Associate Professor (Reader) in Machine Learning
School of Mathematics, The University of Edinburgh
The Maxwell Institute for Mathematical Sciences
Alan Turing Institute | Bayes Centre | Gen AI Lab
School of Mathematics, Gran Sasso Science Institute
email: f dot tudisco at ed.ac.uk
I am looking for a PhD student to work on an exciting project at the intersection of machine learning, computational physics, and fusion energy research.
Predicting turbulence and transport in magnetically confined plasmas is one of the major challenges in developing fusion energy. High-fidelity simulations based on nonlinear gyrokinetic theory can accurately model turbulent behaviour in tokamaks but are extremely computationally expensive, often requiring hundreds of thousands of CPU-hours for a single run.
To make large-scale predictive modelling feasible, researchers use simplified, lower-fidelity models such as linear gyrokinetics or gyro-fluid approximations, but these come at the cost of reduced accuracy.
This PhD project will explore how machine learning can bridge these fidelity levels, combining the accuracy of high-fidelity models with the efficiency of reduced ones. The work will involve:
Applications should be submitted through the University of Edinburgh website.
Important dates:
The application portal will ask you to fill in a research proposal (optional). This can be used as an occasion to write about your scientific interests, why the project fits with those, and any ideas you have for things you would like to do within the PhD project. Please keep the content short and crisp.
For informal inquiries, feel free to reach out to me directly
[1] P. Rodriguez-Fernandez et al., Nonlinear gyrokinetic predictions of SPARC burning plasma profiles enabled by surrogate modeling 2022 Nucl. Fusion 62 076036
[2] J. Candy et al., Multiscale-optimized plasma turbulence simulation on petascale architectures. Computers & Fluids 188 (2019): 125-135.
[3] G. Staebler et al., Quasilinear theory and modelling of gyrokinetic turbulent transport in tokamaks. Nuclear Fusion 64.10 (2024): 103001.
[4] C. Bourdelle et al., A new gyrokinetic quasilinear transport model applied to particle transport in tokamak plasmas. Physics of Plasmas 14.11 (2007).
[5] W. A. Hornsby et al., Gaussian process regression models for the properties of micro-tearing modes in spherical tokamaks. Physics of Plasmas 31.1 (2024).
[6] V. Gopakumar et al., Plasma surrogate modelling using Fourier neural operators. Nuclear Fusion 64.5 (2024): 056025.
[7] L. Zanisi et al., Efficient training sets for surrogate models of tokamak turbulence with active deep ensembles. Nuclear Fusion 64.3 (2024): 036022.
[8] H. Wang et al, Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey, arxiv:2408.12171
[9] T. Li et al, Synthetic Lagrangian turbulence by generative diffusion models, Nature Machine Intelligence 2024
[10] I. Price et al, Probabilistic weather forecasting with machine learning, Nature 2025
[11] H.A. Majid et al, Test-Time Control Over Accuracy-Cost Trade-Offs in Neural Physics Simulators via Recurrent Depth, NeurIPS 2025
[12] H.A. Majid et al, Solaris: A Foundation Model for the Sun, NeurIPS 2024
Abstract: The COVID-19 pandemic shifted academic collaboration from in-person to remote interactions. This study explores, for the first time, the effects on scientific collaborations and impact of such a shift, comparing research output before, during, and after the pandemic. Using large-scale bibliometric data, we track the evolution of collaboration networks and the resulting impact of research over time. Our findings are twofold: first, the geographic distribution of collaborations significantly shifted, with a notable increase in cross-border partnerships after 2020, indicating a reduction in the constraints of geographic proximity. ... Read more
Huge congratulations to PhD students Kevin Zhang and Denis Zorba for winning first place at the ACM ICAIF 2025 Cryptocurrency Forecasting Competition, a flagship international challenge in AI for Finance, under team name “8k3”! They defeated approximately 130 competitors and 740 submitted models.
Their winning approach demonstrates the power of neural oscillators as architectures for time series forecasting. They successfully turned our recent research paper on GNN neural oscillators into a top-performing cryptocurrency forecasting model.
They received praise for their “advanced approaches and innovative solutions for cryptocurrency forecasting” and have presented their work orally at the ICAIF 2025 Award Ceremony on November 16, 2025, at the Sheraton Towers Singapore.
