TY - JOUR
T1 - Projection of diffusions on submanifolds
T2 - Application to mean force computation
AU - Ciccotti, Giovanni
AU - Lelievre, Tony
AU - Vanden-Eijnden, Eric
PY - 2008/3
Y1 - 2008/3
N2 - We consider the problem of sampling a Boltzmann-Gibbs probability distribution when this distribution is restricted (in some suitable sense) on a submanifold ∑ of ℝn implicitly defined by N constraints q1(x) = ⋯ = qN(x) = 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.
AB - We consider the problem of sampling a Boltzmann-Gibbs probability distribution when this distribution is restricted (in some suitable sense) on a submanifold ∑ of ℝn implicitly defined by N constraints q1(x) = ⋯ = qN(x) = 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.
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U2 - 10.1002/cpa.20210
DO - 10.1002/cpa.20210
M3 - Article
AN - SCOPUS:38949150015
SN - 0010-3640
VL - 61
SP - 371
EP - 408
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 3
ER -