12 papers
Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems
Matteo Raviola, Benjamin Peherstorfer
Even when Dirac-Frenkel dynamics determine a well-defined evolution in function space, the corresponding parameter dynamics can be non-unique or ill-conditioned for redundant nonli…
First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems
Shreya Jha, Timo Schorlepp, Nicholas Geissler +2
We introduce First-Order Trajectory Matching (FTM), a surrogate-modeling method that learns the first-order local transport of probability mass from trajectories of stochastic syst…
Stochastic Lifting for Generating Trajectories of Stochastic Physical Systems
Jules Berman, Tobias Blickhan, Benjamin Peherstorfer
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to th…
Two-Parameter Flows for Learning Population Dynamics of Physical Systems
Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory informat…
Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems
Jules Berman, Tobias Blickhan, Benjamin Peherstorfer
Existing work on population dynamics inference often focuses on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are co…
Randomized time stepping of nonlinearly parametrized solutions of evolution problems
Yijun Dong, Paul Schwerdtner, Benjamin Peherstorfer
The Dirac-Frenkel variational principle is a widely used building block for using nonlinear parametrizations in the context of model reduction and numerically solving partial diffe…