SINDYc and MCMC for Prosumer Response Estimation

Research Question

How can we discover the governing dynamics of a prosumer (a household that both consumes and produces energy) from limited measurement data, while honestly quantifying the uncertainty in the identified model so that downstream decisions account for it?

Method

This project combined two 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 equations set that domain experts can inspect.
• MCMC (Markov-Chain Monte Carlo) — Bayesian sampling over the posterior distribution of model parameters given the data, retaining a distribution over plausible parameter values rather than only a point estimate.

The combination produces a sparse, interpretable response model together with posterior parameter distributions. In this study the candidate model library and data were synthetic; the work should therefore be read as a methodological investigation rather than validation on measured prosumer data.

The framework was implemented in Python using Stan/NUTS for posterior sampling and released as open-source software on Zenodo.

Personal Contribution

Frederik Banis was the first author and sole software developer. He developed the SINDYc-MCMC estimation framework, designed the numerical experiments, implemented the software, and wrote the manuscript. Co-authors contributed supervision, methodological guidance, and review.

Validation and Key Results

• The SINDYc-identified model captured prosumer response dynamics with interpretable terms rather than opaque coefficients.
• The experiments compared SINDYc point estimates with MCMC posterior distributions for a two-prosumer synthetic system using five and fifty input sequences.
• Several posterior means were close to the generating parameters, but some inferred distributions departed from the true distributions; the posterior predictive check was also described as suboptimal.
• Using the inferred distributions in stochastic MPC was proposed as a future application, not validated in this paper.

The method was published in Energies (2020), a peer-reviewed open-access journal.

Outputs

• Journal paper: DOI 10.3390/en13123183
• Open-source software: SINDYc and MCMC Framework (Zenodo, v1.1.1)
• PhD thesis: Efficient Operation of Energy Grids, DTU, 2020. DOI 10.11581/DTU.00000334

Collaborators

• DTU Compute, Technical University of Denmark — Henrik Madsen, Niels Kjølstad Poulsen (supervisors)
• Daniela Guericke (co-author)

Status and Next Steps

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

Transfer to current research: The core idea — combining sparse structure identification with posterior inference and explicit model checking — informs uncertainty-aware inference for adaptive biomedical sensing. The application has shifted from synthetic energy-system dynamics to physiological signals.

See the Software catalogue for detailed metadata on the SINDYc and MCMC Framework, and the Methods page for the methodological context.