Applied and computational mathematics
The Applied and Computational Mathematics (ACM) theme at Heriot-Watt is at the forefront of advancing mathematical techniques to address complex real-world challenges. Our team leverages expertise across several diverse areas; Numerical Analysis and Scientific Computing; Particle Systems and Fluid Dynamics; Mathematical Biology; Optimisation, Machine Learning, and Stochastic Methods; and Data Science and Dynamical Systems.
Our research in Numerical Analysis and Scientific Computing concerns the design, study and analysis of cutting-edge algorithms for solving partial and stochastic partial differential equations, linear algebra problems, inverse problems, and uncertainty quantification. This includes the development of tools to enable precise modelling and simulation of phenomena across physics, engineering, finance, biology and medicine.
Research in Particle Systems and Fluid Dynamics tackles key challenges in understanding and modelling complex systems, applying our insights to fields such as traffic flows, rarefied gas dynamics, plasma physics, renewable energy, wave-structure interactions and population dynamics.
In Mathematical Biology, our group's activities encompass several key areas tackling critical questions in ecology, epidemiology, cell biology, biophysics, and medicine. From modelling population dynamics and ecosystem-scale patterns to investigating plant-soil interactions and cancer angiogenesis, we employ multiscale modelling and data-driven methods to gain deeper insights into biological systems. Our research also explores transport processes, wound-healing mechanisms, and intercellular signalling, providing a comprehensive approach to understanding complex biological phenomena.
In Optimisation, Machine Learning, and Stochastic Methods, we integrate computational innovation with data-driven techniques to conduct comprehensive research. Our methodologies are deeply interconnected with activities within the ACM group, addressing high-dimensional challenges in imaging and a wide range of applications.
In Data Science and Dynamical Systems, we strive to enhance the understanding and prediction of dynamic processes in science and engineering. By bridging mathematics and computation, we focus on applications in Bayesian statistics, molecular dynamics, scalable computing, and Koopman operator theory. Our research in uncertainty quantification delivers robust, scalable solutions for tackling complex, high-dimensional challenges.
Across all these areas, we foster collaboration across disciplines and with industry, making significant contributions to advancing scientific knowledge and addressing global challenges. We invite researchers, students, and industry partners to join us as we push the boundary of applied and computational mathematics, to explore opportunities for research, study, and partnership.
Mathematical Sciences are at the core of technological progress, driving innovations in artificial intelligence, data security, and computational modelling that shape critical sectors like finance, healthcare, and engineering. At the School of Mathematical and Computer Sciences (MACS), Heriot-Watt University brings together experts in mathematics, actuarial science, statistics, and computer science to tackle global challenges through interdisciplinary research.
By collaborating with industry and academic partners, MACS plays a pivotal role in supporting Heriot-Watt’s globally renowned research institutes, including The National Robotarium, The Lyell Centre for Earth and Marine Sciences and Technology, The Global Research Institute in Health and Care Technologies, and iNetZ+ Global Research Institute for Net Zero and Beyond. This ensures that MACS research has both theoretical significance and real-world impact, contributing to the university’s mission of advancing global innovation and societal benefit.