# Turning mechanistic models into forecasters by using machine learning

arXiv: https://arxiv.org/abs/2602.04114 · HTML: https://mlsanity.com/paper/2602.04114/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 75 references that are in the map.
- First posted on arXiv 4 Feb 2026.

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

- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Cross-validation: what does it estimate and how well does it do it?](https://mlsanity.com/paper/2104.00673/) (2021)
- [On the Convergence of the SINDy Algorithm](https://mlsanity.com/paper/1805.06445/) (2018)
- [Learning and Planning for Time-Varying MDPs Using Maximum Likelihood Estimation](https://mlsanity.com/paper/1911.12976/) (2019)
- [Dispersion based Recurrent Neural Network Model for Methane Monitoring in Albertan Tailings Ponds](https://mlsanity.com/paper/2411.06741/) (2024)
- [Modeling Atmospheric Data and Identifying Dynamics: Temporal Data-Driven Modeling of Air Pollutants](https://mlsanity.com/paper/2010.06538/) (2020)
- [Inferring the spread of COVID-19: the role of time-varying reporting rate in epidemiological modelling](https://mlsanity.com/paper/2012.15306/) (2020)
- [An early warning indicator trained on stochastic disease-spreading models with different noises](https://mlsanity.com/paper/2403.16233/) (2024)

## Abstract (arXiv)

The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from time-series data using a library of functions constructed from the measured variables. However, these methods typically assume time-invariant coefficients, which limits their ability to capture evolving system dynamics. To overcome this limitation, we allow some of the parameters to vary over time, learn their temporal evolution directly from data, and infer a system of equations that incorporates both constant and time-varying parameters. We then transform this framework into a forecasting model by predicting the time-varying parameters and substituting these predictions into the learned equations. The model is validated using datasets for Susceptible-Infected-Recovered, Consumer--Resource, greenhouse gas concentration, and Cyanobacteria cell count. By dynamically adapting to temporal shifts, our proposed model achieved a mean absolute error below 3% for learning a time series and below 6% for forecasting up to a month ahead. We additionally compare forecasting performance against CNN-LSTM and Gradient Boosting Machine (GBM), and show that our model outperforms these methods across most datasets. Our findings demonstrate that integrating time-varying parameters into data-driven discovery of differential equations improves both modeling accuracy and forecasting performance.