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math.PR2025
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…
math.PR2025
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…
math.PR2025
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…