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
Our group at COMPiLE Lab focuses on mathematical and computational aspects of machine learning and network science. Our research combines tools from applied mathematics, numerical analysis, scientific computing, graph and spectral theories to address pressing challenges in modern machine learning and its applications to classification, language processing, and analysis of complex systems.
We are always looking for new talented and motivated students and postdoctoral scholars to join the team. If you are interested in working with us please get in touch to discuss enrollment in the PhD programs at University of Edinburgh (UK) or GSSI (Italy) as well as available postdoc positions. Some info is available below, but it might be outdated.
On a rolling basis I accept motivated students for internship/thesis projects from UoE students on:
This project aims to develop and advance scalable foundation models for climate simulations. Foundation models, which have revolutionized fields such as natural language processing and biology, are large-scale neural networks trained on extensive datasets to learn generalizable representations. Applying these models to climate science poses unique challenges, as climate phenomena often involve complex interactions between the atmosphere, ocean, and cryosphere, and occur in out-of-distribution (OOD) scenarios, such as abrupt climate changes and tipping points. The project will involve integrating diverse atmospheric, oceanic, and cryospheric data into a comprehensive pre-training dataset, utilizing both observational data and high-resolution numerical simulations. Novel physics-informed loss functions will be introduced during pre-training to enhance the model’s ability to capture fine-scale features critical for accurate climate forecasting. The research will also explore techniques from recent OOD literature, such as domain adaptation and adversarial training, to improve model robustness and performance in predicting rare and extreme climate events Additionally, the project may explore the development of synthetic datasets using physics-aware generative AI techniques. The PhD candidate will have the opportunity to work at the intersection of machine learning, climate science, and high-performance computing, leveraging state-of-the-art computational resources and collaborating with leading experts in the field.
Deep learning has revolutionized various domains, including computer vision, language processing, and scientific computing. However, the growing complexity of neural network architectures alongside the ever-growing size of the available data, has led to computational challenges, making it increasingly important to develop techniques that reduce the number of parameters while maintaining performance, robustness, and model-specific underlying structures. This project topic proposes to investigate structure-preserving parameter reduction methods for neural networks with applications in computer vision, language models, reinforcement learning, and scientific simulation. The project will combine state-of-the-art deterministic and randomized techniques in numerical linear algebra, numerical optimization on smooth manifolds, bi-level optimization, numerical integration of matrix and tensor differential equations, to analyze performance, bias, robustness, and generalization of modern deep learning architectures and design new efficient learning algorithms that reduce memory requirements and training time.
Specific objectives of the project topic are:
The successful student will have opportunities for collaboration within and outside the School of Mathematics at UoE, including industries and scientific labs.
Deep learning ultimately boils down to solving optimization problems with functional constraints. In a variety of modern application settings, these constraints are defined in terms of (partial) differential equations (PDEs). Examples include so-called neural differential equations, where the neural network architecture is designed implicitly as the solution of a PDE, and physics-informed neural networks, where the differential nature of the problem is embedded into the loss function.
These PDE-inspired neural network architectures yield several advantages over standard deep learning models as one can, for instance, exploit the broad literature on dynamical systems and PDEs to analyze their stability and to design more efficient learning algorithms that use fast and robust numerical solvers.
In this project we will combine state-of-the-art deterministic and randomized linear algebra techniques for parallel-in-time integration and optimization, including problems with PDE constraints, to improve the efficiency of learning algorithms. We will consider applications to computer vision, language models, and scientific simulations. A wide variety of problems can be cast as optimization problems with constraints defined in terms of (partial) differential equations, motivating the combination of linear algebra solvers for optimization with deep learning techniques.
The supervisors have a range of experience in numerical linear algebra-inspired algorithms for machine learning, and fast and robust linear algebra solvers for optimization problems constrained by PDEs.
The student on this project should have experience with computational mathematics, for example numerical linear algebra, numerical solution of PDEs, optimization, and coding, as well as an interest in applying such techniques to modern machine learning algorithms.
We welcome applications evert year through the Maxwell Institute’s Graduate School PhD programme in Modelling Analysis and Computation (MAC-MIGS). The application deadline is around end of January and The start date is September. The duration of the PhD programme is 4 years.
The Maxwell Institute for Mathematical Sciences brings together research activities in mathematical sciences at Edinburgh and Heriot-Watt Universities. Members of the Maxwell Institute are academics from the School of Mathematics at the University of Edinburgh and the Departments of Mathematics and of Actuarial Mathematics and Statistics at Heriot-Watt University. The Maxwell Institute builds on the long history of collaboration between the three departments, best exemplified by the establishment and continued operation of the International Centre for Mathematical Sciences (ICMS). Since 2018, the Maxwell Institute has a physical home on the top floor of the Bayes Centre which it shares with the ICMS, creating a hub for mathematical sciences research, training and applications in central Edinburgh.
The MAC-MIGS 2024 programme
The MAC-MIGS 2024 programme offers bespoke, cohort-based training in applied and computational mathematics. During the 4-year programme, students will take 90 credits worth of courses, with the following specialised courses being offered:
The students trained on this programme will have expertise in a broad array of modern mathematical methodologies, including for example Bayesian inference, uncertainty quantification, numerical analysis, machine learning, and fluid dynamics, and of their application in multidisciplinary contexts as well as experience of industrial collaboration.
GSSI is an international school of advanced studies in Mathematics, Physics, Computer Science and Social Science. Located in the city of L’Aquila (Italy), in the heart of the Apennine Mountains east of Rome, the institute offers a stimulating environment, with numerous PhD students and postdoctoral researchers selected internationally every year. English is the official language of the institute.
Applications for the PhD program at GSSI open every year in March with several open positions in all the four areas. Deadline for the application is usually in mid June.
The PhD program consists of four years with qualifying exams to be taken during the first year. The scholarship for the program offers a monthly salary/stipend, research funds and free housing in institute’s residences in the city center of L’Aquila.
More details on how to apply can be found here and here. I am affiliated with the School of Mathematics, but can supervise thesis from both the mathematics and the computer science areas.
The math division at GSSI opens to postdoctoral applications from highly motivated early-career researchers once or twice a year. Positions are usually for the entire school of math and are highly competitive. If you are interested in doing a postdoc with us at GSSI, please contact me and do check out the Home and the Announcements pages on the GSSI webpage for open calls for postdoctoral positions.