When I think about ‘dynamics’/‘dynamical systems’ this is what I mean:
spatiotemporal data is everywhere
Human brain
Medicine (Disease Spread)
Science (Fluids, Climate)
Robotics (Video generation)
Stock Markets
Simulate: Dynamical Representations
Neural Wave Machines (Keller, 2023),
Artificial Kuramoto Oscillatory Networks (Miyato, 2024)
Explain: Discover Potential Differential Equations
Symbolic Regression, LLMs(?)
Acceleration: Replace Simulator
Scaling/Generalisation: Remove Dependency on Grid/Mesh
Operator Based Models
PINNs, Neural Fields
Flexible (data driven): Parameterise the vector field as a NN
Neural ODE (~Flow Matching)
Optical Flow
Gaussian Processes
Modulated NODEs NeurIPS 2024
By iaa
