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

arXiv: https://arxiv.org/abs/2103.02249 · HTML: https://mlsanity.com/paper/2103.02249/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 3 Mar 2021.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [Data-driven reduced-order models via regularized operator inference for a single-injector combustion process](https://mlsanity.com/paper/2008.02862/) (2020)
- [Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms](https://mlsanity.com/paper/2002.09726/) (2020)
- [Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows](https://mlsanity.com/paper/2010.06701/) (2020)

## Built on by (most cited first, 4 of 4)

- [Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method](https://mlsanity.com/paper/2203.00360/) (2022)
- [Volume-Preserving Transformers for Learning Time Series Data with Structure](https://mlsanity.com/paper/2312.11166/) (2023)
- [Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning](https://mlsanity.com/paper/2111.12995/) (2021)
- [Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference](https://mlsanity.com/paper/2402.17698/) (2024)

## Abstract (arXiv)

Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a dynamic model can be built, but for complex dynamic processes, appearing, e.g., in biology, chemical plants, neuroscience, financial markets, this often remains an onerous task. Hence, data-driven modeling of the dynamics process becomes an attractive choice and is supported by the rapid advancement in sensor and measurement technology. A data-driven approach, namely operator inference framework, models a dynamic process, where a particular structure of the nonlinear term is assumed. In this work, we suggest combining the operator inference with certain deep neural network approaches to infer the unknown nonlinear dynamics of the system. The approach uses recent advancements in deep learning and possible prior knowledge of the process if possible. We also briefly discuss several extensions and advantages of the proposed methodology. We demonstrate that the proposed methodology accomplishes the desired tasks for dynamics processes encountered in neural dynamics and the glycolytic oscillator.