The Institute of Natural Sciences is the center for interdisciplinary research and training across applied mathematics, physics, engineering, biology, and life sciences. Current research interests involve scientific and engineering computation, nonlinear complex systems, soft condensed matter physics, material science, modern statistics and data science, science of image processing, physical processes in biological systems, and theoretical and computational neuroscience.
INS faculty is engaged in a wide range of interdisciplinary computational research aimed at developing innovative numerical methods based on multi-scale and multi-physics approaches. Both stochastic and deterministic algorithms are of interest, including molecular dynamics and Monte Carlo methods, boundary element methods, discontinuous Galerkin methods, sparse grid collocation methods, kinetic equation methods, fast solvers for layered and inhomogeneous media, quasi-continuum methods, linear-scaling DFT methods, wavelet and optimization methods for image processing, statistical learning methods, etc.
Research in the soft-matter group at INS is carried out by scientists from physics, chemistry, and applied math. We use a combination of experimental, theoretical, and numerical methods to investigate a wide range of problems, such as protein folding in nanopores, elasticity in liquid crystals, collective bacterial flow, forces in granular packing, and adaptive haemodynamics. Through this unique inter-disciplinary approach, we are not only gaining new insights in the specific problems listed above but also developing versatile methods that can be applied to questions in other branches of science and engineering.
Research of material science at INS includes multi-scale modeling, simulation and theoretical analysis in materials science, including atomistic/continuum coupling methods, numerical homogenization methods for heterogeneous materials, mathematical modeling of crystalline defects including dislocation, grain boundary etc, as well as studies of structural, electronic, and magnetic properties of complex materials and nanoscale structures using atomistic first-principle quantum-mechanical methods.
How the brain codes information and performs its function is the fundamental question in neuroscience. Aiming to understand mechanisms underlying physiological phenomena observed in experiment on scales ranging from the molecular, over the electrophysiological, to that of the imaging, the research of theoretical and computational neuroscience at INS is focused on the analysis of information processing in the brain, development of new efficient computational methods for modeling large-scale neuronal networks, and investigation of new mathematical structures that potentially underlie neuronal dynamics arising in the brain.
Imaging science has emerged as an important interdisciplinary research area. Research at INS is to develop appropriate mathematical models and efficient computational algorithms for image formation, image processing, image analysis, inverse problems in biomedical imaging, compressive sensing and computer vision, leading to diverse applications in science, medicine, engineering, and other fields.
Mathematical Optimization is ubiquitous for information sciences, medical image analysis and many other data-intensive applications in science and engineering. The size and complexity of these problems have posed significant challenges to high performance computing. Our research focuses on the study of the theoretical and computational aspects of both general optimization algorithms and special purpose methods that take advantage of problem structures.
Collaborating with researchers in other disciplines, including biology, engineering, finance, management, medicine, and public health, INS faculty is engaged in research in statistical theory and development of modern statistical methodologies for applications in diverse fields, such as large data sets arising from e.g., biology, economy, and astrophysics.
To classify computational problems in terms of their computational difficulty is the fundamental question in computer science, the implications of which go well beyond computing to all engineering disciplines and to the entire society. In this direction, the research of INS is aiming for dichotomy theorems for certain computational frameworks. That is to say, to give a characterization: If certain conditions are satisfied, the problem is polynomial time computable; otherwise, it is hard.
Computational Economics has emerged as an important interdisciplinary research area between economics and computer science. There are two types of questions in this interdisciplinary research area: To study some economics solution concepts from computational perspective, such as the computational complexity of Nash Equilibrium; and to study some traditional optimization problems taking into the account the rational behavior of agents involved in the problems. INS is involved in both research directions.
Research of quantum information at INS aims at building large-scale photonic processors which have sufficient capacity to explore new frontiers of fundamental quantum information, including quantum communication, quantum computation, and quantum simulation. To achieve this, we are now focusing on developing cutting-edge technologies, including manufacture of photonic chips with femtosecond laser direct writing, storage of broadband light with room-temperature atomic ensembles, and preparation of multi-photon sources.
The research of Geophysical and Astrophysical Fluid Dynamics at INS aims at understanding the large-scale fluid motions on the surface and in the interior of planets, stars and accretion disks. It studies the important role of rotation, stratification, convection and magnetic fields and the internal waves excited by the associated body forces to transport angular momentum and energy. A major research topic is the generation of magnetic fields through the motion of conducting fluids, the so-called dynamo theory. In collaboration with applied mathematicians, simplified analytical and semi-analytical models are developed, together with numerical computation, to understand important phenomena in geophysics and astrophysics. It also aims to compare theoretical results with observations in collaboration with geophysicists and astrophysicists.