Collective Motion and Path-Entropy

Collective Motion is a captivating and highly contemporary area of study that spans applied mathematics, physics, zoology, robotics and machine learning. Research into the subject has only become possible with the advancement of computational capabilities, enabling scientists to explore phenomena exhibited by flocking birds, schooling fish, and swarming bees. The motivation and execution of these remarkable natural occurrences are not yet well understood. Beyond the visual allure, there are various potential applications of Collective Motion, in fields such as CGI graphics, robotics and swarm intelligence. Research has been undertaken on "top-down" models of Collective Motion since the mid-90s. This style of model enforces specific dynamics that broadly mimic observed behaviours, such as alignment, cohesion and collision avoidance. While these models yield some insights into theoretical possibilities, and have close analogies with spin models within physics, their limited ability to
replicate the full complexity of real-world scenarios hampers their practical applicability. More recent work has explored Collective Motion and flocking using "bottom-up" models, using the principals of "Future State Maximization" and "Path-Entropy Maximization" respectfully, motivated by Causal Entropic Forces. In these models, each bird utilizes projected visual states to formulate any
decision to reorientate. Both models can produce highly ordered cohesive flocks that demonstrate marginal opacity. However, both models have only been studied in 2D. This fundamentally limits their applicability to systems involving motion in full 3D (birds, fish etc) and thereby makes comparison with experiment difficult. In this PhD thesis, we are looking to expand previous work to simulate flocking
birds in 3D. Previous 3D models are "top-down", such as the Boids Model which is defined by three simple rules (separation, alignment, and cohesion). We aspire to provide a deeper understanding into flocking behaviour and the validity of the application of "bottom-up" models to 3D Collective Motion. Our core research questions are: How can we translate the 2D projection method to present visual
stimulus in 3D? Can we create improved models for visual projection that are computationally efficient, e.g. using "ray tracing" techniques? Do the flocks demonstrate marginal opacity? Does the algorithm produce complex structures reminiscent of the manifolds seen in nature?

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.