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!
Kalise D, Saluzzi L, Sergey D, 2023, Data-driven tensor train gradient cross approximation for Hamilton-Jacobi-Bellman equations, Siam Journal on Scientific Computing, Vol:45, ISSN:1064-8275, Pages:A2153-A2184
et al., 2023, The role of airspeed variability in fixed-time, fuel-optimal aircraft trajectory planning, Optimization and Engineering, Vol:24, ISSN:1389-4420, Pages:1057-1087
Alla A, Kalise D, Simoncini V, 2023, State-dependent Riccati equation feedback stabilization for nonlinear PDEs, Advances in Computational Mathematics, Vol:49, ISSN:1019-7168
Kalise D, Sharma A, Tretyakov M, 2023, Consensus based optimization via jump-diffusion stochastic differential equations, Mathematical Models and Methods in Applied Sciences (m3as), Vol:33, ISSN:0218-2025, Pages:289-339
et al., 2023, Biologically inspired herding of animal groups by robots, Methods in Ecology and Evolution, Vol:14, ISSN:2041-210X, Pages:479-486