DrTom Chaffey

Project Opportunities

Title: A monotone circuit theory for control and learning in physical networks

Summary of opportunity:

Over the last decade, the rising energy intensiveness of machine learning has spurred a host of innovations in alternative computing architectures. Among them are in-memory computing, where computational and memory devices are collocated, and spiking neural networks, which draw inspiration from the spiking behaviour of biological nervous systems. Such systems use a mix of analog and digital circuits, and the development of a rigorous theory of design and control of such systems requires revisiting the fundamentals of nonlinear circuit and control theory.

Opportunity synopsis:

The projects draws upon the mathematical language of monotone operator theory as a common abstraction of ideas in nonlinear control theory, circuit theory, optimization and neural networks, to develop such a theory of design and control.

The project comprises several subprojects:

1. Non-equilibrium stability theory: current input/output stability analysis is either performed with respect to an equilibrium, which is tractable but restrictive in the context of non-equilibrium behaviours such as spiking of a neuron, or with respect to an arbitrary reference, which lacks tractable verification tools. The project aims to develop a theory of stability of properties in between these two extremes. The key tool will be the Scaled Relative Graph, a graphical tool allowing Nyquist-type analysis of nonlinear systems.
2. Circuit realisation of equilibrium and mixed-equilibrium networks: this project will develop a theory of circuit realisation for particular classes of neural networks, so-called equilibrium networks, and use these as building blocks for systems which exhibit non-equilibrium behaviour such as spiking, drawing on tools from switched and time-varying system theory. Training of such networks will be studied, using hardware-accelerated methods of computing gradients, and their efficacy as machine learning structures will be tested.
3. Optimal control of monotone networks: this project will explore the use of monotone splitting algorithms, from the theory of large-scale convex optimisation, in optimal control problems where the plant has the structure of a monotone circuit. Applications in MPC and learning will be explored.

Offering:
Multiple scholarships are currently available in the areas stipulated above. The successful candidate will be awarded a scholarship for 3.5 years at the RTP stipend rate (currently $41,753 in 2025) subject to satisfactory academic performance. International applicants will receive a tuition fee scholarship for upto 3.5 years.

Successful candidates:

Must have a have a Bachelors degree (1st class honours or equivalent) or a Master's degree in Engineering, Mathematics, Computer Science or a related field, with experience in control theory.

How to apply: To apply, please email Dr Thomas Chaffey the following:

• CV,
• Transcript, and
• A brief cover letter