10 accepted papers
Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We interpret this non-uniqueness as a gauge freedom: nullspace directions that leave the time derivative unchanged can be …
In existing works on population dynamics inference, there is a focus on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamic, gradient flows are optimal in a specific sense: they minimize kinetic ener…
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly with time. The precise transition from current to next state is often modeled as the interplay of a smooth map and an explicit source of randomness. Stochastic Lifting leverages …
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only sampling-time transports from a base distribution to each marginal…
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 the sum of Hankel singular values of state space models leads to a fast decay of these singular values and thus to compres…
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 adapt low-rank weights in time to rapidly predict the evolution of solution fields at new physics parameters and new ini…
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 models can act as surrogates of classical numerical models to efficiently predict the system behavior over the physics…
We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and costs for variance reduction while guaranteeing definiteness, i…
Training neural networks sequentially in time to approximate solution fields of time-dependent partial differential equations can be beneficial for preserving causality and other physics properties; however, the sequential-in-time training is numerically challenging because training errors quickly a…
Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulation methods, motivated by the opportunity to reduce computationa…