We consider the problem of sampling a Boltzmann-Gibbs probability distribution when this distribution is restricted (in some suitable sense) on a submanifold Sigma of R-n implicitly defined by N constraints q(1) (x) = ... = q(N) W = 0 (N < n). This problem arises, for example, in systems subject to hard constraints or in the context of free energy calculations. We prove that the constrained stochastic differential equations (i.e., diffusions) proposed in [7, 13] are ergodic with respect to this restricted distribution. We also construct numerical schemes for the integration of the constrained diffusions. Finally, we show how these schemes can be used to compute the gradient of the free energy associated with the constraints.
Projection of diffusions on submanifolds: Application to mean force computation / Ciccotti, Giovanni; Lelievre, T; VANDEN EIJNDEN, E.. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 61:(2008), pp. 371-408. [10.1002/cpa.20210]
Projection of diffusions on submanifolds: Application to mean force computation
CICCOTTI, Giovanni;
2008
Abstract
We consider the problem of sampling a Boltzmann-Gibbs probability distribution when this distribution is restricted (in some suitable sense) on a submanifold Sigma of R-n implicitly defined by N constraints q(1) (x) = ... = q(N) W = 0 (N < n). This problem arises, for example, in systems subject to hard constraints or in the context of free energy calculations. We prove that the constrained stochastic differential equations (i.e., diffusions) proposed in [7, 13] are ergodic with respect to this restricted distribution. We also construct numerical schemes for the integration of the constrained diffusions. Finally, we show how these schemes can be used to compute the gradient of the free energy associated with the constraints.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.