spectral element methods (SEMs) with regards to accuracy and stability, both of which are very important aspects for under-resolved computations of transitional and turbulent flows. Not surprisingly, eigenanalysis has been used recurrently...

We present a successful deployment of high-fidelity Large-Eddy Simulation (LES) technologies based on spectral/hp element methods to industrial flow problems, which are characterized by high Reynolds numbers and complex geometries. In particular, we describe the numerical methods, software development and steps that were required to perform the imp...

Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/ element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, there...

We present the first eigenanalysis of hybridisable discontinuous Galerkin (HDG) schemes for the advection-diffusion equation in one dimension. This study is also one of the first to include viscous diffusion effects in the eigenanalysis of discontinuous spectral element methods. The interplay between upwind dissipation and viscous diffusion is disc...

We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast multipole method in conjunction with fast Fourier transforms to yield linear complexity and decrease time-to-s...

We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast multipole method in conjunction with fast Fourier transforms to yield linear complexity and decrease time-to-s...

In the simulation of complex multi-scale flows arising in weather and climate modelling, one of the biggest challenges is to satisfy strict service requirements in terms of time to solution and to satisfy budgetary constraints in terms of energy to solution, without compromising the accuracy and stability of the application. These simulations requi...

This document is one of the deliverable reports created for the ESCAPE project. ESCAPE stands for Energy-efficient Scalable Algorithms for Weather Prediction at Exascale. The project develops world-class, extreme-scale computing capabilities for European operational numerical weather prediction and future climate models. This is done by identifying...

The continuous partial differential equations (PDEs) governing a given physical phenomenon, such as the Navier-Stokes equations describing the fluid motion, must be numerically discretised in space and time in order to obtain a solution otherwise not readily available in closed (i.e., analytic) form. While the overall numerical discretization plays...

We apply spectral empirical orthogonal function (SEOF) analysis to educe climate patterns as dominant spatiotemporal modes of variability from reanalysis data. SEOF is a frequency-domain variant of standard empirical orthogonal function (EOF) analysis, and computes modes that represent the statistically most relevant and persistent patterns from an...

Nektar++ is an open-source framework that provides a flexible, performant and scalable platform for the development of solvers for partial differential equations using the high-order spectral/hp element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby a...

In the simulation of complex multi-scale flow problems, such as those arising in weather and climate modelling, one of the biggest challenges is to satisfy operational requirements in terms of time-to-solution and energy-to-solution yet without compromising the accuracy and stability of the calculation. These competing factors require the developme...

High-order spectral element methods (SEM) for large-eddy simulation (LES) are still very limited in industry. One of the main reasons behind this is the lack of robustness of SEM for under-resolved simulations, which can lead to the failure of the computation or to inaccurate results, aspects that are critical in an industrial setting. To help addr...

We introduce a \textit{non-modal} analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems. While strictly speaking only valid for linear problems, the analysis is devised so that it can give critical insights on two questions: (i) Why do spectral element methods suffer from...

This study presents the first eigensolution analysis of hybridisable discontinuous Galerkin (HDG) schemes for the advection-diffusion problem in one dimension, being also one of the first studies to consider effects of viscous diffusion in the eigenanalysis of discontinuous spectral element methods. The study is devoted to the temporal analysis app...

This study focusses on the dispersion and diffusion characteristics of high-order energy-stable flux reconstruction (ESFR) schemes via the spatial eigensolution analysis framework proposed in [1]. The analysis is performed for five ESFR schemes, where the parameter ‘c’ dictating the properties of the specific scheme recovered is chosen such that it...

This work focuses on the accuracy and stability of high-order nodal discontinuous Galerkin (DG) methods for under-resolved turbulence computations. In particular we consider the inviscid Taylor-Green vortex (TGV) flow to analyse the implicit large eddy simulation (iLES) capabilities of DG methods at very high Reynolds numbers. The governing equatio...

This work focuses on the accuracy and stability of high-order nodal discontinuous Galerkin (DG) methods for under-resolved turbulence computations. In particular we consider the inviscid Taylor-Green vortex (TGV) flow to analyse the implicit large eddy simulation (iLES) capabilities of DG methods at very high Reynolds numbers. The governing equatio...

The study focusses on the dispersion and diffusion characteristics of discontinuous spectral element methods - specifically discontinuous Galerkin (DG) - via the spatial eigensolution analysis framework built around a one-dimensional linear problem, namely the linear advection equation. Dispersion and diffusion characteristics are of critical impor...

There is an increasing requirement from both academia and industry for high-fidelity flow simulations that are able to accurately capture complicated and transient flow dynamics in complex geometries. Coupled with the growing availability of high-performance, highly parallel computing resources, there is therefore a demand for scalable numerical me...

The algorithms underlying numerical weather prediction (NWP) and climate models that have been developed in the past few decades face an increasing challenge caused by the paradigm shift imposed by hardware vendors towards more energy-efficient devices. In order to provide a sustainable path to exascale High Performance Computing (HPC), application...

In this paper, we document the capabilities of a novel numerical approach — the immersed boundary lattice Green's function (IBLGF) 1 method — to simulate external incom-pressible flows over complex geometries. This new approach is built upon the immersed boundary method and lattice Green's functions to solve the incompressible Navier-Stokes equatio...

We present estimates of spectral resolution power for under-resolved turbulent Euler flows obtained with high-order discontinuous Galerkin (DG) methods. The ‘1% rule’ based on linear dispersion–diffusion analysis introduced by Moura et al. [J. Comput. Phys. 298 (2015) 695–710] is here adapted for 3D energy spectra and validated through the inviscid...

We suggest a new interpretation of implicit large eddy simulation (iLES) approaches based on discontinuous Galerkin (DG) methods by analogy with the LES-PLB framework [1], where PLB stands for 'projection onto local basis functions'. Within this framework, the DG discretization of the unfiltered compressible Navier-Stokes equations can be recognize...

High-order methods are becoming increasingly attractive in both academia and industry, especially in the context of computational fluid dynamics. However, before they can be more widely adopted, issues such as lack of robustness in terms of numerical stability need to be addressed, particularly when treating industrial-type problems where challengi...

This paper is concerned with the boundary-layer separation in subsonic and transonic flows caused by a two-dimensional isolated wall roughness. The process of the separation is analysed by means of two approaches: the direct numerical simulation (DNS) of the flow using the Navier–Stokes equations, and the numerical solution of the triple-deck equat...

Nektar++ is an open-source software framework designed to support the development of high-performance scalable solvers for partial differential equations using the spectral/ element method. High-order methods are gaining prominence in several engineering and biomedical applications due to their improved accuracy over low-order techniques at reduced...

With high-order methods becoming more widely adopted throughout the field of computational fluid dynamics, the development of new computationally efficient algorithms has increased tremendously in recent years. One of the most recent methods to be developed is the flux reconstruction approach, which allows various well-known high-order schemes to b...

The nature of boundary conditions, and how they are implemented, can have a sig- nificant impact on the stability and accuracy of a Computational Fluid Dynamics (CFD) solver. The objective of this paper is to assess how different boundary conditions impact the performance of compact discontinuous high-order spectral element methods (such as the dis...

A comparative study of different nonlinear hyperelastic isotropic arterial wall models in patient-specific vascular flow simulations in the aortic arch