My research is an N-headed monster (not necessarily a good thing) involving scientific computation and machine learning, optimal control, high-dimensional approximation and agent-based models across scales. I am mostly interested in:
Hamilton-Jacobi-Bellman PDEs: circumventing the curse of dimensionality in very high-dimensional dynamic programming and reinforcement learning problems using scientific computing and machine learning techniques. Applications in optimal feedback control/estimation of nonlinear ODE/PDE dynamics.
Controlling agent-based dynamics across scales: opinion dynamics, pedestrians, swarm robotics, interacting particle systems in general. Optimal control for microscopic, kinetic, and mean-field descriptions. Numerical methods for mean field control and games.
Optimisation and control with PDE constraints: nonlocal dynamics, vibration control, optimal actuator/sensor design, fluid flow control.
PhD supervision: if you are interested in following a PhD in any of the above, please do not hesistate to get in touch! If you can already tell me a bit about your interests, that's much better, but if you have a general idea I'm also happy to talk.
Collaborations, projects: if you need some expertise in optimisation and/or control, computation, or learning, let's talk.
Please visit https://www.dkalise.net for more details!
et al., 2023, Biologically inspired herding of animal groups by robots, Methods in Ecology and Evolution, ISSN:2041-210X
Kalise D, Sharma A, Tretyakov M, 2022, Consensus based optimization via jump-diffusion stochastic differential equations, Mathematical Models and Methods in Applied Sciences (m3as), ISSN:0218-2025
et al., 2022, Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs, Ifac Papersonline, Vol:55, ISSN:2405-8963, Pages:168-173
Albi G, Bicego S, Kalise D, 2022, Supervised learning for kinetic consensus control, MTNS22, Elsevier BV, Pages:103-108, ISSN:2405-8963
Dolgov S, Kalise D, Saluzzi L, 2022, Optimizing semilinear representations for State-dependent Riccati Equation-based feedback control, 25th International Symposium on Mathematical Theory of Networks and Systems (MTNS), ELSEVIER, Pages:510-515, ISSN:2405-8963