👉 Check out the paper: Stuart-Landau Oscillatory Graph Neural Network
Abstract: Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are ill-conditioned. Existing numerical methods for ill-conditioned systems often require careful parameter tuning, preconditioning, or domain-specific expertise to ensure accuracy and stability. In this work, we propose Algebraformer, a Transformer-based architecture that learns to solve linear systems end-to-end, even in the presence of severe ill-conditioning. ... Read more
Thrilled to share that our paper Graph-Convolutional-Beta-VAE for Synthetic Abdominal Aorta Aneurysm Generation has been accepted for publication in Medical & Biological Engineering & Computing. Fantastic work by Francesco Fabbri and several collaborators from GSSI and University of Bordeaux Francesco Viola, Angelo Iollo, and Martino Scarpolini.
Abstract: Generalized friendship paradoxes occur when, on average, our friends have more of some attribute than us. These paradoxes are relevant to many aspects of human interaction, notably in social science and epidemiology. Here, we derive new theoretical results concerning the inevitability of a paradox arising, using a linear algebra perspective. Following the seminal 1991 work of Scott L. Feld, we consider two distinct ways to measure and compare averages, which may be regarded as global and local. ... Read more
Abstract: Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. In this work, we introduce the Complex-Valued Stuart-Landau Graph Neural Network (SLGNN), a novel architecture grounded in Stuart-Landau oscillator dynamics. Stuart-Landau oscillators are canonical models of limit-cycle behavior near Hopf bifurcations, which are fundamental to synchronization theory and are widely used in e.g. neuroscience for mesoscopic brain modeling. ... Read more
Congratulations to Arturo De Marinis for successfully defending his PhD thesis on “Stability and Approximation Properties of Neural Ordinary Differential Equations” at the Gran Sasso Science Institute (GSSI)! It has been a pleasure to work with Arturo and I look forward to seeing the next steps in his career.
Abstract: We study the collective dynamics of coupled Stuart–Landau oscillators, which model limit-cycle behavior near a Hopf bifurcation and serve as the amplitude-phase analogue of the Kuramoto model. Unlike the well-studied phase-reduced systems, the full Stuart–Landau model retains amplitude dynamics, enabling the emergence of rich phenomena such as amplitude death, quenching, and multistable synchronization. We provide a complete analytical classification of asymptotic behaviors for identical natural frequencies, but heterogeneous inherent amplitudes in the finite- setting. ... Read more
Thrilled to share that our paper The graph ∞-Laplacian eigenvalue problem has been accepted for publication in SIAM Journal on Mathematical Analysis. It has been an exciting and inspiring collaboration with Mario Putti, Martin Burger, and Piero Deidda.
Abstract: Influence Maximization (IM) is a pivotal concept in social network analysis, involving the identification of influential nodes within a network to maximize the number of influenced nodes, and has a wide variety of applications that range from viral marketing and information dissemination to public health campaigns. IM can be modeled as a combinatorial optimization problem with a black-box objective function, where the goal is to select seed nodes that maximize the expected influence spread. ... Read more
Thrilled to share that our paper Core-periphery detection in multilayer networks has been accepted for publication in Physical Review Letters, the American Physical Society’s flagship journal. Huge thanks to my collaborator Kai Bergermann!
This work introduces a novel spectral method for simultaneously detecting core-periphery structures in both nodes and layers of multilayer networks. The method reveals fascinating structural insights across diverse real-world networks, from the citation network of complex network scientists to European airline transport and world trade networks. Physical Review Letters is one of the most prestigious venues in physics, making this acceptance particularly exciting for advancing the field of network science.
Abstract: We introduce a nonlinear extension of the joint spectral radius (JSR) for switched discrete-time dynamical systems. The classical JSR characterizes the exponential growth rate of linear switched systems, but its extension to nonlinear systems has remained an open problem. Our approach builds on the framework of nonlinear Perron-Frobenius theory to define a meaningful notion of joint spectral radius for nonlinear switched systems. We establish fundamental properties of this nonlinear JSR, including its relationship to the stability of switched nonlinear systems, and provide computational methods for its approximation. ... Read more
Abstract: Synthetic data generation plays a crucial role in medical research by mitigating privacy concerns and enabling large-scale patient data analysis. This study presents a beta-Variational Autoencoder Graph Convolutional Neural Network framework for generating synthetic Abdominal Aorta Aneurysms (AAA). Using a small real-world dataset, the approach extracts key anatomical features and captures complex statistical relationships within a compact disentangled latent space. To address data limitations, low-impact data augmentation based on Procrustes analysis was employed, preserving anatomical integrity. ... Read more
Congratulations to Dayana Savostianova for successfully defending her PhD thesis at the Gran Sasso Science Institute (GSSI)! It has been a pleasure to work with Dayana and I look forward to seeing the next steps in her career.
