Stochastic filtering, numerics, and machine learning
Contact person: Salvador Ortiz-Latorre
Keywords: stochastic filtering, neural networks, stochastic numerics, sequential Monte Carlo methods, stochastic partial differential equations
Research group: Risk and Stochastics
Department of Mathematics
Stochastic filtering (or data assimilation) consists on the the estimation of a dynamical system with partial and noisy observations. This is is a classical problem in engineering and one can apply filtering techniques in satellite tracking, weather prediction, ecology and volatility modeling among others. Hence, there is a clear need to develop robust an efficient algorithms to solve this estimation problem. The entailed challenges are in the pursuit of both methodological rigour and computational efficiency, while mitigating the “curse of dimensionality” (exponential increase in computational effort when increasing the dimension of the problem) for high dimensional problems.
We are interested in research proposals that are directed towards the theoretical and the computational aspects of solving the filtering problem. We are interested in proposal that expand classical methods as well as proposals that introduce machine learning techniques.
The research proposals may span several methodological approaches within stochastic numerics, machine learning, and Bayesian data assimilation, as well as a number of application domains.
Methodological research topics:
- Physics Informed Neural Networks (PINNs) for the approximation of partial differential equations.
- Generative adversarial networks (GANs) for the learning of probability distributions from data.
- Particle filters
- Uncertainty quantification.
- Stochastic numerics for SDEs.
Relevant application domains
- Climate modelling
- Weather forecasting
- Engineering
- Financial modeling
External partners:
- Statkraft
- SINTEF
- NR
- DNV
- Norwegian Meteorological Institute
Mentoring and internship will be offered by a relevant external partner
