# Continuous Forecasting via Neural Eigen Decomposition

arXiv: https://arxiv.org/abs/2202.00117 · HTML: https://mlsanity.com/paper/2202.00117/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Long Short-Term Memory Kalman Filters:Recurrent Neural Estimators for Pose Regularization](https://mlsanity.com/paper/1708.01885/) (2017)
- [A systematic literature review on state-of-the-art deep learning methods for process prediction](https://mlsanity.com/paper/2101.09320/) (2021)
- [Detecting Rewards Deterioration in Episodic Reinforcement Learning](https://mlsanity.com/paper/2010.11660/) (2020)
- [Intermittent Kalman Filtering: Eigenvalue Cycles and Nonuniform Sampling](https://mlsanity.com/paper/1308.6107/) (2013)

## Built on by (most cited first, 1 of 1)

- [Optimization or Architecture: How to Hack Kalman Filtering](https://mlsanity.com/paper/2310.00675/) (2023)

## Abstract (arXiv)

Neural differential equations predict the derivative of a stochastic process. This allows irregular forecasting with arbitrary time-steps. However, the expressive temporal flexibility often comes with a high sensitivity to noise. In addition, current methods model measurements and control together, limiting generalization to different control policies. These properties severely limit applicability to medical treatment problems, which require reliable forecasting given high noise, limited data and changing treatment policies. We introduce the Neural Eigen-SDE algorithm (NESDE), which relies on piecewise linear dynamics modeling with spectral representation. NESDE provides control over the expressiveness level; decoupling of control from measurements; and closed-form continuous prediction in inference. NESDE is demonstrated to provide robust forecasting in both synthetic and real high-noise medical problems. Finally, we use the learned dynamics models to publish simulated medical gym environments.