Very happy to be organizing the workshop Hidden Structures in Dynamical Systems, Optimisation and Machine Learning this week at the Gran Sasso Science Institute in L’Aquila, as part of the thematic programme on Hidden Structures in Dynamical Systems.
The event brings together researchers working at the intersection of numerical analysis, dynamical systems, optimization, and machine learning, with a focus on uncovering and leveraging latent geometric or algebraic structures in complex models.
All the details can be found at the official workshop page:
Thrilled to share that our COST Action project mSPACE – multiscale Stochastics, Patterns, and Analysis of Combinatorial Environments (CA24122) has been selected for funding by COST!
mSPACE aims to develop a rigorous mathematical foundation for the study of multiscale systems, which emerge in both natural and synthetic contexts due to complex interactions across discrete, continuous, and hybrid domains.
We will explore:
This project brings together a vibrant, interdisciplinary community from across Europe and is committed to equity, inclusion, and broad engagement, including support for female and junior researchers and participation from countries with emerging research programs.
👉 View the full list of accepted actions here
👉 Direct link to our action: CA24122
Looking forward to the exciting years ahead!
Abstract: Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of a network into core nodes, which are highly connected across the network, and peripheral nodes, which are densely connected to the core but sparsely connected among themselves. In this paper, we propose a new model of core-periphery structure in multilayer networks and a nonlinear spectral method that simultaneously detects the corresponding core and periphery structures of both nodes and layers in weighted and directed multilayer networks. ... Read more
I’m excited to share that our research group is presenting two papers this week at the International Conference on Learning Representations (ICLR) in Singapore!
Emanuele Zangrando is attending the conference in person to present our latest work on efficient low-rank fine-tuning techniques for deep neural networks. If you’re at ICLR, come visit us during the poster sessions and let’s talk shop!
Poster Sessions:
GeoLoRA: Geometric integration for parameter-efficient fine-tuning
📍 Friday – Hall 3 + Hall 2B, Poster #457
🔗 Read the paper
dEBORA: Efficient Bilevel Optimization-based low-Rank Adaptation
📍 Saturday – Hall 3 + Hall 2B, Poster #426
🔗 Read the paper
A big thank you to all my fantastic collaborators:
Emanuele Zangrando, Steffen Schotthoefer, Jonas Kusch, Gianluca Ceruti, Sara Venturini, and Francesco Rinaldi.
Looking forward to engaging conversations and feedback from the community!
Abstract: Nonlinear spectral graph theory is an extension of the traditional (linear) spectral graph theory and studies relationships between spectral properties of nonlinear operators defined on a graph and topological properties of the graph itself. Many of these relationships get tighter when going from the linear to the nonlinear case. In this manuscript, we discuss the spectral theory of the graph p-Laplacian operator. In particular we report links between the p-Laplacian spectrum and higher-order Cheeger (or isoperimetric) constants, sphere packing constants, independence and matching numbers of the graph. ... Read more
Abstract: Simplicial complexes (SCs), a generalization of graph models for relational data that account for higher-order relations between data items, have become a popular abstraction for analyzing complex data using tools from topological data analysis or topological signal processing. However, the analysis of many real-world datasets leads to dense SCs with a large number of higher-order interactions. Unfortunately, analyzing such large SCs often has a prohibitive cost in terms of computation time and memory consumption. ... Read more
Abstract: Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified using metrics that measure the similarity of neighbouring node features, such as the Dirichlet energy. While these metrics are related to oversmoothing, we argue they have critical limitations and fail to reliably capture oversmoothing in realistic scenarios. For instance, they provide meaningful insights only for very deep networks and under somewhat strict conditions on the norm of network weights and feature representations. ... Read more
Excited to share that two of my papers have been accepted at ICLR 2025! 🎉🚀
dEBORA: Efficient Bilevel Optimization-based low-Rank Adaptation
Collaborators: E. Zangrando, S. Venturini, F. Rinaldi
GeoLoRA: Geometric Integration for Parameter-Efficient Fine-Tuning
Collaborators: S. Schotthöfer, E. Zangrando, G. Ceruti, J. Kusch
Grateful to my amazing co-authors and looking forward to presenting these works! 💡✨
Abstract: We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by means of a control over the Lipschitz constant $C$ of its flow. Since it is known that $C$ depends on the logarithmic norm of the Jacobian matrix associated with the neural ODE, we tune this parameter at our convenience by suitably perturbing the Jacobian matrix with a perturbation as small as possible in Frobenius norm. ... Read more
Abstract: We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by reducing the maximum error growth subsequent to a perturbation of the initial value. Since the stability depends on the logarithmic norm of the Jacobian matrix associated with the neural ODE, we control the logarithmic norm by perturbing the weight matrices of the neural ODE by a smallest possible perturbation (in Frobenius norm). We do so by engaging an eigenvalue optimisation problem, for which we propose a nested two-level algorithm. ... Read more
Abstract: Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified using metrics that measure the similarity of neighbouring node features, such as the Dirichlet energy. While these metrics are related to oversmoothing, we argue they have critical limitations and fail to reliably capture oversmoothing in realistic scenarios. For instance, they provide meaningful insights only for very deep networks and under somewhat strict conditions on the norm of network weights and feature representations. ... Read more
I am giving a talk today on our recent work on fast preconditioning of higher-order Laplacians from simplicial complexes using the topology of the complex at the CACN Computational Aspects of Complex Networks workshop at the University of Rome Tor Vergata. Thanks Maria Rosa and Daniele for the kind invitation!
