Training neural operators to preserve invariant measures of chaotic attractors
Chaotic systems make long-horizon forecasts difficult because small perturbations in initial
conditions cause trajectories to diverge at an exponential rate. In this setting, neural …
conditions cause trajectories to diverge at an exponential rate. In this setting, neural …
Learning chaotic dynamics with embedded dissipativity
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are
characterized by their sensitivity to initial conditions, which makes accurate prediction …
characterized by their sensitivity to initial conditions, which makes accurate prediction …
Out-of-Domain Generalization in Dynamical Systems Reconstruction
In science we are interested in finding the governing equations, the dynamical rules,
underlying empirical phenomena. While traditionally scientific models are derived through …
underlying empirical phenomena. While traditionally scientific models are derived through …
Multimodal teacher forcing for reconstructing nonlinear dynamical systems
Many, if not most, systems of interest in science are naturally described as nonlinear
dynamical systems (DS). Empirically, we commonly access these systems through time …
dynamical systems (DS). Empirically, we commonly access these systems through time …
4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models
Constraining a numerical weather prediction (NWP) model with observations via 4D
variational (4D-Var) data assimilation is often difficult to implement in practice due to the …
variational (4D-Var) data assimilation is often difficult to implement in practice due to the …
Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Data
In science, we are often interested in obtaining a generative model of the underlying system
dynamics from observed time series. While powerful methods for dynamical systems …
dynamics from observed time series. While powerful methods for dynamical systems …
A hypothesis on ergodicity and the signal‐to‐noise paradox
DJ Brener - Atmospheric Science Letters, 2024 - Wiley Online Library
This letter raises the possibility that ergodicity concerns might have some bearing on the
signal‐to‐noise paradox. This is explored by applying the ergodic theorem to the theory …
signal‐to‐noise paradox. This is explored by applying the ergodic theorem to the theory …
Optimal Recurrent Network Topologies for Dynamical Systems Reconstruction
In dynamical systems reconstruction (DSR) we seek to infer from time series measurements
a generative model of the underlying dynamical process. This is a prime objective in any …
a generative model of the underlying dynamical process. This is a prime objective in any …
A possible link between ergodicity and the signal-to-noise paradox
DJ Brener - arXiv preprint arXiv:2312.04669, 2023 - arxiv.org
This short letter raises the possibility that ergodicity concerns might have some bearing on
the signal-to-noise paradox. This is explored by simply applying the ergodic theorem of …
the signal-to-noise paradox. This is explored by simply applying the ergodic theorem of …
Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics
Many, if not most, systems of interest in science are naturally described as nonlinear
dynamical systems. Empirically, we commonly access these systems through time series …
dynamical systems. Empirically, we commonly access these systems through time series …