Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models
Authors: Sudipto Banerjee, Xiang Chen, Ian Frankenburg, Daniel Zhou
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 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. |
| Researcher Affiliation | Academia | Sudipto Banerjee EMAIL Department of Biostatistics University of California, Los Angeles Los Angeles, CA 90025, USA Xiang Chen EMAIL Department of Biostatistics University of California, Los Angeles Los Angeles, CA 90025, USA Ian Frankenburg EMAIL Department of Biostatistics University of California, Los Angeles Los Angeles, CA 90025, USA Daniel Zhou EMAIL Department of Biostatistics University of California, Los Angeles Los Angeles, CA 90025, USA |
| Pseudocode | Yes | Algorithm 1 Sampling from matrix normal distribution Algorithm 2 Sampling from hyper-T distribution Algorithm 3 Kalman (forward) filter Algorithm 4 Backward sampler Algorithm 5 Forward-filter-backward-sampler algorithm Algorithm 6 Full conditional distributions for p(τ 2 1:T | ). Algorithm 7 Full conditional distributions for p(y1:T | ). Algorithm 8 FFBS for calibration with computer model bias Algorithm 9 Log probability density of the full conditional p(ϕ | ). Algorithm 10 Metropolis random walk algorithm (one step). Algorithm 11 Sampler for estimating mechanistic system parameters using field data |
| Open Source Code | Yes | All computer programs required to reproduce the numerical results in this manuscript are available from the Git Hub repository https://github.com/xiangchen-stat/Bayesian Modeling Mechanistic Systems. |
| Open Datasets | Yes | For our noisy field observations, we utilize the data recorded on the Canadian lynx and snowshoe hare population sizes. (Hewitt, 1917) |
| Dataset Splits | No | For Lotka-Volterra: We generate N = 50 sets of lognormal sampled parameters, so that ηi exp (N(µi, σi)) for i = 1, . . . , 4... For PDE: We generated N = 50 sets of x used in equation (26), and for each input generated solutions over T = 50 time points from the PDE system... We use 40 generated parameters to train the FFBS algorithm... For Network Diffusion: Subsequently, we select a random validation point that is not included in the training set. |
| Hardware Specification | Yes | Computations for the predator-prey system were executed on a laptop running 64-bit Windows 11 with a 12th Gen Intel(R) Core(TM) i7-12700H, 2.30 GHz processor, 32.0 GB RAM at 4800 MHz, 6 GB Graphics Card equipped with multiple GPUs. Computations pertaining to the PDE and network diffusion examples were executed on a laptop running mac OS 14.7.6, equipped with an Apple M3 Max processor (16-core CPU, 40-core GPU) and 64 GB of RAM. |
| Software Dependencies | Yes | We developed our methods in C++ with functions available in R (version 4.4.1) employing the Rcpp package (Eddelbuettel and Fran cois, 2011). We employ de Solve (R package version 1.40) (Soetaert et al., 2010) to solve the system over the range of input parameters. |
| Experiment Setup | Yes | For the Lotka-Volterra equations: We generate N = 50 sets of lognormal sampled parameters, so that ηi exp (N(µi, σi)) for i = 1, . . . , 4, where µi and σi are the respective means and standard deviations of the normal random variables prior to exponentiation. The training data is generated over a Latin hypercube design from the multivariate lognormal with µ1 = µ3 = 0 and µ2 = µ4 = 3, and σ1 = σ2 = σ3 = σ4 = 0.5... For the PDE system: We use 40 generated parameters to train the FFBS algorithm (Algorithm 5), taking L = 10 samples in the backward sampling step, and employ a Gaussian Process to emulate the PDE solution. We use the transfer learning parameters specified in Section 4 set as r = 40 and c = 100... For Calibration: We fix ρ = 1.5 and, analogous to Section 5.1, set the prior for η to be a multivariate lognormal... The samples are generated using Algorithm 11 with L = 20, 000. In this example, we consider a 6 × 6 grid with 36 locations and 26 time points... We use 30,000 samples, with the transfer learning parameters specified in Section 4 set as r = 50 and c = 2. In calibration, we set α1 = α3 = 0 to simplify the analysis. After 10,000 posterior draws... |