Nash Neural Networks: Inferring Utilities from Optimal Behaviour in Epidemics

The context of the research
This PhD project is concerned with applying control-theory to epidemiological problems. In this work we will treat individuals as rational agents who seek to maximise their well-being in the face of an infectious disease.
The aims and objectives of the research
We will employ a new methodology for learning hidden preferences for individuals who target a Nash Equilibrium using Machine learning approach similar to recent develops in Physics Informed Machine Learning (e.g Lagrangian Neural Networks).
The main objectives of this project include seeking to integrate out the Lagrange multipliers in order to learn the utility soley from observable information (i.e the SIR dynamics of the epidemic) and to consider different forms of the utility for both direct/inverse optimal control problems.
There are, however, alternative and potential furhter aims of the research. Such as inferring utilities from open source, opulation-level data. From this we could explore optimal governemtn control of Nash agents and inferring government objectivesm with which to compare against their proposed objectives. Extensions to our epidemics model can also be explored, such as gerneralising to include uncertainty (stochastic optimal control) and utilising different compartments in our data (e.g young and old individuals).
The novelty of the research methodology
Our approach for inferring utilities consistent with a Nash equilibrium is completlty novel. In contrast to previous approached we do not need to assume the functional form of the individual preferences. Further aspect of the novelty include the role of saturating health-care systems in pandemics, later in the project the role of uncertainties in the infomraiton available to individuals.
The potential impact, applications and benefits
We believe there is a pressing need for qunatitative policy making tools to help manage future epidemics of infectious diseases. This may also have applications in other social planning problems.
Possible extensions to this work include modification of the objective function (utility) to mimic other forms used in the literature or more accurate models. Later in the project we look for applications in related fields, including economics, finance or swarm behaviour.
How the research relates to the remit
Fundamentally our work involves developing a new ML approach, applied to control theory, a field in engineering. The research falls into the Engineering, Global uncertainties and Healthcare technologies research areas.

External partner - soft Matter Engineering Lab, Kyoto University - Prof. Ryoichi Yamamoto (Soft Matter Engineering, Department of Chemical Enginerering, Kyoto University). Together with Drs John Molina and Simon Schnyderr they have devleoped novel computational techniques for simulating complex Soft Matter Systems, including colloidal dispersions, celluar tissues, and ploymer melt flows, among others. More recently, in collaboration with Prof. Matthew Turner (PhD supervisor 1), they have worked to establish a theorectical framework for qunatitative poliymaking in a society of rational individuals. In particular, they have studied how taxes and/or government subsidies can be used to align the decison making rational individuals with the socially optimal behaviour during the pandemic, like the ongoing SARS-CoV-2 global pandeimic.
The external partner has agreed to provide technical support and access to high-performance computing resources (Tokyo Univerisyt, Wisterria-BDEC 01, NVIDIA A100 GPU cluster) required for the Machine learning applications of this prokect. The partner has agreed to attend bi-weekly (remote) meetings to discuss the modelling and technical aspects of the work. In addition, the partner has agreed to host me in Kyoto for part of my PhD studies.

In the 2018 Government Office for Science report, 'Computational Modelling: Technological Futures', Greg Clarke, the Secretary of State for Business Energy and Industrial Strategy, wrote "Computational modelling is essential to our future productivity and competitiveness, for businesses of all sizes and across all sectors of the economy". With its focus on computational models, the mathematics that underpin them, and their integration with complex data, the MathSys II CDT will generate diverse impacts beyond academia. This includes impacts on skills, on the economy, on policy and on society.

Impacts on skills.
MathSys II will produce a minimum of 50 PhD graduates to support the growing national demand for advanced mathematical modelling and data analysis skills. The CDT will provide each of them with broad core skills in the MSc, a deep knowledge of their chosen research specialisation in the PhD and a complementary qualification in transferable skills integrated throughout. Graduates will thus acquire the profiles needed to form the next generation of leaders in business, government and academia. They will be supported by an integrated pastoral support framework, including a diverse group of accessible leadership role models. The cohort based environment of the CDT provides a multiplier effect by encouraging cohorts to forge long-lasting professional networks whose value and influence will long outlast the CDT itself. MathSys II will seek to maximise the influence of these networks by providing topical training in Responsible Research and Innovation, by maintaining a robust Equality, Diversity & Inclusion policy, and by integration with Warwick's global network of international partnerships.

Economic impacts.
The research outputs from many MathSys II PhD projects will be of direct economic value to commercial, public sector and charitable external partners. Engagement with CDT partners will facilitate these impacts. This includes co-supervision of PhD and MSc projects, co-creation of Research Study Groups, and a strong commitment to provide placements/internships for CDT students. When commercial innovations or IP are generated, we will work with Warwick Ventures, the commercial arm of the University of Warwick, to commercialise/license IP where appropriate. Economic impact may also come from the creation of new companies by CDT graduates. MathSys II will present entrepreneurship as a viable career option to students. One external partner, Spectra Analytics, was founded by graduates of the preceding Complexity Science CDT, thus providing accessible role models. We will also provide in-house entrepreneurship training via Warwick Ventures and host events by external start-up accelerator Entrepreneur First.

Impacts on policy.
The CDT will influence policy at the national and international level by working with external partners operating in policy. UK examples include Department of Health, Public Health England and DEFRA. International examples include World Health Organisation (WHO) and the European Commission for the Control of Foot-and-mouth Disease (EuFMD). MathSys students will also utilise the recently announced UKRI policy internships scheme.

Impacts on society.
Public engagement will allow CDT students to promote the value of their research to society at large. Aside from social media, suitable local events include DataBeers, Cafe Scientifique, and the Big Bang Fair. MathSys will also promote a socially-oriented ethos of technology for the common good. Concretely, this includes the creation of open-source software, integration of software and data carpentry into our computational and data driven research training and championing open-access to research. We will also contribute to the 'innovation culture and science' strand of Coventry's 2021 City of Culture programme.