English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Efficient simulation of SDEs is essential in many applications, particularlyfor ergodic systems that demand efficient simulation of both short-timedynamics and large-time statistics. However, locally Lipschitz SDEs oftenrequire special treatments such as implicit schemes with small time-steps toaccurately simulate the ergodic measure. We introduce a framework to constructinference-based schemes adaptive to large time-steps (ISALT) from data,achieving a reduction in time by several orders of magnitudes. The key is thestatistical learning of an approximation to the infinite-dimensionaldiscrete-time flow map. We explore the use of numerical schemes (such as theEuler-Maruyama, a hybrid RK4, and an implicit scheme) to derive informed basisfunctions, leading to a parameter inference problem. We introduce a scalablealgorithm to estimate the parameters by least squares, and we prove theconvergence of the estimators as data size increases.  We test the ISALT on three non-globally Lipschitz SDEs: the 1D double-wellpotential, a 2D multi-scale gradient system, and the 3D stochastic Lorenzequation with degenerate noise. Numerical results show that ISALT can toleratetime-step magnitudes larger than plain numerical schemes. It reaches optimalaccuracy in reproducing the invariant measure when the time-step ismedium-large.

ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems