# Deep learning of dynamics and signal-noise decomposition with time-stepping constraints

@article{Rudy2018DeepLO, title={Deep learning of dynamics and signal-noise decomposition with time-stepping constraints}, author={Samuel H. Rudy and J. Nathan Kutz and Steven L. Brunton}, journal={J. Comput. Phys.}, year={2018}, volume={396}, pages={483-506} }

## 123 Citations

### Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint

- Computer ScienceArXiv
- 2021

The proposed approach provides a promising methodology to learn dynamic models, where the first-principle understanding remains opaque, by learning a neural network that implicitly represents the data and an additional network that models the vector fields of the dependent variables.

### Neural ODEs with Irregular and Noisy Data

- Computer ScienceArXiv
- 2022

The proposed framework to learn a model describing the vector ﬁeld is highly eﬀective under noisy measurements and can handle scenarios where dependent variables are not available at the same temporal grid.

### The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation

- Computer ScienceSIAM Journal on Numerical Analysis
- 2022

This work considers the deep network-based LMMs for the discovery of dynamics using the approximation property of deep networks, and indicates, for certain families of LMMs, that the l grid error is bounded by the sum of O(h) and the network approximation error.

### Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence

- Computer ScienceJournal of Machine Learning for Modeling and Computing
- 2022

This paper presents a computational technique to learn thene-scale dynamics from such coarsely observed data and employs inner recurrence of a DNN to recover the ne-scale evolution operator of the underlying system.

### Active operator inference for learning low-dimensional dynamical-system models from noisy data

- Computer ScienceArXiv
- 2021

This work builds on operator inference from scientific machine learning to infer low-dimensional models from high-dimensional state trajectories polluted with noise and shows that, under certain conditions, the inferred operators are unbiased estimators of the well-studied projection-based reduced operators from traditional model reduction.

### Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction

- Computer Science2021 60th IEEE Conference on Decision and Control (CDC)
- 2021

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential…

### LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes

- Computer ScienceArXiv
- 2021

This work suggests combining the operator inference with certain deep neural network approaches to infer the unknown nonlinear dynamics of the system and demonstrates that the proposed methodology accomplishes the desired tasks for dynamics processes encountered in neural dynamics and the glycolytic oscillator.

### Discovery of nonlinear dynamical systems using a Runge–Kutta inspired dictionary-based sparse regression approach

- Computer ScienceProceedings of the Royal Society A
- 2022

This work combines machine learning and dictionary-based learning with numerical analysis tools to discover differential equations from noisy and sparsely sampled measurement data of time-dependent processes, and extends the method to governing equations, containing rational nonlinearities that typically appear in biological networks.

### Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning

- Computer Science
- 2021

This work leverages deep learning to identify low-dimensional quadratic embeddings for high-fidelity dynamical systems and embeds a Runge-Kutta method to avoid the time-derivative computations.

### Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning

- Computer ScienceArXiv
- 2022

This paper presents a computational technique which decreases the variance of the generalization error, thereby improving the reliability of the DNN model to generalize consistently and in the proposed ensemble averaging method.

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