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Found 7 papers, 4 papers with code
Transformation of ReLU-based recurrent neural networks from discrete-time to continuous-time
On the other hand, mathematical analysis of dynamical systems inferred from data is often more convenient and enables additional insights if these are formulated in continuous time, i. e. as systems of ordinary (or partial) differential equations (ODE).
Out-of-Domain Generalization in Dynamical Systems Reconstruction
We explain why and how out-of-domain (OOD) generalization (OODG) in DSR profoundly differs from OODG considered elsewhere in machine learning.
Generalized Teacher Forcing for Learning Chaotic Dynamics
Here we report that a surprisingly simple modification of teacher forcing leads to provably strictly all-time bounded gradients in training on chaotic systems, and, when paired with a simple architectural rearrangement of a tractable RNN design, piecewise-linear RNNs (PLRNNs), allows for faithful reconstruction in spaces of at most the dimensionality of the observed system.
Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems
In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise.
On the difficulty of learning chaotic dynamics with RNNs
Here we offer a comprehensive theoretical treatment of this problem by relating the loss gradients during RNN training to the Lyapunov spectrum of RNN-generated orbits.
Tractable Dendritic RNNs for Identifying Unknown Nonlinear Dynamical Systems
In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise.
Identifying nonlinear dynamical systems with multiple time scales and long-range dependencies
A main theoretical interest in biology and physics is to identify the nonlinear dynamical system (DS) that generated observed time series.
