# Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models

arXiv: https://arxiv.org/abs/2208.06528 · HTML: https://mlsanity.com/paper/2208.06528/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 99 references that are in the map.
- First posted on arXiv 12 Aug 2022.

## Builds on (most cited first, 23 of 23)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Identification of Gaussian Process State Space Models](https://mlsanity.com/paper/1705.10888/) (2017)
- [A multi-resolution approximation for massive spatial datasets](https://mlsanity.com/paper/1507.04789/) (2015)
- [Bayesian Numerical Methods for Nonlinear Partial Differential Equations](https://mlsanity.com/paper/2104.12587/) (2021)
- [Gaussian Processes Over Graphs](https://mlsanity.com/paper/1803.05776/) (2018)
- [Generalized probabilistic principal component analysis of correlated data](https://mlsanity.com/paper/1808.10868/) (2018)
- [Graphical Gaussian Process Models for Highly Multivariate Spatial Data](https://mlsanity.com/paper/2009.04837/) (2020)
- [Gaussian orthogonal latent factor processes for large incomplete matrices of correlated data](https://mlsanity.com/paper/2011.10863/) (2020)
- [A Divide-and-Conquer Bayesian Approach to Large-Scale Kriging](https://mlsanity.com/paper/1712.09767/) (2017)
- [Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments](https://mlsanity.com/paper/1802.00495/) (2018)
- [High-Dimensional Bayesian Geostatistics](https://mlsanity.com/paper/1705.07265/) (2017)
- [Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains](https://mlsanity.com/paper/2003.11208/) (2020)
- [Spatial Factor Modeling: A Bayesian Matrix-Normal Approach for Misaligned Data](https://mlsanity.com/paper/2006.00595/) (2020)
- [Scalable Bayesian Learning for State Space Models using Variational Inference with SMC Samplers](https://mlsanity.com/paper/1805.09406/) (2018)
- [Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lasso](https://mlsanity.com/paper/2101.02404/) (2021)

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

- [Amortized Bayesian inference for actigraph time sheet data from mobile devices](https://mlsanity.com/paper/2602.20611/) (2026)

## Abstract (arXiv)

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary inputs. The emulated learner can then be used to train the system from noisy data achieved by melding information from observed data with the emulated mechanistic system. This joint melding of mechanistic systems employ hierarchical state-space models with Gaussian process regression. Assuming the dynamical system is controlled by a finite collection of inputs, Gaussian process regression learns the effect of these parameters through a number of training runs, driving the stochastic innovations of the spatiotemporal state-space component. This enables efficient modeling of the dynamics over space and time. This article details exact inference with analytically accessible posterior distributions in hierarchical matrix-variate Normal and Wishart models in designing the emulator. This step obviates expensive iterative algorithms such as Markov chain Monte Carlo or variational approximations. We also show how emulation is applicable to large-scale emulation by designing a dynamic Bayesian transfer learning framework. Inference on mechanistic model parameters proceeds using Markov chain Monte Carlo as a post-emulation step using the emulator as a regression component. We demonstrate this framework through solving inverse problems arising in the analysis of ordinary and partial nonlinear differential equations and, in addition, to a black-box computer model generating spatiotemporal dynamics across a graphical model.