Selected Research
Discover our projects
We adopt an interdisciplinary approach for the analysis and forecast of complex systems. Understanding and modeling complex systems require integrating different disciplines with mathematics being the unifying language.
We are also committed to reproducible, open-source and high-performance software as it is a cornerstone of modern science. All our codes related to scientific publications are freely available at github.com/MathEXLab.
We are developing fast forecasting tools for multivariate time series modeling and forecasting. This involve blending data compression techniques, such as autoencoders and spectral proper orthogonal decomposition, with neural networks. The former are used to identify a reduced manifold to decrease the dimension of the problem. The latter are used to forecast the system in the reduced manifold. Given the 'black-box' nature of neural-network approaches, we are developing interpretability methods, to allow for more 'white-box' forecasting workflows. Current application areas include extreme weather prediction, climate resilience and sustaninability, and healthcare.
The project focuses on analysing and forecasting extreme weather events under climate change, by blending dynamical system theory and deep learning technologies. The project also aims to assess damages due to extreme weather events and provide tools to inform policymakers on possible mitigation strategies. This project is funded by MOE (Tier 2 grant).
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- A. Gualandi, D. Faranda, C. Marone, M. Cocco, G. Mengaldo, Deterministic and stochastic chaos characterize laboratory earthquakes, Earth and Planetary Science Letters (2023).
- C Duong, VC Raghuram, A Lee, R Mao, G Mengaldo, E Cambria, Neurosymbolic AI for mining public opinions about wildfires, Cognitive Computation (2023).
The opacity of machine learning decisions in time series analysis poses critical challenges, from mistrust and underutilization of potentially superior technologies to missed opportunities for discovering novel principles in fields like physics and medicine. This project seeks to address these challenges by developing novel post-hoc interpretability tools for neural networks applied to time series and sequential data. By making the decision-making process of neural networks transparent and understandable, this work aims to bridge the gap between artificial intelligence and human expertise, enhancing trust, fostering novel discoveries, and informing effective regulatory policies. This project is funded by MOE (Tier 1) grant.
- H. Turbé, M. Bjelogrlic, C. Lovis, G. Mengaldo, Evaluation of post-hoc interpretability methods in time-series classification, Nature Machine Intelligence (2023).
The key objective of this project is to develop a machine learning framework for the automatic detection of eye disease starting from eye images.
We are developing methods to identify the predictability of coplex systems. The methods are rooted in dynamical system and extreme value theory. These are to be used in conjunction with forecasting methods, both traditional and modern, to improve their perfomance. Current application areas include extreme weather and earthquake modeling and prediction.
REBOT is a project designed to prove the superior efficiency of octopus-inspired manipulation strategies in aquatic environments. The approach begins with mathematical demonstrations through models and simulations, followed by experimental validation using a soft robot arm modeled after an octopus. Successful results could transform underwater robotics by introducing new, efficient grasping techniques that may boost the deployment of robots in various underwater applications, including offshore industries, biology, and oceanography. This project is funded by MOE (Tier 2 grant).
- G Mengaldo, F Renda, S Brunton, and et al, A concise guide to modelling the physics of embodied intelligence in soft robotics, Nature Reviews Physics, pp. 595-610, Nature Publishing Group UK, 09-2022
- YJ Tan, G Mengaldo, C Laschi, Artificial Muscles for Underwater Soft Robots: Materials and Their Interactions, Annual Review of Condensed Matter Physics 15
The DESTRO project, part of a Italy-Singapore Science and Technology Cooperation agreement, is focuses on the study of muscular hydrostats, such as octopus arms and elephant trunks, which function differently in aquatic and terrestrial environments. The project's goal is to understand the underlying principles of these biological systems to inform robotics development. It involves biological research, advanced modeling, and the use of soft robotics technologies and materials from both countries (Italy and Singapore) to simulate and test robotic muscular hydrostats. A soft arm prototype will be examined using a teleoperation platform in Singapore, and the research will leverage Italian and Singaporean expertise in neuroscience to explore human brain control of soft robotic arms with unique shapes and flexibility.
The project aims to explore interdisciplinary research segment at the intersection of science and engineering. Current areas being explored involve the development of spectral element methods for partial differential equations, natural language processing for weather and climate applications, and multiphysics simulations for soft robotics. This project is funded by NUS and MOE (Tier 1 grant).
- N Tonicello, RC Moura, G Lodato, G Mengaldo, Fully-discrete spatial eigenanalysis of discontinuous spectral element methods: insights into well-resolved and under-resolved vortical flows, Computers & Fluids (2023)
- A. Gualandi, D. Faranda, C. Marone, M. Cocco, G. Mengaldo , Deterministic and stochastic chaos characterize laboratory earthquakes, Earth and Planetary Science Letters (2023).
- A. Lario, R. Maulik, O. T. Schmidt, G. Rozza, G. Mengaldo , Neural-network learning of SPOD latent dynamics, Journal of Computational Physics (2022).
- G. Mengaldo , F. Renda, S. L. Brunton, M. Bächer, M. Calisti, C. Duriez, G. S. Chirikjian, C. Laschi, A concise guide to modelling the physics of embodied intelligence in soft robotics, Nature Reviews Physics (2022).
- M. W. Hess, A. Lario, G. Mengaldo , G. Rozza, Reduced order modeling for spectral element methods: current developments in Nektar++ and further perspectives, Selected Papers from the 2021 ICOSAHOM Conference, Vienna, Austria (2022).
- R. Maulik, V. Rao, J. Wang, G. Mengaldo , E. Constantinescu, B. Lusch, P. Balaprakash, I. Foster, R. Kotamarthi, Efficient high-dimensional variational data assimilation with machine-learned reduced-order models, Geoscientific Model Development (2022).
- R. C. Moura, A. F. C. Silva, G. Mengaldo , S. J. Sherwin, Spectral/hp element methods' linear mechanism of (apparent) energy transfer in Fourier space: Insights into dispersion analysis for implicit LES, Journal of Computational Physics (2022).
- R. Maulik, G. Mengaldo , PyParSVD: A streaming, distributed and randomized singular-value-decomposition library, 2021 7th International Workshop on Data Analysis and Reduction for Big Scientific Data (2021).
The project aims to reveal latent flow physics form PIV (optical flow) measurements using physics informed neural networks (PINNs). This project received seed grant from NUS Temasek Laboratory.
We are using numerical analysis to develop high-fidelity simulation tools for multiscale, multi-physics problems governed by partial differential equations. The main focus is on spectral element methods, with applications in engineering flow simulation, and soft-robotics multi-physics modeling.
We are developing a project in collaboration with ECMWF , Argonne National Laboratory (USA), CNRS (France), and University of Cambridge (United Kingdom), the latter starting from 2023. The primary objective of the project is to provide a fast computational framework for extended-range extreme weather forecasts, as well as quantify damage and develop mitigation strategies for extreme weather events.
We are developing a project in collaboration with University of Geneva (Switzerland), Scuola Superiore Sant'Anna (Italy), and University of Cambridge (United Kingdom), the latter starting from 2023. The primary objective of the project is to develop novel post-hoc interpretability tools for neural networks applied to time series and sequential data.
‣ Imperial College London (UK)
‣ KAUST (Saudi Arabia)
‣ University of Toronto (Canada)
‣ University of Waterloo (Canada)
