Scalable Bayesian reduced-order models for simulating
high-dimensional multiscale dynamical systems.
Phaedon-Stelios Koutsourelakis (CEE, Cornell)
While existing mathematical descriptions can accurately
account for phenomena at microscopic scales, these are
often high-dimensional, stochastic and their applicability
over macroscopic time scales of physical interest is
computationally infeasible or impractical. In complex systems,
with limited physical insight on the coherent behavior of
their constituents, the only available information is data
obtained from simulations of the trajectories of huge numbers
of degrees of freedom over microscopic time scales.
This paper discusses a Bayesian approach to deriving
probabilistic coarse-grained models that simultaneously
address the problems of identifying appropriate reduced
coordinates and the effective dynamics in this
lower-dimensional representation. At the core of the models
proposed lie simple, low-dimensional dynamical systems which
serve as the building blocks of the global model. These
approximate the latent, generating sources and parameterize
the reduced-order dynamics. We discuss parallelizable, online
inference and learning algorithms that employ Sequential
Monte Carlo samplers and scale linearly with the dimensionality
of the observed dynamics. We propose a Bayesian adaptive
time-integration scheme that utilizes probabilistic predictive
estimates and enables rigorous concurrent s imulation over
macroscopic time scales. The data-driven perspective advocated
assimilates computational and experimental data and thus can
materialize data-model fusion. It can deal with applications
that lack a mathematical description and where only observational
data is available. Furthermore, it makes non-intrusive use
of existing computational models.
This is joint work with E. Bilionis.