3 citations · 6 across the 15 of their papers we have counts for
19 papers
One-Step Generative Surrogate Models via Block-Triangular Joint Drifting
Nicholas Geissler, Shreya Jha, Ricardo Baptista +1
Drifting provides a direct route to one-step generative models, but applying it directly to stochastic transition modeling requires multiple samples of the next state conditioned o…
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…
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…
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…
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…
Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction
Paul Schwerdtner, Prakash Mohan, Julie Bessac +2
Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to 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…
Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds
Philipp Weder, Paul Schwerdtner, Benjamin Peherstorfer
Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov barrier that affects transport-dominated problems. In this work, we build on the reduced dynam…
Empirical sparse regression on quadratic manifolds
Paul Schwerdtner, Serkan Gugercin, Benjamin Peherstorfer
Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition an…
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…
Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction
Paul Schwerdtner, Prakash Mohan, Aleksandra Pachalieva +3
This work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in-situ analysis of numerical simulation data on the Petab…
Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations
Huan Zhang, Yifan Chen, Eric Vanden-Eijnden +1
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial different…
Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction
Paul Schwerdtner, Benjamin Peherstorfer
Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections on…
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…