3 citations · 5 across the 8 of their papers we have counts for
9 papers
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…
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…
Hankel Singular Value Regularization for Highly Compressible State Space Models
Paul Schwerdtner, Jules Berman, Benjamin Peherstorfer
Deep neural networks using state space models as layers are well suited for long-range sequence tasks but can be challenging to compress after training. We use that regularizing th…
DICE: Discrete inverse continuity equation for learning population dynamics
Tobias Blickhan, Jules Berman, Andrew Stuart +1
We introduce the Discrete Inverse Continuity Equation (DICE) method, a generative modeling approach that learns the evolution of a stochastic process from given sample populations…
Parametric model reduction of mean-field and stochastic systems via higher-order action matching
Jules Berman, Tobias Blickhan, Benjamin Peherstorfer
The aim of this work is to learn models of population dynamics of physical systems that feature stochastic and mean-field effects and that depend on physics parameters. The learned…
CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations
Jules Berman, Benjamin Peherstorfer
This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously…
Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes
Paul Schwerdtner, Philipp Schulze, Jules Berman +1
This work focuses on the conservation of quantities such as Hamiltonians, mass, and momentum when solution fields of partial differential equations are approximated with nonlinear…
Randomized Sparse Neural Galerkin Schemes for Solving Evolution Equations with Deep Networks
Jules Berman, Benjamin Peherstorfer
Training neural networks sequentially in time to approximate solution fields of time-dependent partial differential equations can be beneficial for preserving causality and other p…