I am giving a talk today on our recent work on exploiting low-rank geometry to reduce memory and computational footprints in deep learning pipelines at the LoRAINNe’24 workshop on LOw-Rank Approximations and their Interactions with Neural NEtworks.
Thrilled to join the Generative AI Lab (GAIL) at the University of Edinburgh as a GAIL Fellow! Looking forward to the exciting journey ahead 🚀✨ gail.ed.ac.uk
I am giving a talk today on our recent work on exploiting low-rank geometry to reduce memory and computational footprints in deep learning pipelines at the Numerical Analysis Seminar of the University of Bath. Thanks Matthias, James, Aaron for the kind invitation!
Abstract: We analyze various formulations of the $\infty$-Laplacian eigenvalue problem on graphs, comparing their properties and highlighting their respective advantages and limitations. First, we investigate the graph $\infty$-eigenpairs arising as limits of $p$-Laplacian eigenpairs, extending key results from the continuous setting to the discrete domain. We prove that every limit of $p$-Laplacian eigenpair, for $p$ going to $\infty$, satisfies a limit eigenvalue equation and establish that the corresponding eigenvalue can be bounded from below by the packing radius of the graph, indexed by the number of nodal domains induced by the eigenfunction. ... Read more
Abstract: Low-rank adaptation methods are a popular approach for parameter-efficient fine-tuning of large-scale neural networks. However, selecting the optimal rank for each layer remains a challenging problem that significantly affects both performance and efficiency. In this paper, we introduce a novel bilevel optimization strategy that simultaneously trains both matrix and tensor low-rank adapters, dynamically selecting the optimal rank for each layer. Our method avoids the use of implicit differentiation in the computation of the hypergradient, and integrates a stochastic away-step variant of the Frank-Wolfe algorithm, eliminating the need for projection and providing identifiability guarantees of the optimal rank structure. ... Read more
Abstract: Low-Rank Adaptation (LoRA) has become a widely used method for parameter-efficient fine-tuning of large-scale, pre-trained neural networks. However, LoRA and its extensions face several challenges, including the need for rank adaptivity, robustness, and computational efficiency during the fine-tuning process. We introduce GeoLoRA, a novel approach that addresses these limitations by leveraging dynamical low-rank approximation theory. GeoLoRA requires only a single backpropagation pass over the small-rank adapters, significantly reducing computational cost as compared to similar dynamical low-rank training methods and making it faster than popular baselines such as AdaLoRA. ... Read more
Abstract: Adversarial attacks on deep neural network models have seen rapid development and are extensively used to study the stability of these networks. Among various adversarial strategies, Projected Gradient Descent (PGD) is a widely adopted method in computer vision due to its effectiveness and quick implementation, making it suitable for adversarial training. In this work, we observe that in many cases, the perturbations computed using PGD predominantly affect only a portion of the singular value spectrum of the original image, suggesting that these perturbations are approximately low-rank. ... Read more
Excited to announce that our paper “Solaris: A Foundation Model for the Sun” has been accepted to the Foundation Models for Science workshop at NeurIPS 2024! 🌞
We’ve developed Solaris, the first foundation model to forecast the Sun’s atmosphere. By leveraging 13 years of full-disk, multi-wavelength solar imagery from the Solar Dynamics Observatory—spanning an entire solar cycle—we’ve pre-trained Solaris to make 12-hour interval forecasts. This is a significant step towards capturing the complex dynamics of the solar atmosphere and transforming solar forecasting. Can’t wait to share more at the conference!
