# Approximate Latent Force Model Inference

arXiv: https://arxiv.org/abs/2109.11851 · HTML: https://mlsanity.com/paper/2109.11851/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Neural ODE Processes](https://mlsanity.com/paper/2103.12413/) (2021)
- [Learning unknown ODE models with Gaussian processes](https://mlsanity.com/paper/1803.04303/) (2018)
- [Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs](https://mlsanity.com/paper/1804.04378/) (2018)
- [Deep learning with differential Gaussian process flows](https://mlsanity.com/paper/1810.04066/) (2018)
- [Black-Box Inference for Non-Linear Latent Force Models](https://mlsanity.com/paper/1906.09199/) (2019)
- [Gaussian Process Latent Force Models for Learning and Stochastic Control of Physical Systems](https://mlsanity.com/paper/1709.05409/) (2017)
- [Patient-Specific Effects of Medication Using Latent Force Models with Gaussian Processes](https://mlsanity.com/paper/1906.00226/) (2019)
- [Physically-Inspired Gaussian Process Models for Post-Transcriptional Regulation in Drosophila](https://mlsanity.com/paper/1808.10026/) (2018)
- [Gene Regulatory Network Inference with Latent Force Models](https://mlsanity.com/paper/2010.02555/) (2020)

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

- [Deep Latent Force Models: ODE-based Process Convolutions for Bayesian Deep Learning](https://mlsanity.com/paper/2311.14828/) (2023)

## Abstract (arXiv)

Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes, yielding interpretable parameters and dynamics-imposed latent functions. However, the existing inference techniques associated with these models rely on the exact computation of posterior kernel terms which are seldom available in analytical form. Most applications relevant to practitioners, such as Hill equations or diffusion equations, are hence intractable. In this paper, we overcome these computational problems by proposing a variational solution to a general class of non-linear and parabolic partial differential equation latent force models. Further, we show that a neural operator approach can scale our model to thousands of instances, enabling fast, distributed computation. We demonstrate the efficacy and flexibility of our framework by achieving competitive performance on several tasks where the kernels are of varying degrees of tractability.