6 papers
Optimal response for stochastic differential equations in with perturbations on the drift term
Gianmarco Del Sarto, Franco Flandoli, Stefano Galatolo +2
We study stochastic differential equations on the -dimensional flat torus with drift and perturbation coefficients in and…
Path-Kernel Method for Differentiating Unstable Diffusions
Angxiu Ni
We derive and prove the path-kernel formula for the linear response (parameter-derivative of averaged statistics) of SDEs. The parameter may affect the drift coefficient, the diffu…
Divergence-kernel method for linear responses of densities and generative models
Angxiu Ni
We derive the divergence-kernel formula for the linear response of random dynamical systems. Specifically, the pathwise expression is for the parameter-derivative of the marginal o…
Adjoint path-kernel method for backpropagation and data assimilation in unstable diffusions
Angxiu Ni
We derive the adjoint path-kernel method for computing parameter-gradients (linear responses) of SDEs. Its cost is almost independent of the number of parameters, and it works for…
Divergence-Kernel method for scores of random systems
Angxiu Ni
We derive the divergence-kernel formula for the scores of random dynamical systems, then formally pass to the continuous-time limit of SDEs. Our formula works for multiplicative no…
Optimal Response for Hyperbolic Systems by the fast adjoint response method
Stefano Galatolo, Angxiu Ni
In a uniformly hyperbolic system, we consider the problem of finding the optimal infinitesimal perturbation to apply to the system, from a certain set of feasible ones, to maxi…