Huge contratulations to my students and main contributors Harris Abdul Majid and Pietro Sittoni!
🚀 Excited to share that our paper Geometry-aware training of factorized layers in tensor Tucker format has been accepted at NeurIPS 2024!
A huge thanks to an amazing team of collaborators and especially to my student Emanuele Zangrando, first author, for their outstanding work. Together, we explored a novel training approach for Tucker-decomposed neural network layers, which dynamically adjusts ranks during training and achieves high compression rates without sacrificing performance.
Looking forward to presenting this and discussing it with the community at NeurIPS!
Thrilled to join the Bayes Innovation Fellows cohort at the University of Edinburgh! 🎉 Excited for the journey ahead as we work to bring cutting-edge machine learning models for language processing and forecasting into real-world applications. A big thank you to the Bayes Centre for this incredible opportunity! Check out the official announcements here and here.
Very excited that our paper, What we should learn from pandemic publishing, has been published in Nature Human Behaviour! This work is the result of a fantastic collaboration between colleagues from the medical school, social sciences, and applied mathematics. A special shoutout to Sara Venturini and Satyaki Sikdar for their incredible contributions and dedication.
Abstract: Authors of COVID-19 papers produced during the pandemic were overwhelmingly not subject matter experts. Such a massive inflow of scholars from different expertise areas is both an asset and a potential problem. Domain-informed scientific collaboration is the key to preparing for future crises. Please cite this paper as: @article{sikdar2024what, author = {Sikdar, Satyaki and Venturini, Sara and Charpignon, Marie-Laure and Kumar, Sagar and Rinaldi, Francesco and Tudisco, Francesco and Fortunato, Santo and Majumder, Maimuna S. ... Read more
Excited to be organizing a two-day workshop in Edinburgh on Recent advancements in uncertainty quantification for scientific machine learning, artificial intelligence and sampling algorithms.
The workshop brings together experts from seemingly disparate scientific domains such as applied probability, multi-scale modeling, interacting particle systems, optimal transport in Data Science, statistical deep learning, numerical simulation of Stochastic Differential Equations, and uncertainty quantification.
Below is the program:
3/9 Tuesday (1PM-6PM)
1PM-2PM: Aretha Teckentrup, Uncertainty-aware surrogate models for inverse problems
2PM-3PM: Eric Hall, Global Sensitivity Analysis for Deep Learning of Complex Systems
3PM-3:30PM: Coffee break
3:30PM-6PM: Poster session
4/9 Wednesday (10AM-12:30PM)
10AM-11AM: Nicos Georgiou, Various models for queuing systems in tandem
11AM-11:30AM: coffee break
11:30AM-12:30PM: Nikolas Nusken, Bridging transport and variational inference: a new objective for optimal control.
Angelo Alberto Casulli has officially joined our Numerical Analysis and Data Science group at GSSI. Welcome Angelo!
Overjoyed to announce I’ve become father for the second time today; feeling incredibly blessed and grateful! 👶❣️
Delighted that our work Cholesky-like Preconditioner for Hodge Laplacians via Heavy Collapsible Subcomplex has been accepted on SIAM Journal on Matrix Analysis and Applications. Great work designing fast and effective topology-driven preconditioners for higher-order Laplacians led by my former student Tony Savostianov.
Abstract: Using drones to perform human-related tasks can play a key role in various fields, such as defense, disaster response, agriculture, healthcare, and many others. The drone delivery packing problem (DDPP) arises in the context of logistics in response to an increasing demand in the delivery process along with the necessity of lowering human intervention. The DDPP is usually formulated as a combinatorial optimization problem, aiming to minimize drone usage with specific battery constraints while ensuring timely consistent deliveries with fixed locations and energy budget. ... Read more
Very happy that our work A nonlinear spectral core-periphery detection method for multiplex networks has been accepted on Proceedings Royal Society A. Exciting collaboration with Kai Bergermann and Martin Stoll!
I am giving a talk today on our recent work on exploiting low-rank geometry to reduce memory and computational footprints in deep learning pipelines at the ICMS workshop on Big Data Inverse Problems in Edinburgh (UK).
I am giving a talk today on our recent work on model comperssion algorithms and analysis for deep learning, at the SIAM Conference on Applied Linear Algebra in Paris, France. Thanks Rima Khouja for the kind invitation!