SINDYc and MCMC Framework

Problem and Research Question

System identification — learning a dynamical model from measurement data — often forces a choice between two unsatisfying extremes. A black-box machine learning model can fit the data but yields opaque coefficients that domain experts cannot inspect or validate. A pure first-principles model is interpretable but requires detailed physical knowledge that is often unavailable, and it does not quantify the uncertainty in its parameters. The central question this software addresses: how can a researcher discover an interpretable governing-equation model from limited data while retaining a posterior distribution over its identified parameters?

The framework was built to support prosumer response estimation (see the related publication and project page) but is designed as a general, reusable tool for sparse system identification with uncertainty quantification.

Method

This is a software publication. The detail page therefore focuses on the software’s purpose, architecture, and usage rather than on research results, which are covered by the prosumer response publication page.

The SINDYc and MCMC Framework combines two complementary approaches:

• SINDYc (Sparse Identification of Nonlinear Dynamics with control) — a data-driven method that selects a parsimonious dynamical model from a library of candidate basis functions, including physical terms such as differential equations and control inputs. Rather than fitting a black-box neural network, SINDYc yields an interpretable set of equations that domain experts can inspect and validate.
• MCMC (Markov-Chain Monte Carlo) — Bayesian sampling over the posterior distribution of model parameters given the data, retaining a range of plausible parameter values rather than only a point estimate.

The combination produces a sparse, inspectable model with posterior parameter distributions. Calibration and downstream decision quality must be assessed for each application; the associated paper is a synthetic methodological study, not a real-world control validation.

Architecture and Usage

• Implementation: Python, with Stan/NUTS for posterior sampling.
• Inputs: measurement time series (state, control inputs, covariates).
• Outputs: a sparse identified model with posterior distributions over parameters, suitable for downstream prediction and control under uncertainty.
• Reproducibility: archived on Zenodo (10.5281/zenodo.3911952) with a pinned version (v1.1.1) and DOI for citable, reproducible research.

Personal Contribution

Frederik Banis was the sole author and developer of the framework. He designed the SINDYc-MCMC estimation pipeline, implemented the Python and Stan/NUTS integration, and packaged the software for open-source release.

Validation and Key Results

• The framework was used in the synthetic prosumer response study (Banis et al., Energies, 2020), where SINDYc estimates and MCMC posterior distributions were compared under different amounts of input data.
• Some inferred distributions reproduced the generating parameters better than others, and the paper reported limitations in its posterior predictive check. Downstream stochastic control remained proposed future work.
• The software was archived on Zenodo with a DOI and version tag for reproducibility, meeting the criteria for a citable software publication.

Related Outputs

• Software: SINDYc and MCMC Framework, Zenodo, v1.1.1. DOI: 10.5281/zenodo.3911952
• Companion journal paper: Prosumer Response Estimation Using SINDYc in Conjunction with Markov-Chain Monte-Carlo Sampling, Energies, 2020. DOI: 10.3390/en13123183 — see the publication page for the research results obtained with this software.
• Case study: SINDYc and MCMC for Prosumer Response Estimation — the broader project context.
• Publication catalogue entry: data/publications.yaml, id 9.
• PhD thesis: Efficient Operation of Energy Grids, DTU, 2020. DOI: 10.11581/DTU.00000334

Collaborators and Institutions

• DTU Compute, Technical University of Denmark — host institution for the research program the software supports (supervisors Henrik Madsen and Niels Kjølstad Poulsen). The software itself is sole-authored.

Status and Next Steps

Status: Published (2020, software). The software is archived on Zenodo for reproducibility and is no longer actively maintained (historical).

Transfer to current research: The core idea — combining mechanistic structure identification with Bayesian uncertainty quantification — is the part of the methodological base for uncertainty-aware inference in adaptive biomedical sensing. The shift is from energy-system dynamics to physiological signal models, while the reusable idea is sparse identification followed by posterior inference and explicit model checking.

See the related project page for the broader research context, the Software catalogue for software metadata, and the Methods page for the methodological framework.