Chair in Applied Mathematics
What are your research interests and what is the focus of your current research?
Kody Law leads the Data Centric Science and Engineering group at the University of Manchester, which conducts research at the forefront of foundational methods and algorithms for Data Centric Science and Engineering, spanning across the fertile intersection of computational applied mathematics, computational statistics, artificial intelligence, and machine learning.
Multilevel Monte Carlo methods for Bayesian computation are of particular interest — specifically multi-index, multi-fidelity, and randomized versions. Surrogate modelling (supervised learning) is another area of research in the group which is picking up momentum.
Geometric and topological data analysis methods, for example for nonlinear dimensionality reduction, are nascent areas of interest. Since the impact of a method is only realized once it is applied, the group is also heavily engaged in applications, including advanced materials and manufacturing, subsurface, numerical weather prediction, fusion energy science, and quantum information science.
What are some projects or breakthroughs you wish to highlight?
Here are some recent papers.
- Sparse online variational Bayesian regression. K. J.H. Law and V. Zankin. SIAM/ASA J. Unc. Quant., in press (2022).
- Certified dimension reduction in nonlinear Bayesian inverse problems. O. Zahm, T. Cui, K. J. H. Law, A. Spantini, Y. M. Marzouk. Mathematics of Computation, in press (2022).
- Randomized multilevel Monte Carlo for embarrassingly parallel inference. A. Jasra, K. J. H. Law, A. Tarakanov, and F. Yu. In: Nichols J. et al. (eds) Driving Scientific and Engineering Discoveries Through the Integration of Experiment, Big Data, and Modeling and Simulation. SMC 2021. Communications in Computer and Information Science, vol 1512. Springer, Cham. https://doi.org/10.1007/978-3-030-96498-6_1SMC21 (2022).
- Unbiased Filtering of a Class of Partially Observed Diffusions. A. Jasra, K. J. H. Law, and F. Yu. Advances in Applied Probability, in press (2022).
- A Bayesian analysis of classical shadows. J. M. Lukens, K. J.H. Law, and R. S. Bennink. Nature pj Quantum Information 7(1), 1-10 (2021).
What memberships and awards do you hold/have you held in the past?
Turing Fellow, ELLIS Fellow. Member of SIAM, IMA, ASA, ISBA, ACM.
What is the biggest challenge in Data Science and AI right now?
Quantification of uncertainty in deep learning is a big challenge, particularly outside the range of training data (e.g. extrapolation vs. interpolation), where classical approaches are prone to incorrect and overconfident predictions. Reinforcement learning is a very promising, and very broad, direction, with a lot of potential.
What real world challenges do you see Data Science and AI meeting in the next 25 years?
It is difficult to find an area where Data Science and AI is not having a huge impact. In the span of 25 years, I think there will be very few areas, if any, which have not been transformed by this technology. I think it is unlikely that we will figure out how to artificially generate certain intrinsically human qualities which we do not understand, like creativity and consciousness, in the next 25 years. Therefore, I doubt sentient robots will exist in this timeframe.